N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, "Universal quantum computation with continuous-variable cluster states," Phys. Rev. Lett. 97, 110501 (2006).

[Crossref]
[PubMed]

J. Zhang and S. L. Braunstein, "Continuous-variable Gaussian analog of cluster states," Phys. Rev. A 73, 032318 (2006).

[Crossref]

M. A. Nielsen, "Cluster-state quantum computation," Rep. Math. Phys. 57, 147-161 (2006).

[Crossref]

A. M. Lance, H. Jeong, N. B. Grosse, T. Symul, T. C. Ralph, and P. K. Lam, "Quantum-state engineering with continuous-variable postselection," Phys. Rev. A 73, 041801(R) (2006).

[Crossref]

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, "Experimental one-way quantum computing," Nature 434, 169-176 (2005).

[Crossref]
[PubMed]

R. Filip, P. Marek, and U. L. Andersen, "Measurement-induced continuous-variable quantum interactions," Phys. Rev. A 71, 042308 (2005).

[Crossref]

D. E. Browne and T. Rudolph, "Resource-efficient linear optical quantum computation," Phys. Rev. Lett. 95, 010501 (2005).

[Crossref]
[PubMed]

S. L. Braunstein, "Squeezing as an irreducible resource," Phys. Rev. A 71, 055801 (2005).

[Crossref]

S. L. Braunstein and P. van Loock, "Quantum information with continuous variables," Rev. Mod. Phys. 77, 513-577 (2005).

[Crossref]

J. M. Geremia, J. K. Stockton, and H. Mabuchi, "Real-time quantum feedback control of atomic spin-squeezing," Science 304, 270-273 (2004).

[Crossref]
[PubMed]

M. A. Nielsen, "Optical quantum computation using cluster states," Phys. Rev. Lett. 93, 040503 (2004).

[Crossref]
[PubMed]

S. D. Bartlett and W. J. Munro, "Quantum teleportation of optical quantum gates," Phys. Rev. Lett. 90, 117901 (2003).

[Crossref]
[PubMed]

S. D. Bartlett, B. C. Sanders, S. L. Braunstein, and K. Nemoto, "Efficient classical simulation of continuous variable quantum information processes," Phys. Rev. Lett. 88, 097904 (2002).

[Crossref]
[PubMed]

E. Knill, R. Laflamme, and G. J. Milburn, "A scheme for efficient quantum computation with linear optics," Nature 409, 46-52 (2001).

[Crossref]
[PubMed]

R. Raussendorf and H. J. Briegel, "A one-way quantum computer," Phys. Rev. Lett. 86, 5188-5191 (2001).

[Crossref]
[PubMed]

B. Julsgaard, A. Kozhekin, and E. S. Polzik, "Experimental long-lived entanglement of two macroscopic objects," Nature 413, 400-403 (2001).

[Crossref]
[PubMed]

D. Gottesman, A. Kitaev, and J. Preskill, "Encoding a qubit in an oscillator," Phys. Rev. A 64, 012310 (2001).

[Crossref]

X. Zhou, D. W. Leung, and I. L. Chuang, "Methodology for quantum logic gate construction," Phys. Rev. A 62, 052316 (2000).

[Crossref]

S. Lloyd and S. L. Braunstein, "Quantum computation over continuous variables," Phys. Rev. Lett. 82, 1784-1787 (1999).

[Crossref]

D. Gottesman and I. L. Chuang, "Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations," Nature 402, 390-393 (1999).

[Crossref]

P. Grangier, J. A. Levenson, and J.-P. Poizat, "Quantum non-demolition measurements in optics," Nature 396, 537-542 (1998).

[Crossref]

S. L. Braunstein and H. J. Kimble, "Teleportation of continuous quantum variables," Phys. Rev. Lett. 80, 869-872 (1998).

[Crossref]

R. Filip, P. Marek, and U. L. Andersen, "Measurement-induced continuous-variable quantum interactions," Phys. Rev. A 71, 042308 (2005).

[Crossref]

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, "Experimental one-way quantum computing," Nature 434, 169-176 (2005).

[Crossref]
[PubMed]

S. D. Bartlett and W. J. Munro, "Quantum teleportation of optical quantum gates," Phys. Rev. Lett. 90, 117901 (2003).

[Crossref]
[PubMed]

S. D. Bartlett, B. C. Sanders, S. L. Braunstein, and K. Nemoto, "Efficient classical simulation of continuous variable quantum information processes," Phys. Rev. Lett. 88, 097904 (2002).

[Crossref]
[PubMed]

J. Zhang and S. L. Braunstein, "Continuous-variable Gaussian analog of cluster states," Phys. Rev. A 73, 032318 (2006).

[Crossref]

S. L. Braunstein and P. van Loock, "Quantum information with continuous variables," Rev. Mod. Phys. 77, 513-577 (2005).

[Crossref]

S. L. Braunstein, "Squeezing as an irreducible resource," Phys. Rev. A 71, 055801 (2005).

[Crossref]

S. D. Bartlett, B. C. Sanders, S. L. Braunstein, and K. Nemoto, "Efficient classical simulation of continuous variable quantum information processes," Phys. Rev. Lett. 88, 097904 (2002).

[Crossref]
[PubMed]

S. Lloyd and S. L. Braunstein, "Quantum computation over continuous variables," Phys. Rev. Lett. 82, 1784-1787 (1999).

[Crossref]

S. L. Braunstein and H. J. Kimble, "Teleportation of continuous quantum variables," Phys. Rev. Lett. 80, 869-872 (1998).

[Crossref]

R. Raussendorf and H. J. Briegel, "A one-way quantum computer," Phys. Rev. Lett. 86, 5188-5191 (2001).

[Crossref]
[PubMed]

D. E. Browne and T. Rudolph, "Resource-efficient linear optical quantum computation," Phys. Rev. Lett. 95, 010501 (2005).

[Crossref]
[PubMed]

X. Zhou, D. W. Leung, and I. L. Chuang, "Methodology for quantum logic gate construction," Phys. Rev. A 62, 052316 (2000).

[Crossref]

D. Gottesman and I. L. Chuang, "Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations," Nature 402, 390-393 (1999).

[Crossref]

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

R. Filip, P. Marek, and U. L. Andersen, "Measurement-induced continuous-variable quantum interactions," Phys. Rev. A 71, 042308 (2005).

[Crossref]

J. M. Geremia, J. K. Stockton, and H. Mabuchi, "Real-time quantum feedback control of atomic spin-squeezing," Science 304, 270-273 (2004).

[Crossref]
[PubMed]

D. Gottesman, A. Kitaev, and J. Preskill, "Encoding a qubit in an oscillator," Phys. Rev. A 64, 012310 (2001).

[Crossref]

D. Gottesman and I. L. Chuang, "Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations," Nature 402, 390-393 (1999).

[Crossref]

P. Grangier, J. A. Levenson, and J.-P. Poizat, "Quantum non-demolition measurements in optics," Nature 396, 537-542 (1998).

[Crossref]

A. M. Lance, H. Jeong, N. B. Grosse, T. Symul, T. C. Ralph, and P. K. Lam, "Quantum-state engineering with continuous-variable postselection," Phys. Rev. A 73, 041801(R) (2006).

[Crossref]

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, "Universal quantum computation with continuous-variable cluster states," Phys. Rev. Lett. 97, 110501 (2006).

[Crossref]
[PubMed]

A. M. Lance, H. Jeong, N. B. Grosse, T. Symul, T. C. Ralph, and P. K. Lam, "Quantum-state engineering with continuous-variable postselection," Phys. Rev. A 73, 041801(R) (2006).

[Crossref]

B. Julsgaard, A. Kozhekin, and E. S. Polzik, "Experimental long-lived entanglement of two macroscopic objects," Nature 413, 400-403 (2001).

[Crossref]
[PubMed]

S. L. Braunstein and H. J. Kimble, "Teleportation of continuous quantum variables," Phys. Rev. Lett. 80, 869-872 (1998).

[Crossref]

D. Gottesman, A. Kitaev, and J. Preskill, "Encoding a qubit in an oscillator," Phys. Rev. A 64, 012310 (2001).

[Crossref]

E. Knill, R. Laflamme, and G. J. Milburn, "A scheme for efficient quantum computation with linear optics," Nature 409, 46-52 (2001).

[Crossref]
[PubMed]

B. Julsgaard, A. Kozhekin, and E. S. Polzik, "Experimental long-lived entanglement of two macroscopic objects," Nature 413, 400-403 (2001).

[Crossref]
[PubMed]

E. Knill, R. Laflamme, and G. J. Milburn, "A scheme for efficient quantum computation with linear optics," Nature 409, 46-52 (2001).

[Crossref]
[PubMed]

A. M. Lance, H. Jeong, N. B. Grosse, T. Symul, T. C. Ralph, and P. K. Lam, "Quantum-state engineering with continuous-variable postselection," Phys. Rev. A 73, 041801(R) (2006).

[Crossref]

A. M. Lance, H. Jeong, N. B. Grosse, T. Symul, T. C. Ralph, and P. K. Lam, "Quantum-state engineering with continuous-variable postselection," Phys. Rev. A 73, 041801(R) (2006).

[Crossref]

X. Zhou, D. W. Leung, and I. L. Chuang, "Methodology for quantum logic gate construction," Phys. Rev. A 62, 052316 (2000).

[Crossref]

P. Grangier, J. A. Levenson, and J.-P. Poizat, "Quantum non-demolition measurements in optics," Nature 396, 537-542 (1998).

[Crossref]

S. Lloyd and S. L. Braunstein, "Quantum computation over continuous variables," Phys. Rev. Lett. 82, 1784-1787 (1999).

[Crossref]

J. M. Geremia, J. K. Stockton, and H. Mabuchi, "Real-time quantum feedback control of atomic spin-squeezing," Science 304, 270-273 (2004).

[Crossref]
[PubMed]

R. Filip, P. Marek, and U. L. Andersen, "Measurement-induced continuous-variable quantum interactions," Phys. Rev. A 71, 042308 (2005).

[Crossref]

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, "Universal quantum computation with continuous-variable cluster states," Phys. Rev. Lett. 97, 110501 (2006).

[Crossref]
[PubMed]

E. Knill, R. Laflamme, and G. J. Milburn, "A scheme for efficient quantum computation with linear optics," Nature 409, 46-52 (2001).

[Crossref]
[PubMed]

D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 1994).

S. D. Bartlett and W. J. Munro, "Quantum teleportation of optical quantum gates," Phys. Rev. Lett. 90, 117901 (2003).

[Crossref]
[PubMed]

S. D. Bartlett, B. C. Sanders, S. L. Braunstein, and K. Nemoto, "Efficient classical simulation of continuous variable quantum information processes," Phys. Rev. Lett. 88, 097904 (2002).

[Crossref]
[PubMed]

M. A. Nielsen, "Cluster-state quantum computation," Rep. Math. Phys. 57, 147-161 (2006).

[Crossref]

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, "Universal quantum computation with continuous-variable cluster states," Phys. Rev. Lett. 97, 110501 (2006).

[Crossref]
[PubMed]

M. A. Nielsen, "Optical quantum computation using cluster states," Phys. Rev. Lett. 93, 040503 (2004).

[Crossref]
[PubMed]

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

P. Grangier, J. A. Levenson, and J.-P. Poizat, "Quantum non-demolition measurements in optics," Nature 396, 537-542 (1998).

[Crossref]

B. Julsgaard, A. Kozhekin, and E. S. Polzik, "Experimental long-lived entanglement of two macroscopic objects," Nature 413, 400-403 (2001).

[Crossref]
[PubMed]

D. Gottesman, A. Kitaev, and J. Preskill, "Encoding a qubit in an oscillator," Phys. Rev. A 64, 012310 (2001).

[Crossref]

A. M. Lance, H. Jeong, N. B. Grosse, T. Symul, T. C. Ralph, and P. K. Lam, "Quantum-state engineering with continuous-variable postselection," Phys. Rev. A 73, 041801(R) (2006).

[Crossref]

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, "Universal quantum computation with continuous-variable cluster states," Phys. Rev. Lett. 97, 110501 (2006).

[Crossref]
[PubMed]

R. Raussendorf and H. J. Briegel, "A one-way quantum computer," Phys. Rev. Lett. 86, 5188-5191 (2001).

[Crossref]
[PubMed]

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, "Experimental one-way quantum computing," Nature 434, 169-176 (2005).

[Crossref]
[PubMed]

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, "Experimental one-way quantum computing," Nature 434, 169-176 (2005).

[Crossref]
[PubMed]

D. E. Browne and T. Rudolph, "Resource-efficient linear optical quantum computation," Phys. Rev. Lett. 95, 010501 (2005).

[Crossref]
[PubMed]

S. D. Bartlett, B. C. Sanders, S. L. Braunstein, and K. Nemoto, "Efficient classical simulation of continuous variable quantum information processes," Phys. Rev. Lett. 88, 097904 (2002).

[Crossref]
[PubMed]

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, "Experimental one-way quantum computing," Nature 434, 169-176 (2005).

[Crossref]
[PubMed]

J. M. Geremia, J. K. Stockton, and H. Mabuchi, "Real-time quantum feedback control of atomic spin-squeezing," Science 304, 270-273 (2004).

[Crossref]
[PubMed]

A. M. Lance, H. Jeong, N. B. Grosse, T. Symul, T. C. Ralph, and P. K. Lam, "Quantum-state engineering with continuous-variable postselection," Phys. Rev. A 73, 041801(R) (2006).

[Crossref]

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, "Universal quantum computation with continuous-variable cluster states," Phys. Rev. Lett. 97, 110501 (2006).

[Crossref]
[PubMed]

S. L. Braunstein and P. van Loock, "Quantum information with continuous variables," Rev. Mod. Phys. 77, 513-577 (2005).

[Crossref]

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, "Experimental one-way quantum computing," Nature 434, 169-176 (2005).

[Crossref]
[PubMed]

D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 1994).

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, "Experimental one-way quantum computing," Nature 434, 169-176 (2005).

[Crossref]
[PubMed]

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, "Universal quantum computation with continuous-variable cluster states," Phys. Rev. Lett. 97, 110501 (2006).

[Crossref]
[PubMed]

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, "Experimental one-way quantum computing," Nature 434, 169-176 (2005).

[Crossref]
[PubMed]

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, "Experimental one-way quantum computing," Nature 434, 169-176 (2005).

[Crossref]
[PubMed]

J. Zhang and S. L. Braunstein, "Continuous-variable Gaussian analog of cluster states," Phys. Rev. A 73, 032318 (2006).

[Crossref]

X. Zhou, D. W. Leung, and I. L. Chuang, "Methodology for quantum logic gate construction," Phys. Rev. A 62, 052316 (2000).

[Crossref]

P. Grangier, J. A. Levenson, and J.-P. Poizat, "Quantum non-demolition measurements in optics," Nature 396, 537-542 (1998).

[Crossref]

B. Julsgaard, A. Kozhekin, and E. S. Polzik, "Experimental long-lived entanglement of two macroscopic objects," Nature 413, 400-403 (2001).

[Crossref]
[PubMed]

D. Gottesman and I. L. Chuang, "Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations," Nature 402, 390-393 (1999).

[Crossref]

E. Knill, R. Laflamme, and G. J. Milburn, "A scheme for efficient quantum computation with linear optics," Nature 409, 46-52 (2001).

[Crossref]
[PubMed]

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, "Experimental one-way quantum computing," Nature 434, 169-176 (2005).

[Crossref]
[PubMed]

X. Zhou, D. W. Leung, and I. L. Chuang, "Methodology for quantum logic gate construction," Phys. Rev. A 62, 052316 (2000).

[Crossref]

D. Gottesman, A. Kitaev, and J. Preskill, "Encoding a qubit in an oscillator," Phys. Rev. A 64, 012310 (2001).

[Crossref]

R. Filip, P. Marek, and U. L. Andersen, "Measurement-induced continuous-variable quantum interactions," Phys. Rev. A 71, 042308 (2005).

[Crossref]

A. M. Lance, H. Jeong, N. B. Grosse, T. Symul, T. C. Ralph, and P. K. Lam, "Quantum-state engineering with continuous-variable postselection," Phys. Rev. A 73, 041801(R) (2006).

[Crossref]

J. Zhang and S. L. Braunstein, "Continuous-variable Gaussian analog of cluster states," Phys. Rev. A 73, 032318 (2006).

[Crossref]

S. L. Braunstein, "Squeezing as an irreducible resource," Phys. Rev. A 71, 055801 (2005).

[Crossref]

R. Raussendorf and H. J. Briegel, "A one-way quantum computer," Phys. Rev. Lett. 86, 5188-5191 (2001).

[Crossref]
[PubMed]

S. Lloyd and S. L. Braunstein, "Quantum computation over continuous variables," Phys. Rev. Lett. 82, 1784-1787 (1999).

[Crossref]

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, "Universal quantum computation with continuous-variable cluster states," Phys. Rev. Lett. 97, 110501 (2006).

[Crossref]
[PubMed]

S. D. Bartlett and W. J. Munro, "Quantum teleportation of optical quantum gates," Phys. Rev. Lett. 90, 117901 (2003).

[Crossref]
[PubMed]

M. A. Nielsen, "Optical quantum computation using cluster states," Phys. Rev. Lett. 93, 040503 (2004).

[Crossref]
[PubMed]

D. E. Browne and T. Rudolph, "Resource-efficient linear optical quantum computation," Phys. Rev. Lett. 95, 010501 (2005).

[Crossref]
[PubMed]

S. D. Bartlett, B. C. Sanders, S. L. Braunstein, and K. Nemoto, "Efficient classical simulation of continuous variable quantum information processes," Phys. Rev. Lett. 88, 097904 (2002).

[Crossref]
[PubMed]

S. L. Braunstein and H. J. Kimble, "Teleportation of continuous quantum variables," Phys. Rev. Lett. 80, 869-872 (1998).

[Crossref]

M. A. Nielsen, "Cluster-state quantum computation," Rep. Math. Phys. 57, 147-161 (2006).

[Crossref]

S. L. Braunstein and P. van Loock, "Quantum information with continuous variables," Rev. Mod. Phys. 77, 513-577 (2005).

[Crossref]

J. M. Geremia, J. K. Stockton, and H. Mabuchi, "Real-time quantum feedback control of atomic spin-squeezing," Science 304, 270-273 (2004).

[Crossref]
[PubMed]

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

D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 1994).

Usually, the quantum optical phase-space displacement operator D(α)=exp(αâdagger−α*â) is used to describe the displacements in Alice's measurement basis and Bob's correction operation for continuous-variable quantum teleportation. Here, we prefer to stick to the WH group elements, where Z(v)X(u) differs from D(α) only by a global phase with α=u+iv. Alice's measurement basis is then described by [Z(v)X(u) big dot times 1]integral dx∣x›∣x›√π. Bob's correction operation would be Z(v)X(u) in this case. In a communication rather than computation scenario where Alice and Bob are spatially separated, of course, Alice needs to send the results u and v to Bob via a classical channel.