M. Steffen, M. Ansmann, R. C. Bialczak, N. Katz, E. Lucero, R. McDermott, M. Neeley, E. M. Weig, A. N. Cleland, and J. M. Martinis, "Measurement of the entanglement of two superconducting qubits via state tomography," Science 313, 1423-1425 (2006).

[CrossRef]
[PubMed]

A. Gilchrist, N. K. Langford, and M. A. Nielsen, "Distance measures to compare real and ideal quantum processes," Phys. Rev. A 71, 062310 (2005).

[CrossRef]

N. K. Langford, T. J. Weinhold, R. Prevedel, A. Gilchrist, J. L. O'Brien, G. J. Pryde, and A. G. White, "Demonstration of a simple entangling optical gate and its use in Bell-state analysis," Phys. Rev. Lett. 95, 210504 (2005).

[CrossRef]
[PubMed]

H. F. Hofmann, "Complementary classical fidelities as an efficient criterion for the evaluation of experimentally realized quantum operations," Phys. Rev. Lett. 94, 160504 (2005).

[CrossRef]
[PubMed]

J. L. O'Brien, G. J. Pryde, A. Gilchrist, D. F. V. James, N. K. Langford, T. C. Ralph, and A. G. White, "Quantum process tomography of a controlled-NOT gate," Phys. Rev. Lett. 93, 080502 (2004).

[CrossRef]
[PubMed]

N. A. Peters, J. B. Altepeter, D. A. Branning, E. R. Jeffrey, T.-C. Wei, and P. G. Kwiat, "Maximally entangled mixed states: creation and concentration," Phys. Rev. Lett. 92, 133601 (2004).

[CrossRef]
[PubMed]

J. B. Altepeter, D. Branning, E. Jeffrey, T. C. Wei, P. G. Kwiat, R. T. Thew, J. L. OBrien, M. A. Nielsen, and A. G. White, "Ancilla-assisted quantum process tomography," Phys. Rev. Lett. 93, 193601 (2003).

[CrossRef]

G. M. D'Ariano and P. L. Presti, "Imprinting a complete information about a quantum channel on its output state," Phys. Rev. Lett. 91, 047902 (2003).

[CrossRef]
[PubMed]

F. De Martini, A. Mazzei, M. Ricci, and G. M. D'Ariano, "Exploiting quantum parallelism of entanglement for a complete experimental quantum characterization of a single qubit device," Phys. Rev. A 67, 062307 (2003).

[CrossRef]

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, "Realization of the Cirac-Zoller controlled-NOT quantum gate," Nature 422, 408-411 (2003).

[CrossRef]
[PubMed]

J. L. O'Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-NOT gate," Nature 426, 264-267 (2003).

[CrossRef]
[PubMed]

M. Barbieri, F. De Martini, G. Di Nepi, P. Mataloni, G. M. D'Ariano, and C. Macchiavello, "Detection of entanglement with polarized photons: experimental realization of an entanglement witness," Phys. Rev. Lett. 91, 227901 (2003).

[CrossRef]
[PubMed]

O. Gühne, P. Hyllus, D. Bruß, A. Ekert, M. Lewenstein, C. Macchiavello, and A. Sanpera, "Detection of entanglement with few local measurements," Phys. Rev. A 66, 062305 (2002).

[CrossRef]

M. J. Bremner, C. M. Dawson, J. L. Dodd, A. Gilchrist, A. W. Harrow, D. Mortimer, M. A. Nielsen, and T. J. Osborne, "Practical scheme for quantum computation with any two-qubit entangling gate," Phys. Rev. Lett. 89, 247902 (2002).

[CrossRef]
[PubMed]

J. L. Dodd and M. A. Nielsen, "A simple operational interpretation of the fidelity," Phys. Rev. A 66, 044301 (2002).

[CrossRef]

M. A. Nielsen, "A simple formula for the average gate fidelity of a quantum dynamical operation," Phys. Lett. A 303, 249-252 (2002).

[CrossRef]

J. I. Cirac, W. Dür, B. Kraus, and M. Lewenstein, "Entangling operations and their implementation using a small amount of entanglement," Phys. Rev. Lett. 86, 544-547 (2001).

[CrossRef]
[PubMed]

A. M. Childs, I. L. Chuang, and D. W. Leung, "Realization of quantum process tomography in NMR," Phys. Rev. A 64, 012314 (2001).

[CrossRef]

W. J. Munro, K. Nemoto, and A. G. White, "The Bell inequality: a measure of entanglement?" J. Mod. Opt. 48, 1239-1246 (2001).

[CrossRef]

W. J. Munro, D. F. V. James, A. G. White, and P. G. Kwiat, "Maximizing the entanglement of two mixed qubits," Phys. Rev. A 64, 030302 (2001).

[CrossRef]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, "Measurement of qubits," Phys. Rev. A 64, 052312 (2001).

[CrossRef]

A. G. White, D. F. V. James, W. J. Munro, and P. G. Kwiat, "Exploring Hilbert space: accurate characterization of quantum information," Phys. Rev. A 65, 012301 (2001).

[CrossRef]

B. M. Terhal, "Bell inequalities and the separability criterion," Phys. Lett. A 271, 319-326 (2000).

[CrossRef]

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, "Experimental entanglement of four particles," Nature 404, 256-259 (2000).

[CrossRef]
[PubMed]

B. M. Terhal and P. Horodecki, "Schmidt number for density matrices," Phys. Rev. A 61, 040301(R) (2000).

[CrossRef]

V. Coffman, J. Kundu, and W. K. Wootters, "Distributed entanglement," Phys. Rev. A 61, 052306 (2000).

[CrossRef]

M. Horodecki, P. Horodecki, and R. Horodecki, "General teleportation channel, singlet fraction, and quasidistillation," Phys. Rev. A 60, 1888-1898 (1999).

[CrossRef]

A. G. White, D. F. V. James, P. H. Eberhard, and P. G. Kwiat, "Nonmaximally entangled states: production, characterization, and utilization," Phys. Rev. Lett. 83, 3103-3107 (1999).

[CrossRef]

W. K. Wootters, "Entanglement of formation of an arbitrary state of two qubits," Phys. Rev. Lett. 80, 2245-2248 (1998).

[CrossRef]

M. A. Nielsen, E. Knill, and R. Laflamme, "Complete quantum teleportation using nuclear magnetic resonance," Nature 396, 52-55 (1998).

[CrossRef]

I. L. Chuang and M. A. Nielsen, "Prescription for experimental determination of the dynamics of a quantum black box," J. Mod. Opt. 44, 732-744 (1997).

J. F. Poyatos, J. I. Cirac, and P. Zoller, "Complete characterization of a quantum process: the two-bit quantum gate," Phys. Rev. Lett. 78, 390-393 (1997).

[CrossRef]

M. Horodecki, P. Horodecki, and R. Horodecki, "Separability of mixed states: necessary and sufficient conditions," Phys. Lett. A 223, 1-8 (1996).

[CrossRef]

A. Jamiolkowski, "Linear transformations which preserve trace and positive semidefiniteness of operators," Rep. Math. Phys. 3, 275-278 (1972).

[CrossRef]

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, "Proposed experiment to test local hidden-variable theories," Phys. Rev. Lett. 23, 880-884 (1969).

[CrossRef]

J. S. Bell, "On the Einstein-Podolsky-Rosen paradox," Physics (Long Island City, N.Y.) 1, 195-200 (1964).

[CrossRef]

R. Alicki, "False qubits II. Entanglement of Josephson junctions," arXiv.org e-Print archive, quantum physics/0609122, 16 September 2006, http://www.arxiv.org/abs/quant-ph/0609122.

N. A. Peters, J. B. Altepeter, D. A. Branning, E. R. Jeffrey, T.-C. Wei, and P. G. Kwiat, "Maximally entangled mixed states: creation and concentration," Phys. Rev. Lett. 92, 133601 (2004).

[CrossRef]
[PubMed]

J. B. Altepeter, D. Branning, E. Jeffrey, T. C. Wei, P. G. Kwiat, R. T. Thew, J. L. OBrien, M. A. Nielsen, and A. G. White, "Ancilla-assisted quantum process tomography," Phys. Rev. Lett. 93, 193601 (2003).

[CrossRef]

M. Steffen, M. Ansmann, R. C. Bialczak, N. Katz, E. Lucero, R. McDermott, M. Neeley, E. M. Weig, A. N. Cleland, and J. M. Martinis, "Measurement of the entanglement of two superconducting qubits via state tomography," Science 313, 1423-1425 (2006).

[CrossRef]
[PubMed]

M. Barbieri, F. De Martini, G. Di Nepi, P. Mataloni, G. M. D'Ariano, and C. Macchiavello, "Detection of entanglement with polarized photons: experimental realization of an entanglement witness," Phys. Rev. Lett. 91, 227901 (2003).

[CrossRef]
[PubMed]

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, "Realization of the Cirac-Zoller controlled-NOT quantum gate," Nature 422, 408-411 (2003).

[CrossRef]
[PubMed]

J. S. Bell, "On the Einstein-Podolsky-Rosen paradox," Physics (Long Island City, N.Y.) 1, 195-200 (1964).

[CrossRef]

M. Steffen, M. Ansmann, R. C. Bialczak, N. Katz, E. Lucero, R. McDermott, M. Neeley, E. M. Weig, A. N. Cleland, and J. M. Martinis, "Measurement of the entanglement of two superconducting qubits via state tomography," Science 313, 1423-1425 (2006).

[CrossRef]
[PubMed]

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, "Realization of the Cirac-Zoller controlled-NOT quantum gate," Nature 422, 408-411 (2003).

[CrossRef]
[PubMed]

R. Blume-Kohout and P. Hayden, "Accurate quantum state estimation via 'Keeping the experimentalist honest'," arXiv.org e-Print archive, quantum physics/0603116, 14 March 2006, http://www.arxiv.org/abs/quant-ph/0603116.

J. B. Altepeter, D. Branning, E. Jeffrey, T. C. Wei, P. G. Kwiat, R. T. Thew, J. L. OBrien, M. A. Nielsen, and A. G. White, "Ancilla-assisted quantum process tomography," Phys. Rev. Lett. 93, 193601 (2003).

[CrossRef]

J. L. O'Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-NOT gate," Nature 426, 264-267 (2003).

[CrossRef]
[PubMed]

N. A. Peters, J. B. Altepeter, D. A. Branning, E. R. Jeffrey, T.-C. Wei, and P. G. Kwiat, "Maximally entangled mixed states: creation and concentration," Phys. Rev. Lett. 92, 133601 (2004).

[CrossRef]
[PubMed]

M. J. Bremner, C. M. Dawson, J. L. Dodd, A. Gilchrist, A. W. Harrow, D. Mortimer, M. A. Nielsen, and T. J. Osborne, "Practical scheme for quantum computation with any two-qubit entangling gate," Phys. Rev. Lett. 89, 247902 (2002).

[CrossRef]
[PubMed]

O. Gühne, P. Hyllus, D. Bruß, A. Ekert, M. Lewenstein, C. Macchiavello, and A. Sanpera, "Detection of entanglement with few local measurements," Phys. Rev. A 66, 062305 (2002).

[CrossRef]

J. L. Brylinski and R. K. Brylinski, "Computational mathematics," in Mathematics of Quantum Computation, R.K.Brylinski and G.Chen, eds. (Chapman & Hall/CRC Press, 2002), Chap. 2.

J. L. Brylinski and R. K. Brylinski, "Computational mathematics," in Mathematics of Quantum Computation, R.K.Brylinski and G.Chen, eds. (Chapman & Hall/CRC Press, 2002), Chap. 2.

A. M. Childs, I. L. Chuang, and D. W. Leung, "Realization of quantum process tomography in NMR," Phys. Rev. A 64, 012314 (2001).

[CrossRef]

A. M. Childs, I. L. Chuang, and D. W. Leung, "Realization of quantum process tomography in NMR," Phys. Rev. A 64, 012314 (2001).

[CrossRef]

I. L. Chuang and M. A. Nielsen, "Prescription for experimental determination of the dynamics of a quantum black box," J. Mod. Opt. 44, 732-744 (1997).

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge U. Press, 2000).

J. I. Cirac, W. Dür, B. Kraus, and M. Lewenstein, "Entangling operations and their implementation using a small amount of entanglement," Phys. Rev. Lett. 86, 544-547 (2001).

[CrossRef]
[PubMed]

J. F. Poyatos, J. I. Cirac, and P. Zoller, "Complete characterization of a quantum process: the two-bit quantum gate," Phys. Rev. Lett. 78, 390-393 (1997).

[CrossRef]

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, "Proposed experiment to test local hidden-variable theories," Phys. Rev. Lett. 23, 880-884 (1969).

[CrossRef]

M. Steffen, M. Ansmann, R. C. Bialczak, N. Katz, E. Lucero, R. McDermott, M. Neeley, E. M. Weig, A. N. Cleland, and J. M. Martinis, "Measurement of the entanglement of two superconducting qubits via state tomography," Science 313, 1423-1425 (2006).

[CrossRef]
[PubMed]

V. Coffman, J. Kundu, and W. K. Wootters, "Distributed entanglement," Phys. Rev. A 61, 052306 (2000).

[CrossRef]

F. De Martini, A. Mazzei, M. Ricci, and G. M. D'Ariano, "Exploiting quantum parallelism of entanglement for a complete experimental quantum characterization of a single qubit device," Phys. Rev. A 67, 062307 (2003).

[CrossRef]

G. M. D'Ariano and P. L. Presti, "Imprinting a complete information about a quantum channel on its output state," Phys. Rev. Lett. 91, 047902 (2003).

[CrossRef]
[PubMed]

M. Barbieri, F. De Martini, G. Di Nepi, P. Mataloni, G. M. D'Ariano, and C. Macchiavello, "Detection of entanglement with polarized photons: experimental realization of an entanglement witness," Phys. Rev. Lett. 91, 227901 (2003).

[CrossRef]
[PubMed]

M. J. Bremner, C. M. Dawson, J. L. Dodd, A. Gilchrist, A. W. Harrow, D. Mortimer, M. A. Nielsen, and T. J. Osborne, "Practical scheme for quantum computation with any two-qubit entangling gate," Phys. Rev. Lett. 89, 247902 (2002).

[CrossRef]
[PubMed]

M. Barbieri, F. De Martini, G. Di Nepi, P. Mataloni, G. M. D'Ariano, and C. Macchiavello, "Detection of entanglement with polarized photons: experimental realization of an entanglement witness," Phys. Rev. Lett. 91, 227901 (2003).

[CrossRef]
[PubMed]

F. De Martini, A. Mazzei, M. Ricci, and G. M. D'Ariano, "Exploiting quantum parallelism of entanglement for a complete experimental quantum characterization of a single qubit device," Phys. Rev. A 67, 062307 (2003).

[CrossRef]

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, "Realization of the Cirac-Zoller controlled-NOT quantum gate," Nature 422, 408-411 (2003).

[CrossRef]
[PubMed]

M. Barbieri, F. De Martini, G. Di Nepi, P. Mataloni, G. M. D'Ariano, and C. Macchiavello, "Detection of entanglement with polarized photons: experimental realization of an entanglement witness," Phys. Rev. Lett. 91, 227901 (2003).

[CrossRef]
[PubMed]

J. L. Dodd and M. A. Nielsen, "A simple operational interpretation of the fidelity," Phys. Rev. A 66, 044301 (2002).

[CrossRef]

M. J. Bremner, C. M. Dawson, J. L. Dodd, A. Gilchrist, A. W. Harrow, D. Mortimer, M. A. Nielsen, and T. J. Osborne, "Practical scheme for quantum computation with any two-qubit entangling gate," Phys. Rev. Lett. 89, 247902 (2002).

[CrossRef]
[PubMed]

A. Doherty and A. Gilchrist, Department of Physics, University of Queensland, Brisbane QLD 4072, Australia are preparing a manuscript to be called "Quantum tomography using convex optimisation."

J. I. Cirac, W. Dür, B. Kraus, and M. Lewenstein, "Entangling operations and their implementation using a small amount of entanglement," Phys. Rev. Lett. 86, 544-547 (2001).

[CrossRef]
[PubMed]

A. G. White, D. F. V. James, P. H. Eberhard, and P. G. Kwiat, "Nonmaximally entangled states: production, characterization, and utilization," Phys. Rev. Lett. 83, 3103-3107 (1999).

[CrossRef]

O. Gühne, P. Hyllus, D. Bruß, A. Ekert, M. Lewenstein, C. Macchiavello, and A. Sanpera, "Detection of entanglement with few local measurements," Phys. Rev. A 66, 062305 (2002).

[CrossRef]

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, "Realization of the Cirac-Zoller controlled-NOT quantum gate," Nature 422, 408-411 (2003).

[CrossRef]
[PubMed]

A. Gilchrist, N. K. Langford, and M. A. Nielsen, "Distance measures to compare real and ideal quantum processes," Phys. Rev. A 71, 062310 (2005).

[CrossRef]

N. K. Langford, T. J. Weinhold, R. Prevedel, A. Gilchrist, J. L. O'Brien, G. J. Pryde, and A. G. White, "Demonstration of a simple entangling optical gate and its use in Bell-state analysis," Phys. Rev. Lett. 95, 210504 (2005).

[CrossRef]
[PubMed]

J. L. O'Brien, G. J. Pryde, A. Gilchrist, D. F. V. James, N. K. Langford, T. C. Ralph, and A. G. White, "Quantum process tomography of a controlled-NOT gate," Phys. Rev. Lett. 93, 080502 (2004).

[CrossRef]
[PubMed]

M. J. Bremner, C. M. Dawson, J. L. Dodd, A. Gilchrist, A. W. Harrow, D. Mortimer, M. A. Nielsen, and T. J. Osborne, "Practical scheme for quantum computation with any two-qubit entangling gate," Phys. Rev. Lett. 89, 247902 (2002).

[CrossRef]
[PubMed]

A. Doherty and A. Gilchrist, Department of Physics, University of Queensland, Brisbane QLD 4072, Australia are preparing a manuscript to be called "Quantum tomography using convex optimisation."

O. Gühne, P. Hyllus, D. Bruß, A. Ekert, M. Lewenstein, C. Macchiavello, and A. Sanpera, "Detection of entanglement with few local measurements," Phys. Rev. A 66, 062305 (2002).

[CrossRef]

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, "Realization of the Cirac-Zoller controlled-NOT quantum gate," Nature 422, 408-411 (2003).

[CrossRef]
[PubMed]

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, "Realization of the Cirac-Zoller controlled-NOT quantum gate," Nature 422, 408-411 (2003).

[CrossRef]
[PubMed]

M. J. Bremner, C. M. Dawson, J. L. Dodd, A. Gilchrist, A. W. Harrow, D. Mortimer, M. A. Nielsen, and T. J. Osborne, "Practical scheme for quantum computation with any two-qubit entangling gate," Phys. Rev. Lett. 89, 247902 (2002).

[CrossRef]
[PubMed]

R. Blume-Kohout and P. Hayden, "Accurate quantum state estimation via 'Keeping the experimentalist honest'," arXiv.org e-Print archive, quantum physics/0603116, 14 March 2006, http://www.arxiv.org/abs/quant-ph/0603116.

H. F. Hofmann, "Complementary classical fidelities as an efficient criterion for the evaluation of experimentally realized quantum operations," Phys. Rev. Lett. 94, 160504 (2005).

[CrossRef]
[PubMed]

H. F. Hofmann, R. Okamoto, and S. Takeuchi, "Analysis of an experimental quantum logic gate by complementary classical operations," arXiv.org e-Print archive, quantum physics/0608005, 1 August 2006, http://www.arxiv.org/abs/quant-ph/0608005.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, "Proposed experiment to test local hidden-variable theories," Phys. Rev. Lett. 23, 880-884 (1969).

[CrossRef]

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, "Proposed experiment to test local hidden-variable theories," Phys. Rev. Lett. 23, 880-884 (1969).

[CrossRef]

M. Horodecki, P. Horodecki, and R. Horodecki, "General teleportation channel, singlet fraction, and quasidistillation," Phys. Rev. A 60, 1888-1898 (1999).

[CrossRef]

M. Horodecki, P. Horodecki, and R. Horodecki, "Separability of mixed states: necessary and sufficient conditions," Phys. Lett. A 223, 1-8 (1996).

[CrossRef]

B. M. Terhal and P. Horodecki, "Schmidt number for density matrices," Phys. Rev. A 61, 040301(R) (2000).

[CrossRef]

M. Horodecki, P. Horodecki, and R. Horodecki, "General teleportation channel, singlet fraction, and quasidistillation," Phys. Rev. A 60, 1888-1898 (1999).

[CrossRef]

M. Horodecki, P. Horodecki, and R. Horodecki, "Separability of mixed states: necessary and sufficient conditions," Phys. Lett. A 223, 1-8 (1996).

[CrossRef]

M. Horodecki, P. Horodecki, and R. Horodecki, "General teleportation channel, singlet fraction, and quasidistillation," Phys. Rev. A 60, 1888-1898 (1999).

[CrossRef]

M. Horodecki, P. Horodecki, and R. Horodecki, "Separability of mixed states: necessary and sufficient conditions," Phys. Lett. A 223, 1-8 (1996).

[CrossRef]

O. Gühne, P. Hyllus, D. Bruß, A. Ekert, M. Lewenstein, C. Macchiavello, and A. Sanpera, "Detection of entanglement with few local measurements," Phys. Rev. A 66, 062305 (2002).

[CrossRef]

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, "Experimental entanglement of four particles," Nature 404, 256-259 (2000).

[CrossRef]
[PubMed]

J. L. O'Brien, G. J. Pryde, A. Gilchrist, D. F. V. James, N. K. Langford, T. C. Ralph, and A. G. White, "Quantum process tomography of a controlled-NOT gate," Phys. Rev. Lett. 93, 080502 (2004).

[CrossRef]
[PubMed]

W. J. Munro, D. F. V. James, A. G. White, and P. G. Kwiat, "Maximizing the entanglement of two mixed qubits," Phys. Rev. A 64, 030302 (2001).

[CrossRef]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, "Measurement of qubits," Phys. Rev. A 64, 052312 (2001).

[CrossRef]

A. G. White, D. F. V. James, W. J. Munro, and P. G. Kwiat, "Exploring Hilbert space: accurate characterization of quantum information," Phys. Rev. A 65, 012301 (2001).

[CrossRef]

A. G. White, D. F. V. James, P. H. Eberhard, and P. G. Kwiat, "Nonmaximally entangled states: production, characterization, and utilization," Phys. Rev. Lett. 83, 3103-3107 (1999).

[CrossRef]

A. Jamiolkowski, "Linear transformations which preserve trace and positive semidefiniteness of operators," Rep. Math. Phys. 3, 275-278 (1972).

[CrossRef]

J. B. Altepeter, D. Branning, E. Jeffrey, T. C. Wei, P. G. Kwiat, R. T. Thew, J. L. OBrien, M. A. Nielsen, and A. G. White, "Ancilla-assisted quantum process tomography," Phys. Rev. Lett. 93, 193601 (2003).

[CrossRef]

N. A. Peters, J. B. Altepeter, D. A. Branning, E. R. Jeffrey, T.-C. Wei, and P. G. Kwiat, "Maximally entangled mixed states: creation and concentration," Phys. Rev. Lett. 92, 133601 (2004).

[CrossRef]
[PubMed]

M. Steffen, M. Ansmann, R. C. Bialczak, N. Katz, E. Lucero, R. McDermott, M. Neeley, E. M. Weig, A. N. Cleland, and J. M. Martinis, "Measurement of the entanglement of two superconducting qubits via state tomography," Science 313, 1423-1425 (2006).

[CrossRef]
[PubMed]

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, "Experimental entanglement of four particles," Nature 404, 256-259 (2000).

[CrossRef]
[PubMed]

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, "Experimental entanglement of four particles," Nature 404, 256-259 (2000).

[CrossRef]
[PubMed]

M. A. Nielsen, E. Knill, and R. Laflamme, "Complete quantum teleportation using nuclear magnetic resonance," Nature 396, 52-55 (1998).

[CrossRef]

J. I. Cirac, W. Dür, B. Kraus, and M. Lewenstein, "Entangling operations and their implementation using a small amount of entanglement," Phys. Rev. Lett. 86, 544-547 (2001).

[CrossRef]
[PubMed]

V. Coffman, J. Kundu, and W. K. Wootters, "Distributed entanglement," Phys. Rev. A 61, 052306 (2000).

[CrossRef]

N. A. Peters, J. B. Altepeter, D. A. Branning, E. R. Jeffrey, T.-C. Wei, and P. G. Kwiat, "Maximally entangled mixed states: creation and concentration," Phys. Rev. Lett. 92, 133601 (2004).

[CrossRef]
[PubMed]

J. B. Altepeter, D. Branning, E. Jeffrey, T. C. Wei, P. G. Kwiat, R. T. Thew, J. L. OBrien, M. A. Nielsen, and A. G. White, "Ancilla-assisted quantum process tomography," Phys. Rev. Lett. 93, 193601 (2003).

[CrossRef]

W. J. Munro, D. F. V. James, A. G. White, and P. G. Kwiat, "Maximizing the entanglement of two mixed qubits," Phys. Rev. A 64, 030302 (2001).

[CrossRef]

A. G. White, D. F. V. James, W. J. Munro, and P. G. Kwiat, "Exploring Hilbert space: accurate characterization of quantum information," Phys. Rev. A 65, 012301 (2001).

[CrossRef]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, "Measurement of qubits," Phys. Rev. A 64, 052312 (2001).

[CrossRef]

A. G. White, D. F. V. James, P. H. Eberhard, and P. G. Kwiat, "Nonmaximally entangled states: production, characterization, and utilization," Phys. Rev. Lett. 83, 3103-3107 (1999).

[CrossRef]

M. A. Nielsen, E. Knill, and R. Laflamme, "Complete quantum teleportation using nuclear magnetic resonance," Nature 396, 52-55 (1998).

[CrossRef]

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, "Realization of the Cirac-Zoller controlled-NOT quantum gate," Nature 422, 408-411 (2003).

[CrossRef]
[PubMed]

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, "Experimental entanglement of four particles," Nature 404, 256-259 (2000).

[CrossRef]
[PubMed]

A. Gilchrist, N. K. Langford, and M. A. Nielsen, "Distance measures to compare real and ideal quantum processes," Phys. Rev. A 71, 062310 (2005).

[CrossRef]

N. K. Langford, T. J. Weinhold, R. Prevedel, A. Gilchrist, J. L. O'Brien, G. J. Pryde, and A. G. White, "Demonstration of a simple entangling optical gate and its use in Bell-state analysis," Phys. Rev. Lett. 95, 210504 (2005).

[CrossRef]
[PubMed]

J. L. O'Brien, G. J. Pryde, A. Gilchrist, D. F. V. James, N. K. Langford, T. C. Ralph, and A. G. White, "Quantum process tomography of a controlled-NOT gate," Phys. Rev. Lett. 93, 080502 (2004).

[CrossRef]
[PubMed]

A. M. Childs, I. L. Chuang, and D. W. Leung, "Realization of quantum process tomography in NMR," Phys. Rev. A 64, 012314 (2001).

[CrossRef]

D. W. Leung, "Towards robust quantum computation," arXiv.org e-Print archive, computer science/10012017, 20 December 2002, http://arxiv.org/abs/cs.CC/0012017.

O. Gühne, P. Hyllus, D. Bruß, A. Ekert, M. Lewenstein, C. Macchiavello, and A. Sanpera, "Detection of entanglement with few local measurements," Phys. Rev. A 66, 062305 (2002).

[CrossRef]

J. I. Cirac, W. Dür, B. Kraus, and M. Lewenstein, "Entangling operations and their implementation using a small amount of entanglement," Phys. Rev. Lett. 86, 544-547 (2001).

[CrossRef]
[PubMed]

M. Mohseni and D. A. Lidar, "Direct characterization of quantum dynamics: I. General theory," arXiv.org e-Print archive, quantum physics/0601033, 5 January 2006, http://www.arxiv.org/abs/quant-ph/0601033.

M. Steffen, M. Ansmann, R. C. Bialczak, N. Katz, E. Lucero, R. McDermott, M. Neeley, E. M. Weig, A. N. Cleland, and J. M. Martinis, "Measurement of the entanglement of two superconducting qubits via state tomography," Science 313, 1423-1425 (2006).

[CrossRef]
[PubMed]

M. Barbieri, F. De Martini, G. Di Nepi, P. Mataloni, G. M. D'Ariano, and C. Macchiavello, "Detection of entanglement with polarized photons: experimental realization of an entanglement witness," Phys. Rev. Lett. 91, 227901 (2003).

[CrossRef]
[PubMed]

O. Gühne, P. Hyllus, D. Bruß, A. Ekert, M. Lewenstein, C. Macchiavello, and A. Sanpera, "Detection of entanglement with few local measurements," Phys. Rev. A 66, 062305 (2002).

[CrossRef]

M. Steffen, M. Ansmann, R. C. Bialczak, N. Katz, E. Lucero, R. McDermott, M. Neeley, E. M. Weig, A. N. Cleland, and J. M. Martinis, "Measurement of the entanglement of two superconducting qubits via state tomography," Science 313, 1423-1425 (2006).

[CrossRef]
[PubMed]

M. Barbieri, F. De Martini, G. Di Nepi, P. Mataloni, G. M. D'Ariano, and C. Macchiavello, "Detection of entanglement with polarized photons: experimental realization of an entanglement witness," Phys. Rev. Lett. 91, 227901 (2003).

[CrossRef]
[PubMed]

F. De Martini, A. Mazzei, M. Ricci, and G. M. D'Ariano, "Exploiting quantum parallelism of entanglement for a complete experimental quantum characterization of a single qubit device," Phys. Rev. A 67, 062307 (2003).

[CrossRef]

M. Steffen, M. Ansmann, R. C. Bialczak, N. Katz, E. Lucero, R. McDermott, M. Neeley, E. M. Weig, A. N. Cleland, and J. M. Martinis, "Measurement of the entanglement of two superconducting qubits via state tomography," Science 313, 1423-1425 (2006).

[CrossRef]
[PubMed]

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, "Experimental entanglement of four particles," Nature 404, 256-259 (2000).

[CrossRef]
[PubMed]

M. Mohseni and D. A. Lidar, "Direct characterization of quantum dynamics: I. General theory," arXiv.org e-Print archive, quantum physics/0601033, 5 January 2006, http://www.arxiv.org/abs/quant-ph/0601033.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, "Experimental entanglement of four particles," Nature 404, 256-259 (2000).

[CrossRef]
[PubMed]

M. J. Bremner, C. M. Dawson, J. L. Dodd, A. Gilchrist, A. W. Harrow, D. Mortimer, M. A. Nielsen, and T. J. Osborne, "Practical scheme for quantum computation with any two-qubit entangling gate," Phys. Rev. Lett. 89, 247902 (2002).

[CrossRef]
[PubMed]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, "Measurement of qubits," Phys. Rev. A 64, 052312 (2001).

[CrossRef]

A. G. White, D. F. V. James, W. J. Munro, and P. G. Kwiat, "Exploring Hilbert space: accurate characterization of quantum information," Phys. Rev. A 65, 012301 (2001).

[CrossRef]

W. J. Munro, K. Nemoto, and A. G. White, "The Bell inequality: a measure of entanglement?" J. Mod. Opt. 48, 1239-1246 (2001).

[CrossRef]

W. J. Munro, D. F. V. James, A. G. White, and P. G. Kwiat, "Maximizing the entanglement of two mixed qubits," Phys. Rev. A 64, 030302 (2001).

[CrossRef]

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, "Experimental entanglement of four particles," Nature 404, 256-259 (2000).

[CrossRef]
[PubMed]

M. Steffen, M. Ansmann, R. C. Bialczak, N. Katz, E. Lucero, R. McDermott, M. Neeley, E. M. Weig, A. N. Cleland, and J. M. Martinis, "Measurement of the entanglement of two superconducting qubits via state tomography," Science 313, 1423-1425 (2006).

[CrossRef]
[PubMed]

W. J. Munro, K. Nemoto, and A. G. White, "The Bell inequality: a measure of entanglement?" J. Mod. Opt. 48, 1239-1246 (2001).

[CrossRef]

A. Gilchrist, N. K. Langford, and M. A. Nielsen, "Distance measures to compare real and ideal quantum processes," Phys. Rev. A 71, 062310 (2005).

[CrossRef]

J. B. Altepeter, D. Branning, E. Jeffrey, T. C. Wei, P. G. Kwiat, R. T. Thew, J. L. OBrien, M. A. Nielsen, and A. G. White, "Ancilla-assisted quantum process tomography," Phys. Rev. Lett. 93, 193601 (2003).

[CrossRef]

J. L. Dodd and M. A. Nielsen, "A simple operational interpretation of the fidelity," Phys. Rev. A 66, 044301 (2002).

[CrossRef]

M. J. Bremner, C. M. Dawson, J. L. Dodd, A. Gilchrist, A. W. Harrow, D. Mortimer, M. A. Nielsen, and T. J. Osborne, "Practical scheme for quantum computation with any two-qubit entangling gate," Phys. Rev. Lett. 89, 247902 (2002).

[CrossRef]
[PubMed]

M. A. Nielsen, "A simple formula for the average gate fidelity of a quantum dynamical operation," Phys. Lett. A 303, 249-252 (2002).

[CrossRef]

M. A. Nielsen, E. Knill, and R. Laflamme, "Complete quantum teleportation using nuclear magnetic resonance," Nature 396, 52-55 (1998).

[CrossRef]

I. L. Chuang and M. A. Nielsen, "Prescription for experimental determination of the dynamics of a quantum black box," J. Mod. Opt. 44, 732-744 (1997).

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge U. Press, 2000).

J. B. Altepeter, D. Branning, E. Jeffrey, T. C. Wei, P. G. Kwiat, R. T. Thew, J. L. OBrien, M. A. Nielsen, and A. G. White, "Ancilla-assisted quantum process tomography," Phys. Rev. Lett. 93, 193601 (2003).

[CrossRef]

N. K. Langford, T. J. Weinhold, R. Prevedel, A. Gilchrist, J. L. O'Brien, G. J. Pryde, and A. G. White, "Demonstration of a simple entangling optical gate and its use in Bell-state analysis," Phys. Rev. Lett. 95, 210504 (2005).

[CrossRef]
[PubMed]

J. L. O'Brien, G. J. Pryde, A. Gilchrist, D. F. V. James, N. K. Langford, T. C. Ralph, and A. G. White, "Quantum process tomography of a controlled-NOT gate," Phys. Rev. Lett. 93, 080502 (2004).

[CrossRef]
[PubMed]

J. L. O'Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-NOT gate," Nature 426, 264-267 (2003).

[CrossRef]
[PubMed]

H. F. Hofmann, R. Okamoto, and S. Takeuchi, "Analysis of an experimental quantum logic gate by complementary classical operations," arXiv.org e-Print archive, quantum physics/0608005, 1 August 2006, http://www.arxiv.org/abs/quant-ph/0608005.

M. J. Bremner, C. M. Dawson, J. L. Dodd, A. Gilchrist, A. W. Harrow, D. Mortimer, M. A. Nielsen, and T. J. Osborne, "Practical scheme for quantum computation with any two-qubit entangling gate," Phys. Rev. Lett. 89, 247902 (2002).

[CrossRef]
[PubMed]

N. A. Peters, J. B. Altepeter, D. A. Branning, E. R. Jeffrey, T.-C. Wei, and P. G. Kwiat, "Maximally entangled mixed states: creation and concentration," Phys. Rev. Lett. 92, 133601 (2004).

[CrossRef]
[PubMed]

J. F. Poyatos, J. I. Cirac, and P. Zoller, "Complete characterization of a quantum process: the two-bit quantum gate," Phys. Rev. Lett. 78, 390-393 (1997).

[CrossRef]

G. M. D'Ariano and P. L. Presti, "Imprinting a complete information about a quantum channel on its output state," Phys. Rev. Lett. 91, 047902 (2003).

[CrossRef]
[PubMed]

N. K. Langford, T. J. Weinhold, R. Prevedel, A. Gilchrist, J. L. O'Brien, G. J. Pryde, and A. G. White, "Demonstration of a simple entangling optical gate and its use in Bell-state analysis," Phys. Rev. Lett. 95, 210504 (2005).

[CrossRef]
[PubMed]

N. K. Langford, T. J. Weinhold, R. Prevedel, A. Gilchrist, J. L. O'Brien, G. J. Pryde, and A. G. White, "Demonstration of a simple entangling optical gate and its use in Bell-state analysis," Phys. Rev. Lett. 95, 210504 (2005).

[CrossRef]
[PubMed]

J. L. O'Brien, G. J. Pryde, A. Gilchrist, D. F. V. James, N. K. Langford, T. C. Ralph, and A. G. White, "Quantum process tomography of a controlled-NOT gate," Phys. Rev. Lett. 93, 080502 (2004).

[CrossRef]
[PubMed]

J. L. O'Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-NOT gate," Nature 426, 264-267 (2003).

[CrossRef]
[PubMed]

J. L. O'Brien, G. J. Pryde, A. Gilchrist, D. F. V. James, N. K. Langford, T. C. Ralph, and A. G. White, "Quantum process tomography of a controlled-NOT gate," Phys. Rev. Lett. 93, 080502 (2004).

[CrossRef]
[PubMed]

J. L. O'Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-NOT gate," Nature 426, 264-267 (2003).

[CrossRef]
[PubMed]

F. De Martini, A. Mazzei, M. Ricci, and G. M. D'Ariano, "Exploiting quantum parallelism of entanglement for a complete experimental quantum characterization of a single qubit device," Phys. Rev. A 67, 062307 (2003).

[CrossRef]

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, "Realization of the Cirac-Zoller controlled-NOT quantum gate," Nature 422, 408-411 (2003).

[CrossRef]
[PubMed]

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, "Realization of the Cirac-Zoller controlled-NOT quantum gate," Nature 422, 408-411 (2003).

[CrossRef]
[PubMed]

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, "Experimental entanglement of four particles," Nature 404, 256-259 (2000).

[CrossRef]
[PubMed]

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, "Experimental entanglement of four particles," Nature 404, 256-259 (2000).

[CrossRef]
[PubMed]

O. Gühne, P. Hyllus, D. Bruß, A. Ekert, M. Lewenstein, C. Macchiavello, and A. Sanpera, "Detection of entanglement with few local measurements," Phys. Rev. A 66, 062305 (2002).

[CrossRef]

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, "Realization of the Cirac-Zoller controlled-NOT quantum gate," Nature 422, 408-411 (2003).

[CrossRef]
[PubMed]

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, "Proposed experiment to test local hidden-variable theories," Phys. Rev. Lett. 23, 880-884 (1969).

[CrossRef]

M. Steffen, M. Ansmann, R. C. Bialczak, N. Katz, E. Lucero, R. McDermott, M. Neeley, E. M. Weig, A. N. Cleland, and J. M. Martinis, "Measurement of the entanglement of two superconducting qubits via state tomography," Science 313, 1423-1425 (2006).

[CrossRef]
[PubMed]

H. F. Hofmann, R. Okamoto, and S. Takeuchi, "Analysis of an experimental quantum logic gate by complementary classical operations," arXiv.org e-Print archive, quantum physics/0608005, 1 August 2006, http://www.arxiv.org/abs/quant-ph/0608005.

B. M. Terhal and P. Horodecki, "Schmidt number for density matrices," Phys. Rev. A 61, 040301(R) (2000).

[CrossRef]

B. M. Terhal, "Bell inequalities and the separability criterion," Phys. Lett. A 271, 319-326 (2000).

[CrossRef]

J. B. Altepeter, D. Branning, E. Jeffrey, T. C. Wei, P. G. Kwiat, R. T. Thew, J. L. OBrien, M. A. Nielsen, and A. G. White, "Ancilla-assisted quantum process tomography," Phys. Rev. Lett. 93, 193601 (2003).

[CrossRef]

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, "Experimental entanglement of four particles," Nature 404, 256-259 (2000).

[CrossRef]
[PubMed]

J. B. Altepeter, D. Branning, E. Jeffrey, T. C. Wei, P. G. Kwiat, R. T. Thew, J. L. OBrien, M. A. Nielsen, and A. G. White, "Ancilla-assisted quantum process tomography," Phys. Rev. Lett. 93, 193601 (2003).

[CrossRef]

N. A. Peters, J. B. Altepeter, D. A. Branning, E. R. Jeffrey, T.-C. Wei, and P. G. Kwiat, "Maximally entangled mixed states: creation and concentration," Phys. Rev. Lett. 92, 133601 (2004).

[CrossRef]
[PubMed]

M. Steffen, M. Ansmann, R. C. Bialczak, N. Katz, E. Lucero, R. McDermott, M. Neeley, E. M. Weig, A. N. Cleland, and J. M. Martinis, "Measurement of the entanglement of two superconducting qubits via state tomography," Science 313, 1423-1425 (2006).

[CrossRef]
[PubMed]

N. K. Langford, T. J. Weinhold, R. Prevedel, A. Gilchrist, J. L. O'Brien, G. J. Pryde, and A. G. White, "Demonstration of a simple entangling optical gate and its use in Bell-state analysis," Phys. Rev. Lett. 95, 210504 (2005).

[CrossRef]
[PubMed]

N. K. Langford, T. J. Weinhold, R. Prevedel, A. Gilchrist, J. L. O'Brien, G. J. Pryde, and A. G. White, "Demonstration of a simple entangling optical gate and its use in Bell-state analysis," Phys. Rev. Lett. 95, 210504 (2005).

[CrossRef]
[PubMed]

J. L. O'Brien, G. J. Pryde, A. Gilchrist, D. F. V. James, N. K. Langford, T. C. Ralph, and A. G. White, "Quantum process tomography of a controlled-NOT gate," Phys. Rev. Lett. 93, 080502 (2004).

[CrossRef]
[PubMed]

J. B. Altepeter, D. Branning, E. Jeffrey, T. C. Wei, P. G. Kwiat, R. T. Thew, J. L. OBrien, M. A. Nielsen, and A. G. White, "Ancilla-assisted quantum process tomography," Phys. Rev. Lett. 93, 193601 (2003).

[CrossRef]

J. L. O'Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-NOT gate," Nature 426, 264-267 (2003).

[CrossRef]
[PubMed]

W. J. Munro, D. F. V. James, A. G. White, and P. G. Kwiat, "Maximizing the entanglement of two mixed qubits," Phys. Rev. A 64, 030302 (2001).

[CrossRef]

W. J. Munro, K. Nemoto, and A. G. White, "The Bell inequality: a measure of entanglement?" J. Mod. Opt. 48, 1239-1246 (2001).

[CrossRef]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, "Measurement of qubits," Phys. Rev. A 64, 052312 (2001).

[CrossRef]

A. G. White, D. F. V. James, W. J. Munro, and P. G. Kwiat, "Exploring Hilbert space: accurate characterization of quantum information," Phys. Rev. A 65, 012301 (2001).

[CrossRef]

A. G. White, D. F. V. James, P. H. Eberhard, and P. G. Kwiat, "Nonmaximally entangled states: production, characterization, and utilization," Phys. Rev. Lett. 83, 3103-3107 (1999).

[CrossRef]

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, "Experimental entanglement of four particles," Nature 404, 256-259 (2000).

[CrossRef]
[PubMed]

V. Coffman, J. Kundu, and W. K. Wootters, "Distributed entanglement," Phys. Rev. A 61, 052306 (2000).

[CrossRef]

W. K. Wootters, "Entanglement of formation of an arbitrary state of two qubits," Phys. Rev. Lett. 80, 2245-2248 (1998).

[CrossRef]

M. Ziman, "Notes on optimality of direct characterisation of quantum dynamics," arXiv.org e-Print archive, quantum physics/0603151, 17 March 2006, http://www.arxiv.org/abs/quant-ph/0603151.

J. F. Poyatos, J. I. Cirac, and P. Zoller, "Complete characterization of a quantum process: the two-bit quantum gate," Phys. Rev. Lett. 78, 390-393 (1997).

[CrossRef]

W. J. Munro, K. Nemoto, and A. G. White, "The Bell inequality: a measure of entanglement?" J. Mod. Opt. 48, 1239-1246 (2001).

[CrossRef]

I. L. Chuang and M. A. Nielsen, "Prescription for experimental determination of the dynamics of a quantum black box," J. Mod. Opt. 44, 732-744 (1997).

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, "Realization of the Cirac-Zoller controlled-NOT quantum gate," Nature 422, 408-411 (2003).

[CrossRef]
[PubMed]

J. L. O'Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-NOT gate," Nature 426, 264-267 (2003).

[CrossRef]
[PubMed]

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, "Experimental entanglement of four particles," Nature 404, 256-259 (2000).

[CrossRef]
[PubMed]

M. A. Nielsen, E. Knill, and R. Laflamme, "Complete quantum teleportation using nuclear magnetic resonance," Nature 396, 52-55 (1998).

[CrossRef]

M. A. Nielsen, "A simple formula for the average gate fidelity of a quantum dynamical operation," Phys. Lett. A 303, 249-252 (2002).

[CrossRef]

M. Horodecki, P. Horodecki, and R. Horodecki, "Separability of mixed states: necessary and sufficient conditions," Phys. Lett. A 223, 1-8 (1996).

[CrossRef]

B. M. Terhal, "Bell inequalities and the separability criterion," Phys. Lett. A 271, 319-326 (2000).

[CrossRef]

O. Gühne, P. Hyllus, D. Bruß, A. Ekert, M. Lewenstein, C. Macchiavello, and A. Sanpera, "Detection of entanglement with few local measurements," Phys. Rev. A 66, 062305 (2002).

[CrossRef]

B. M. Terhal and P. Horodecki, "Schmidt number for density matrices," Phys. Rev. A 61, 040301(R) (2000).

[CrossRef]

A. Gilchrist, N. K. Langford, and M. A. Nielsen, "Distance measures to compare real and ideal quantum processes," Phys. Rev. A 71, 062310 (2005).

[CrossRef]

J. L. Dodd and M. A. Nielsen, "A simple operational interpretation of the fidelity," Phys. Rev. A 66, 044301 (2002).

[CrossRef]

V. Coffman, J. Kundu, and W. K. Wootters, "Distributed entanglement," Phys. Rev. A 61, 052306 (2000).

[CrossRef]

W. J. Munro, D. F. V. James, A. G. White, and P. G. Kwiat, "Maximizing the entanglement of two mixed qubits," Phys. Rev. A 64, 030302 (2001).

[CrossRef]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, "Measurement of qubits," Phys. Rev. A 64, 052312 (2001).

[CrossRef]

A. G. White, D. F. V. James, W. J. Munro, and P. G. Kwiat, "Exploring Hilbert space: accurate characterization of quantum information," Phys. Rev. A 65, 012301 (2001).

[CrossRef]

F. De Martini, A. Mazzei, M. Ricci, and G. M. D'Ariano, "Exploiting quantum parallelism of entanglement for a complete experimental quantum characterization of a single qubit device," Phys. Rev. A 67, 062307 (2003).

[CrossRef]

M. Horodecki, P. Horodecki, and R. Horodecki, "General teleportation channel, singlet fraction, and quasidistillation," Phys. Rev. A 60, 1888-1898 (1999).

[CrossRef]

A. M. Childs, I. L. Chuang, and D. W. Leung, "Realization of quantum process tomography in NMR," Phys. Rev. A 64, 012314 (2001).

[CrossRef]

J. L. O'Brien, G. J. Pryde, A. Gilchrist, D. F. V. James, N. K. Langford, T. C. Ralph, and A. G. White, "Quantum process tomography of a controlled-NOT gate," Phys. Rev. Lett. 93, 080502 (2004).

[CrossRef]
[PubMed]

N. K. Langford, T. J. Weinhold, R. Prevedel, A. Gilchrist, J. L. O'Brien, G. J. Pryde, and A. G. White, "Demonstration of a simple entangling optical gate and its use in Bell-state analysis," Phys. Rev. Lett. 95, 210504 (2005).

[CrossRef]
[PubMed]

J. I. Cirac, W. Dür, B. Kraus, and M. Lewenstein, "Entangling operations and their implementation using a small amount of entanglement," Phys. Rev. Lett. 86, 544-547 (2001).

[CrossRef]
[PubMed]

H. F. Hofmann, "Complementary classical fidelities as an efficient criterion for the evaluation of experimentally realized quantum operations," Phys. Rev. Lett. 94, 160504 (2005).

[CrossRef]
[PubMed]

W. K. Wootters, "Entanglement of formation of an arbitrary state of two qubits," Phys. Rev. Lett. 80, 2245-2248 (1998).

[CrossRef]

N. A. Peters, J. B. Altepeter, D. A. Branning, E. R. Jeffrey, T.-C. Wei, and P. G. Kwiat, "Maximally entangled mixed states: creation and concentration," Phys. Rev. Lett. 92, 133601 (2004).

[CrossRef]
[PubMed]

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, "Proposed experiment to test local hidden-variable theories," Phys. Rev. Lett. 23, 880-884 (1969).

[CrossRef]

J. F. Poyatos, J. I. Cirac, and P. Zoller, "Complete characterization of a quantum process: the two-bit quantum gate," Phys. Rev. Lett. 78, 390-393 (1997).

[CrossRef]

J. B. Altepeter, D. Branning, E. Jeffrey, T. C. Wei, P. G. Kwiat, R. T. Thew, J. L. OBrien, M. A. Nielsen, and A. G. White, "Ancilla-assisted quantum process tomography," Phys. Rev. Lett. 93, 193601 (2003).

[CrossRef]

G. M. D'Ariano and P. L. Presti, "Imprinting a complete information about a quantum channel on its output state," Phys. Rev. Lett. 91, 047902 (2003).

[CrossRef]
[PubMed]

M. Barbieri, F. De Martini, G. Di Nepi, P. Mataloni, G. M. D'Ariano, and C. Macchiavello, "Detection of entanglement with polarized photons: experimental realization of an entanglement witness," Phys. Rev. Lett. 91, 227901 (2003).

[CrossRef]
[PubMed]

A. G. White, D. F. V. James, P. H. Eberhard, and P. G. Kwiat, "Nonmaximally entangled states: production, characterization, and utilization," Phys. Rev. Lett. 83, 3103-3107 (1999).

[CrossRef]

M. J. Bremner, C. M. Dawson, J. L. Dodd, A. Gilchrist, A. W. Harrow, D. Mortimer, M. A. Nielsen, and T. J. Osborne, "Practical scheme for quantum computation with any two-qubit entangling gate," Phys. Rev. Lett. 89, 247902 (2002).

[CrossRef]
[PubMed]

J. S. Bell, "On the Einstein-Podolsky-Rosen paradox," Physics (Long Island City, N.Y.) 1, 195-200 (1964).

[CrossRef]

A. Jamiolkowski, "Linear transformations which preserve trace and positive semidefiniteness of operators," Rep. Math. Phys. 3, 275-278 (1972).

[CrossRef]

M. Steffen, M. Ansmann, R. C. Bialczak, N. Katz, E. Lucero, R. McDermott, M. Neeley, E. M. Weig, A. N. Cleland, and J. M. Martinis, "Measurement of the entanglement of two superconducting qubits via state tomography," Science 313, 1423-1425 (2006).

[CrossRef]
[PubMed]

R. Alicki, "False qubits II. Entanglement of Josephson junctions," arXiv.org e-Print archive, quantum physics/0609122, 16 September 2006, http://www.arxiv.org/abs/quant-ph/0609122.

The partial transpose of ^p , with respect to an orthonormal basis {∣b›} of qubit two, is given by ^p ^{T2}=Sum_{bb'}∣b′›‹b∣^p∣b′›‹b∣.

R.J.Hughes, ed., "A quantum information science and technology roadmap," Rep. LA-UR-04-1778, ARDA, April 2, 2004, http://qist.lanl.gov/.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge U. Press, 2000).

J. L. Brylinski and R. K. Brylinski, "Computational mathematics," in Mathematics of Quantum Computation, R.K.Brylinski and G.Chen, eds. (Chapman & Hall/CRC Press, 2002), Chap. 2.

On the qubit characteristic sphere the equal-weight superpositions form a great circle midway between the logical states. For example, on the Bloch sphere they lie on the equator, which can be accessed with π/2 pulses; on the Poincaré sphere they lie on the great circle containing the diagonally and circularly polarized states.

To be conclusive in this regard, Bell's inequality requires high-efficiency spacelike separated measurements, a feat not yet achieved in any experimental architecture.

Note that an operator sum representation is not unique and that there is unitary freedom in its choice.

Assuming that count statistics were the dominant source of uncertainty, 1000 Poissonian-distributed data sets (and hence reconstructed density matrices) were generated from each observed data set. The tangle, entropy, and fidelity were calculated for all 1000, yielding the standard deviation of each measure about the mean.

A. Doherty and A. Gilchrist, Department of Physics, University of Queensland, Brisbane QLD 4072, Australia are preparing a manuscript to be called "Quantum tomography using convex optimisation."

R. Blume-Kohout and P. Hayden, "Accurate quantum state estimation via 'Keeping the experimentalist honest'," arXiv.org e-Print archive, quantum physics/0603116, 14 March 2006, http://www.arxiv.org/abs/quant-ph/0603116.

D. W. Leung, "Towards robust quantum computation," arXiv.org e-Print archive, computer science/10012017, 20 December 2002, http://arxiv.org/abs/cs.CC/0012017.

M. Mohseni and D. A. Lidar, "Direct characterization of quantum dynamics: I. General theory," arXiv.org e-Print archive, quantum physics/0601033, 5 January 2006, http://www.arxiv.org/abs/quant-ph/0601033.

M. Ziman, "Notes on optimality of direct characterisation of quantum dynamics," arXiv.org e-Print archive, quantum physics/0603151, 17 March 2006, http://www.arxiv.org/abs/quant-ph/0603151.

H. F. Hofmann, R. Okamoto, and S. Takeuchi, "Analysis of an experimental quantum logic gate by complementary classical operations," arXiv.org e-Print archive, quantum physics/0608005, 1 August 2006, http://www.arxiv.org/abs/quant-ph/0608005.