Abstract

Ascertaining the large-scale properties of the whole from the properties of its parts is a highly relevant problem in many branches of physics. Here, we investigate a special variant of this task when the parts carry no signs of the global properties in the context of quantum correlation properties in a multipartite optical system. Specifically, we prove experimentally the predicted existence of a three-qubit quantum state with genuine multipartite entanglement (GME) that can be certified solely from its separable two-qubit reduced density matrices. The qubits are encoded into different degrees of freedom of a pair of correlated photons, and the state is prepared by letting the photons propagate through a linear optical circuit. The presence of GME is verified by finding numerically a fully decomposable entanglement witness acting nontrivially only on the reductions of the global state. Our result confirms the viability of detection of emerging global properties of composite quantum systems from the parts that lack the properties.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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2018 (2)

R. Stárek, M. Miková, I. Straka, M. Dušek, M. Ježek, J. Fiurášek, and M. Mičuda, “Experimental realization of SWAP operation on hyper-encoded qubits,” Opt. Express 26, 8443–8452 (2018).
[Crossref]

M. Paraschiv, N. Miklin, T. Moroder, and O. Gühne, “Proving genuine multiparticle entanglement from separable nearest-neighbor marginals,” Phys. Rev. A 98, 062102 (2018).
[Crossref]

2016 (1)

N. Miklin, T. Moroder, and O. Gühne, “Multiparticle entanglement as an emergent phenomenon,” Phys. Rev. A 93, 020104 (2016).
[Crossref]

2015 (2)

C. Schwemmer, L. Knips, D. Richart, H. Weinfurter, T. Moroder, M. Kleinmann, and O. Gühne, “Systematic errors in current quantum state tomography tools,” Phys. Rev. Lett. 114, 080403 (2015).
[Crossref]

M. Mičuda, M. Miková, I. Straka, M. Sedlák, M. Dušek, M. Ježek, and J. Fiurášek, “Tomographic characterization of a linear optical quantum Toffoli gate,” Phys. Rev. A 92, 032312 (2015).
[Crossref]

2014 (1)

L. Chen, O. Gittsovich, K. Modi, and M. Piani, “Role of correlations in two-body-marginal problem,” Phys. Rev. A 90, 042314 (2014).
[Crossref]

2013 (1)

M. Mičuda, M. Sedlák, I. Straka, M. Miková, M. Dušek, M. Ježek, and J. Fiurášek, “Efficient experimental estimation of fidelity of linear optical quantum Toffoli gate,” Phys. Rev. Lett. 111, 160407 (2013).
[Crossref]

2011 (1)

B. Jungnitsch, T. Moroder, and O. Gühne, “Taming multiparticle entanglement,” Phys. Rev. Lett. 106, 190502 (2011).
[Crossref]

2010 (1)

B. P. Lanyon, J. D. Whitfield, G. G. Gillett, M. E. Goggin, M. P. Almeida, I. Kassal, J. D. Biamonte, M. Mohseni, B. J. Powell, M. Barbieri, A. Aspuru-Guzik, and A. G. White, “Towards quantum chemistry on a quantum computer,” Nat. Chem. 2, 106–111 (2010).
[Crossref]

2009 (2)

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

G. Tóth, C. Knapp, O. Gühne, and H.-J. Briegel, “Spin squeezing and entanglement,” Phys. Rev. A 79, 042334 (2009).
[Crossref]

2008 (1)

L. Amico, R. Fazio, A. Osterloh, and V. Vedral, “Entanglement in many-body systems,” Rev. Mod. Phys. 80, 517–576 (2008).
[Crossref]

2007 (1)

G. Tóth, C. Knapp, O. Gühne, and H.-J. Briegel, “Optimal spin squeezing inequalities detect bound entanglement in spin models,” Phys. Rev. Lett. 99, 250405 (2007).
[Crossref]

2005 (4)

G. Tóth, “Entanglement witnesses in spin models,” Phys. Rev. A 71, 010301(R) (2005).
[Crossref]

N. K. Langford, T. J. Weinhold, R. Prevedel, K. J. Resch, 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]

N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505(2005).
[Crossref]

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Demonstration of an optical quantum controlled-NOT gate without path interference,” Phys. Rev. Lett. 95, 210506 (2005).
[Crossref]

2004 (1)

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306, 1330–1336 (2004).
[Crossref]

2003 (3)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 264–267 (2003).
[Crossref]

J. L. O’Brien, G. J. Pryde, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
[Crossref]

M. Ježek, J. Fiurášek, and Z. Hradil, “Quantum inference of states and processes,” Phys. Rev. A 68, 012305 (2003).
[Crossref]

2002 (1)

T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White, “Linear optical controlled-NOT gate in the coincidence basis,” Phys. Rev. A 65, 062324 (2002).
[Crossref]

2001 (1)

R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. 86, 5188–5191 (2001).
[Crossref]

2000 (2)

B. M. Terhal, “Bell inequalities and the separability criterion,” Phys. Lett. A 271, 319–326 (2000).
[Crossref]

M. Lewenstein, B. Kraus, J. I. Cirac, and P. Horodecki, “Optimization of entanglement witnesses,” Phys. Rev. A 62, 052310 (2000).
[Crossref]

1996 (3)

L. Vandenberghe and S. Boyd, “Semidefinite programming,” SIAM Rev. 38, 49–95 (1996).
[Crossref]

A. Peres, “Separability criterion for density matrices,” Phys. Rev. Lett. 77, 1413–1415 (1996).
[Crossref]

M. Horodecki, P. Horodecki, and R. Horodecki, “Separability of mixed states: necessary and sufficient conditions,” Phys. Lett. A 223, 1–8 (1996).
[Crossref]

1972 (1)

P. W. Anderson, “More is different,” Science 177, 393–396 (1972).
[Crossref]

Almeida, M. P.

B. P. Lanyon, J. D. Whitfield, G. G. Gillett, M. E. Goggin, M. P. Almeida, I. Kassal, J. D. Biamonte, M. Mohseni, B. J. Powell, M. Barbieri, A. Aspuru-Guzik, and A. G. White, “Towards quantum chemistry on a quantum computer,” Nat. Chem. 2, 106–111 (2010).
[Crossref]

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

Amico, L.

L. Amico, R. Fazio, A. Osterloh, and V. Vedral, “Entanglement in many-body systems,” Rev. Mod. Phys. 80, 517–576 (2008).
[Crossref]

Anderson, P. W.

P. W. Anderson, “More is different,” Science 177, 393–396 (1972).
[Crossref]

Aspuru-Guzik, A.

B. P. Lanyon, J. D. Whitfield, G. G. Gillett, M. E. Goggin, M. P. Almeida, I. Kassal, J. D. Biamonte, M. Mohseni, B. J. Powell, M. Barbieri, A. Aspuru-Guzik, and A. G. White, “Towards quantum chemistry on a quantum computer,” Nat. Chem. 2, 106–111 (2010).
[Crossref]

Barbieri, M.

B. P. Lanyon, J. D. Whitfield, G. G. Gillett, M. E. Goggin, M. P. Almeida, I. Kassal, J. D. Biamonte, M. Mohseni, B. J. Powell, M. Barbieri, A. Aspuru-Guzik, and A. G. White, “Towards quantum chemistry on a quantum computer,” Nat. Chem. 2, 106–111 (2010).
[Crossref]

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

Bell, T. B.

T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White, “Linear optical controlled-NOT gate in the coincidence basis,” Phys. Rev. A 65, 062324 (2002).
[Crossref]

Biamonte, J. D.

B. P. Lanyon, J. D. Whitfield, G. G. Gillett, M. E. Goggin, M. P. Almeida, I. Kassal, J. D. Biamonte, M. Mohseni, B. J. Powell, M. Barbieri, A. Aspuru-Guzik, and A. G. White, “Towards quantum chemistry on a quantum computer,” Nat. Chem. 2, 106–111 (2010).
[Crossref]

Boyd, S.

L. Vandenberghe and S. Boyd, “Semidefinite programming,” SIAM Rev. 38, 49–95 (1996).
[Crossref]

Branning, D.

J. L. O’Brien, G. J. Pryde, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
[Crossref]

Briegel, H. J.

R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. 86, 5188–5191 (2001).
[Crossref]

Briegel, H.-J.

G. Tóth, C. Knapp, O. Gühne, and H.-J. Briegel, “Spin squeezing and entanglement,” Phys. Rev. A 79, 042334 (2009).
[Crossref]

G. Tóth, C. Knapp, O. Gühne, and H.-J. Briegel, “Optimal spin squeezing inequalities detect bound entanglement in spin models,” Phys. Rev. Lett. 99, 250405 (2007).
[Crossref]

Chen, L.

L. Chen, O. Gittsovich, K. Modi, and M. Piani, “Role of correlations in two-body-marginal problem,” Phys. Rev. A 90, 042314 (2014).
[Crossref]

Cirac, J. I.

M. Lewenstein, B. Kraus, J. I. Cirac, and P. Horodecki, “Optimization of entanglement witnesses,” Phys. Rev. A 62, 052310 (2000).
[Crossref]

Dušek, M.

R. Stárek, M. Miková, I. Straka, M. Dušek, M. Ježek, J. Fiurášek, and M. Mičuda, “Experimental realization of SWAP operation on hyper-encoded qubits,” Opt. Express 26, 8443–8452 (2018).
[Crossref]

M. Mičuda, M. Miková, I. Straka, M. Sedlák, M. Dušek, M. Ježek, and J. Fiurášek, “Tomographic characterization of a linear optical quantum Toffoli gate,” Phys. Rev. A 92, 032312 (2015).
[Crossref]

M. Mičuda, M. Sedlák, I. Straka, M. Miková, M. Dušek, M. Ježek, and J. Fiurášek, “Efficient experimental estimation of fidelity of linear optical quantum Toffoli gate,” Phys. Rev. Lett. 111, 160407 (2013).
[Crossref]

Fazio, R.

L. Amico, R. Fazio, A. Osterloh, and V. Vedral, “Entanglement in many-body systems,” Rev. Mod. Phys. 80, 517–576 (2008).
[Crossref]

Fiurášek, J.

R. Stárek, M. Miková, I. Straka, M. Dušek, M. Ježek, J. Fiurášek, and M. Mičuda, “Experimental realization of SWAP operation on hyper-encoded qubits,” Opt. Express 26, 8443–8452 (2018).
[Crossref]

M. Mičuda, M. Miková, I. Straka, M. Sedlák, M. Dušek, M. Ježek, and J. Fiurášek, “Tomographic characterization of a linear optical quantum Toffoli gate,” Phys. Rev. A 92, 032312 (2015).
[Crossref]

M. Mičuda, M. Sedlák, I. Straka, M. Miková, M. Dušek, M. Ježek, and J. Fiurášek, “Efficient experimental estimation of fidelity of linear optical quantum Toffoli gate,” Phys. Rev. Lett. 111, 160407 (2013).
[Crossref]

M. Ježek, J. Fiurášek, and Z. Hradil, “Quantum inference of states and processes,” Phys. Rev. A 68, 012305 (2003).
[Crossref]

Gilchrist, A.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

N. K. Langford, T. J. Weinhold, R. Prevedel, K. J. Resch, 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]

Gillett, G. G.

B. P. Lanyon, J. D. Whitfield, G. G. Gillett, M. E. Goggin, M. P. Almeida, I. Kassal, J. D. Biamonte, M. Mohseni, B. J. Powell, M. Barbieri, A. Aspuru-Guzik, and A. G. White, “Towards quantum chemistry on a quantum computer,” Nat. Chem. 2, 106–111 (2010).
[Crossref]

Giovannetti, V.

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306, 1330–1336 (2004).
[Crossref]

Gittsovich, O.

L. Chen, O. Gittsovich, K. Modi, and M. Piani, “Role of correlations in two-body-marginal problem,” Phys. Rev. A 90, 042314 (2014).
[Crossref]

Goggin, M. E.

B. P. Lanyon, J. D. Whitfield, G. G. Gillett, M. E. Goggin, M. P. Almeida, I. Kassal, J. D. Biamonte, M. Mohseni, B. J. Powell, M. Barbieri, A. Aspuru-Guzik, and A. G. White, “Towards quantum chemistry on a quantum computer,” Nat. Chem. 2, 106–111 (2010).
[Crossref]

Greenberger, D. M.

D. M. Greenberger, M. Horne, and A. Zeilinger, Bell’s Theorem, Quantum Theory, and Conceptions of the Universe, M. Kafatos, ed. (Kluwer, 1989), p. 69.

Gühne, O.

M. Paraschiv, N. Miklin, T. Moroder, and O. Gühne, “Proving genuine multiparticle entanglement from separable nearest-neighbor marginals,” Phys. Rev. A 98, 062102 (2018).
[Crossref]

N. Miklin, T. Moroder, and O. Gühne, “Multiparticle entanglement as an emergent phenomenon,” Phys. Rev. A 93, 020104 (2016).
[Crossref]

C. Schwemmer, L. Knips, D. Richart, H. Weinfurter, T. Moroder, M. Kleinmann, and O. Gühne, “Systematic errors in current quantum state tomography tools,” Phys. Rev. Lett. 114, 080403 (2015).
[Crossref]

B. Jungnitsch, T. Moroder, and O. Gühne, “Taming multiparticle entanglement,” Phys. Rev. Lett. 106, 190502 (2011).
[Crossref]

G. Tóth, C. Knapp, O. Gühne, and H.-J. Briegel, “Spin squeezing and entanglement,” Phys. Rev. A 79, 042334 (2009).
[Crossref]

G. Tóth, C. Knapp, O. Gühne, and H.-J. Briegel, “Optimal spin squeezing inequalities detect bound entanglement in spin models,” Phys. Rev. Lett. 99, 250405 (2007).
[Crossref]

Hofmann, H. F.

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Demonstration of an optical quantum controlled-NOT gate without path interference,” Phys. Rev. Lett. 95, 210506 (2005).
[Crossref]

Horne, M.

D. M. Greenberger, M. Horne, and A. Zeilinger, Bell’s Theorem, Quantum Theory, and Conceptions of the Universe, M. Kafatos, ed. (Kluwer, 1989), p. 69.

Horodecki, M.

M. Horodecki, P. Horodecki, and R. Horodecki, “Separability of mixed states: necessary and sufficient conditions,” Phys. Lett. A 223, 1–8 (1996).
[Crossref]

Horodecki, P.

M. Lewenstein, B. Kraus, J. I. Cirac, and P. Horodecki, “Optimization of entanglement witnesses,” Phys. Rev. A 62, 052310 (2000).
[Crossref]

M. Horodecki, P. Horodecki, and R. Horodecki, “Separability of mixed states: necessary and sufficient conditions,” Phys. Lett. A 223, 1–8 (1996).
[Crossref]

Horodecki, R.

M. Horodecki, P. Horodecki, and R. Horodecki, “Separability of mixed states: necessary and sufficient conditions,” Phys. Lett. A 223, 1–8 (1996).
[Crossref]

Hradil, Z.

M. Ježek, J. Fiurášek, and Z. Hradil, “Quantum inference of states and processes,” Phys. Rev. A 68, 012305 (2003).
[Crossref]

Jennewein, T.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

Ježek, M.

R. Stárek, M. Miková, I. Straka, M. Dušek, M. Ježek, J. Fiurášek, and M. Mičuda, “Experimental realization of SWAP operation on hyper-encoded qubits,” Opt. Express 26, 8443–8452 (2018).
[Crossref]

M. Mičuda, M. Miková, I. Straka, M. Sedlák, M. Dušek, M. Ježek, and J. Fiurášek, “Tomographic characterization of a linear optical quantum Toffoli gate,” Phys. Rev. A 92, 032312 (2015).
[Crossref]

M. Mičuda, M. Sedlák, I. Straka, M. Miková, M. Dušek, M. Ježek, and J. Fiurášek, “Efficient experimental estimation of fidelity of linear optical quantum Toffoli gate,” Phys. Rev. Lett. 111, 160407 (2013).
[Crossref]

M. Ježek, J. Fiurášek, and Z. Hradil, “Quantum inference of states and processes,” Phys. Rev. A 68, 012305 (2003).
[Crossref]

Jungnitsch, B.

B. Jungnitsch, T. Moroder, and O. Gühne, “Taming multiparticle entanglement,” Phys. Rev. Lett. 106, 190502 (2011).
[Crossref]

Kassal, I.

B. P. Lanyon, J. D. Whitfield, G. G. Gillett, M. E. Goggin, M. P. Almeida, I. Kassal, J. D. Biamonte, M. Mohseni, B. J. Powell, M. Barbieri, A. Aspuru-Guzik, and A. G. White, “Towards quantum chemistry on a quantum computer,” Nat. Chem. 2, 106–111 (2010).
[Crossref]

Kiesel, N.

N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505(2005).
[Crossref]

Kleinmann, M.

C. Schwemmer, L. Knips, D. Richart, H. Weinfurter, T. Moroder, M. Kleinmann, and O. Gühne, “Systematic errors in current quantum state tomography tools,” Phys. Rev. Lett. 114, 080403 (2015).
[Crossref]

Knapp, C.

G. Tóth, C. Knapp, O. Gühne, and H.-J. Briegel, “Spin squeezing and entanglement,” Phys. Rev. A 79, 042334 (2009).
[Crossref]

G. Tóth, C. Knapp, O. Gühne, and H.-J. Briegel, “Optimal spin squeezing inequalities detect bound entanglement in spin models,” Phys. Rev. Lett. 99, 250405 (2007).
[Crossref]

Knill, E.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 264–267 (2003).
[Crossref]

Knips, L.

C. Schwemmer, L. Knips, D. Richart, H. Weinfurter, T. Moroder, M. Kleinmann, and O. Gühne, “Systematic errors in current quantum state tomography tools,” Phys. Rev. Lett. 114, 080403 (2015).
[Crossref]

Kraus, B.

M. Lewenstein, B. Kraus, J. I. Cirac, and P. Horodecki, “Optimization of entanglement witnesses,” Phys. Rev. A 62, 052310 (2000).
[Crossref]

Laflamme, R.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 264–267 (2003).
[Crossref]

Langford, N. K.

N. K. Langford, T. J. Weinhold, R. Prevedel, K. J. Resch, 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]

T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White, “Linear optical controlled-NOT gate in the coincidence basis,” Phys. Rev. A 65, 062324 (2002).
[Crossref]

Lanyon, B. P.

B. P. Lanyon, J. D. Whitfield, G. G. Gillett, M. E. Goggin, M. P. Almeida, I. Kassal, J. D. Biamonte, M. Mohseni, B. J. Powell, M. Barbieri, A. Aspuru-Guzik, and A. G. White, “Towards quantum chemistry on a quantum computer,” Nat. Chem. 2, 106–111 (2010).
[Crossref]

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

Lewenstein, M.

M. Lewenstein, B. Kraus, J. I. Cirac, and P. Horodecki, “Optimization of entanglement witnesses,” Phys. Rev. A 62, 052310 (2000).
[Crossref]

Lloyd, S.

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306, 1330–1336 (2004).
[Crossref]

Löfberg, J.

J. Löfberg, “YALMIP: a toolbox for modeling and optimization in MATLAB,” in Proceedings of the CACSD Conference (2004).

Maccone, L.

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306, 1330–1336 (2004).
[Crossref]

Micuda, M.

R. Stárek, M. Miková, I. Straka, M. Dušek, M. Ježek, J. Fiurášek, and M. Mičuda, “Experimental realization of SWAP operation on hyper-encoded qubits,” Opt. Express 26, 8443–8452 (2018).
[Crossref]

M. Mičuda, M. Miková, I. Straka, M. Sedlák, M. Dušek, M. Ježek, and J. Fiurášek, “Tomographic characterization of a linear optical quantum Toffoli gate,” Phys. Rev. A 92, 032312 (2015).
[Crossref]

M. Mičuda, M. Sedlák, I. Straka, M. Miková, M. Dušek, M. Ježek, and J. Fiurášek, “Efficient experimental estimation of fidelity of linear optical quantum Toffoli gate,” Phys. Rev. Lett. 111, 160407 (2013).
[Crossref]

Miklin, N.

M. Paraschiv, N. Miklin, T. Moroder, and O. Gühne, “Proving genuine multiparticle entanglement from separable nearest-neighbor marginals,” Phys. Rev. A 98, 062102 (2018).
[Crossref]

N. Miklin, T. Moroder, and O. Gühne, “Multiparticle entanglement as an emergent phenomenon,” Phys. Rev. A 93, 020104 (2016).
[Crossref]

Miková, M.

R. Stárek, M. Miková, I. Straka, M. Dušek, M. Ježek, J. Fiurášek, and M. Mičuda, “Experimental realization of SWAP operation on hyper-encoded qubits,” Opt. Express 26, 8443–8452 (2018).
[Crossref]

M. Mičuda, M. Miková, I. Straka, M. Sedlák, M. Dušek, M. Ježek, and J. Fiurášek, “Tomographic characterization of a linear optical quantum Toffoli gate,” Phys. Rev. A 92, 032312 (2015).
[Crossref]

M. Mičuda, M. Sedlák, I. Straka, M. Miková, M. Dušek, M. Ježek, and J. Fiurášek, “Efficient experimental estimation of fidelity of linear optical quantum Toffoli gate,” Phys. Rev. Lett. 111, 160407 (2013).
[Crossref]

Milburn, G. J.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 264–267 (2003).
[Crossref]

Modi, K.

L. Chen, O. Gittsovich, K. Modi, and M. Piani, “Role of correlations in two-body-marginal problem,” Phys. Rev. A 90, 042314 (2014).
[Crossref]

Mohseni, M.

B. P. Lanyon, J. D. Whitfield, G. G. Gillett, M. E. Goggin, M. P. Almeida, I. Kassal, J. D. Biamonte, M. Mohseni, B. J. Powell, M. Barbieri, A. Aspuru-Guzik, and A. G. White, “Towards quantum chemistry on a quantum computer,” Nat. Chem. 2, 106–111 (2010).
[Crossref]

Moroder, T.

M. Paraschiv, N. Miklin, T. Moroder, and O. Gühne, “Proving genuine multiparticle entanglement from separable nearest-neighbor marginals,” Phys. Rev. A 98, 062102 (2018).
[Crossref]

N. Miklin, T. Moroder, and O. Gühne, “Multiparticle entanglement as an emergent phenomenon,” Phys. Rev. A 93, 020104 (2016).
[Crossref]

C. Schwemmer, L. Knips, D. Richart, H. Weinfurter, T. Moroder, M. Kleinmann, and O. Gühne, “Systematic errors in current quantum state tomography tools,” Phys. Rev. Lett. 114, 080403 (2015).
[Crossref]

B. Jungnitsch, T. Moroder, and O. Gühne, “Taming multiparticle entanglement,” Phys. Rev. Lett. 106, 190502 (2011).
[Crossref]

O’Brien, J. L.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

N. K. Langford, T. J. Weinhold, R. Prevedel, K. J. Resch, 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]

J. L. O’Brien, G. J. Pryde, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
[Crossref]

Okamoto, R.

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Demonstration of an optical quantum controlled-NOT gate without path interference,” Phys. Rev. Lett. 95, 210506 (2005).
[Crossref]

Osterloh, A.

L. Amico, R. Fazio, A. Osterloh, and V. Vedral, “Entanglement in many-body systems,” Rev. Mod. Phys. 80, 517–576 (2008).
[Crossref]

Paraschiv, M.

M. Paraschiv, N. Miklin, T. Moroder, and O. Gühne, “Proving genuine multiparticle entanglement from separable nearest-neighbor marginals,” Phys. Rev. A 98, 062102 (2018).
[Crossref]

Paris, M.

M. Paris and J. Řeháček, Quantum State Estimation, Vol. 649 of Lecture Notes in Physics (Springer, 2004).

Peres, A.

A. Peres, “Separability criterion for density matrices,” Phys. Rev. Lett. 77, 1413–1415 (1996).
[Crossref]

Piani, M.

L. Chen, O. Gittsovich, K. Modi, and M. Piani, “Role of correlations in two-body-marginal problem,” Phys. Rev. A 90, 042314 (2014).
[Crossref]

Powell, B. J.

B. P. Lanyon, J. D. Whitfield, G. G. Gillett, M. E. Goggin, M. P. Almeida, I. Kassal, J. D. Biamonte, M. Mohseni, B. J. Powell, M. Barbieri, A. Aspuru-Guzik, and A. G. White, “Towards quantum chemistry on a quantum computer,” Nat. Chem. 2, 106–111 (2010).
[Crossref]

Prevedel, R.

N. K. Langford, T. J. Weinhold, R. Prevedel, K. J. Resch, 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]

Pryde, G. J.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

N. K. Langford, T. J. Weinhold, R. Prevedel, K. J. Resch, 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]

J. L. O’Brien, G. J. Pryde, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
[Crossref]

Ralph, T. C.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

J. L. O’Brien, G. J. Pryde, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
[Crossref]

T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White, “Linear optical controlled-NOT gate in the coincidence basis,” Phys. Rev. A 65, 062324 (2002).
[Crossref]

Raussendorf, R.

R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. 86, 5188–5191 (2001).
[Crossref]

Rehácek, J.

M. Paris and J. Řeháček, Quantum State Estimation, Vol. 649 of Lecture Notes in Physics (Springer, 2004).

Resch, K. J.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

N. K. Langford, T. J. Weinhold, R. Prevedel, K. J. Resch, 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]

Richart, D.

C. Schwemmer, L. Knips, D. Richart, H. Weinfurter, T. Moroder, M. Kleinmann, and O. Gühne, “Systematic errors in current quantum state tomography tools,” Phys. Rev. Lett. 114, 080403 (2015).
[Crossref]

Sasaki, K.

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Demonstration of an optical quantum controlled-NOT gate without path interference,” Phys. Rev. Lett. 95, 210506 (2005).
[Crossref]

Schmid, C.

N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505(2005).
[Crossref]

Schwemmer, C.

C. Schwemmer, L. Knips, D. Richart, H. Weinfurter, T. Moroder, M. Kleinmann, and O. Gühne, “Systematic errors in current quantum state tomography tools,” Phys. Rev. Lett. 114, 080403 (2015).
[Crossref]

Sedlák, M.

M. Mičuda, M. Miková, I. Straka, M. Sedlák, M. Dušek, M. Ježek, and J. Fiurášek, “Tomographic characterization of a linear optical quantum Toffoli gate,” Phys. Rev. A 92, 032312 (2015).
[Crossref]

M. Mičuda, M. Sedlák, I. Straka, M. Miková, M. Dušek, M. Ježek, and J. Fiurášek, “Efficient experimental estimation of fidelity of linear optical quantum Toffoli gate,” Phys. Rev. Lett. 111, 160407 (2013).
[Crossref]

Stárek, R.

Straka, I.

R. Stárek, M. Miková, I. Straka, M. Dušek, M. Ježek, J. Fiurášek, and M. Mičuda, “Experimental realization of SWAP operation on hyper-encoded qubits,” Opt. Express 26, 8443–8452 (2018).
[Crossref]

M. Mičuda, M. Miková, I. Straka, M. Sedlák, M. Dušek, M. Ježek, and J. Fiurášek, “Tomographic characterization of a linear optical quantum Toffoli gate,” Phys. Rev. A 92, 032312 (2015).
[Crossref]

M. Mičuda, M. Sedlák, I. Straka, M. Miková, M. Dušek, M. Ježek, and J. Fiurášek, “Efficient experimental estimation of fidelity of linear optical quantum Toffoli gate,” Phys. Rev. Lett. 111, 160407 (2013).
[Crossref]

Takeuchi, S.

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Demonstration of an optical quantum controlled-NOT gate without path interference,” Phys. Rev. Lett. 95, 210506 (2005).
[Crossref]

Terhal, B. M.

B. M. Terhal, “Bell inequalities and the separability criterion,” Phys. Lett. A 271, 319–326 (2000).
[Crossref]

Tóth, G.

G. Tóth, C. Knapp, O. Gühne, and H.-J. Briegel, “Spin squeezing and entanglement,” Phys. Rev. A 79, 042334 (2009).
[Crossref]

G. Tóth, C. Knapp, O. Gühne, and H.-J. Briegel, “Optimal spin squeezing inequalities detect bound entanglement in spin models,” Phys. Rev. Lett. 99, 250405 (2007).
[Crossref]

G. Tóth, “Entanglement witnesses in spin models,” Phys. Rev. A 71, 010301(R) (2005).
[Crossref]

Ursin, R.

N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505(2005).
[Crossref]

Vandenberghe, L.

L. Vandenberghe and S. Boyd, “Semidefinite programming,” SIAM Rev. 38, 49–95 (1996).
[Crossref]

Vedral, V.

L. Amico, R. Fazio, A. Osterloh, and V. Vedral, “Entanglement in many-body systems,” Rev. Mod. Phys. 80, 517–576 (2008).
[Crossref]

Weber, U.

N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505(2005).
[Crossref]

Weinfurter, H.

C. Schwemmer, L. Knips, D. Richart, H. Weinfurter, T. Moroder, M. Kleinmann, and O. Gühne, “Systematic errors in current quantum state tomography tools,” Phys. Rev. Lett. 114, 080403 (2015).
[Crossref]

N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505(2005).
[Crossref]

Weinhold, T. J.

N. K. Langford, T. J. Weinhold, R. Prevedel, K. J. Resch, 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]

White, A. G.

B. P. Lanyon, J. D. Whitfield, G. G. Gillett, M. E. Goggin, M. P. Almeida, I. Kassal, J. D. Biamonte, M. Mohseni, B. J. Powell, M. Barbieri, A. Aspuru-Guzik, and A. G. White, “Towards quantum chemistry on a quantum computer,” Nat. Chem. 2, 106–111 (2010).
[Crossref]

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

N. K. Langford, T. J. Weinhold, R. Prevedel, K. J. Resch, 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]

T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White, “Linear optical controlled-NOT gate in the coincidence basis,” Phys. Rev. A 65, 062324 (2002).
[Crossref]

Whitfield, J. D.

B. P. Lanyon, J. D. Whitfield, G. G. Gillett, M. E. Goggin, M. P. Almeida, I. Kassal, J. D. Biamonte, M. Mohseni, B. J. Powell, M. Barbieri, A. Aspuru-Guzik, and A. G. White, “Towards quantum chemistry on a quantum computer,” Nat. Chem. 2, 106–111 (2010).
[Crossref]

Zeilinger, A.

D. M. Greenberger, M. Horne, and A. Zeilinger, Bell’s Theorem, Quantum Theory, and Conceptions of the Universe, M. Kafatos, ed. (Kluwer, 1989), p. 69.

Nat. Chem. (1)

B. P. Lanyon, J. D. Whitfield, G. G. Gillett, M. E. Goggin, M. P. Almeida, I. Kassal, J. D. Biamonte, M. Mohseni, B. J. Powell, M. Barbieri, A. Aspuru-Guzik, and A. G. White, “Towards quantum chemistry on a quantum computer,” Nat. Chem. 2, 106–111 (2010).
[Crossref]

Nat. Phys. (1)

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

Nature (2)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 264–267 (2003).
[Crossref]

J. L. O’Brien, G. J. Pryde, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
[Crossref]

Opt. Express (1)

Phys. Lett. A (2)

M. Horodecki, P. Horodecki, and R. Horodecki, “Separability of mixed states: necessary and sufficient conditions,” Phys. Lett. A 223, 1–8 (1996).
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B. M. Terhal, “Bell inequalities and the separability criterion,” Phys. Lett. A 271, 319–326 (2000).
[Crossref]

Phys. Rev. A (9)

M. Lewenstein, B. Kraus, J. I. Cirac, and P. Horodecki, “Optimization of entanglement witnesses,” Phys. Rev. A 62, 052310 (2000).
[Crossref]

G. Tóth, C. Knapp, O. Gühne, and H.-J. Briegel, “Spin squeezing and entanglement,” Phys. Rev. A 79, 042334 (2009).
[Crossref]

L. Chen, O. Gittsovich, K. Modi, and M. Piani, “Role of correlations in two-body-marginal problem,” Phys. Rev. A 90, 042314 (2014).
[Crossref]

N. Miklin, T. Moroder, and O. Gühne, “Multiparticle entanglement as an emergent phenomenon,” Phys. Rev. A 93, 020104 (2016).
[Crossref]

T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White, “Linear optical controlled-NOT gate in the coincidence basis,” Phys. Rev. A 65, 062324 (2002).
[Crossref]

G. Tóth, “Entanglement witnesses in spin models,” Phys. Rev. A 71, 010301(R) (2005).
[Crossref]

M. Mičuda, M. Miková, I. Straka, M. Sedlák, M. Dušek, M. Ježek, and J. Fiurášek, “Tomographic characterization of a linear optical quantum Toffoli gate,” Phys. Rev. A 92, 032312 (2015).
[Crossref]

M. Ježek, J. Fiurášek, and Z. Hradil, “Quantum inference of states and processes,” Phys. Rev. A 68, 012305 (2003).
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M. Paraschiv, N. Miklin, T. Moroder, and O. Gühne, “Proving genuine multiparticle entanglement from separable nearest-neighbor marginals,” Phys. Rev. A 98, 062102 (2018).
[Crossref]

Phys. Rev. Lett. (9)

C. Schwemmer, L. Knips, D. Richart, H. Weinfurter, T. Moroder, M. Kleinmann, and O. Gühne, “Systematic errors in current quantum state tomography tools,” Phys. Rev. Lett. 114, 080403 (2015).
[Crossref]

R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. 86, 5188–5191 (2001).
[Crossref]

G. Tóth, C. Knapp, O. Gühne, and H.-J. Briegel, “Optimal spin squeezing inequalities detect bound entanglement in spin models,” Phys. Rev. Lett. 99, 250405 (2007).
[Crossref]

N. K. Langford, T. J. Weinhold, R. Prevedel, K. J. Resch, 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]

N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505(2005).
[Crossref]

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Demonstration of an optical quantum controlled-NOT gate without path interference,” Phys. Rev. Lett. 95, 210506 (2005).
[Crossref]

M. Mičuda, M. Sedlák, I. Straka, M. Miková, M. Dušek, M. Ježek, and J. Fiurášek, “Efficient experimental estimation of fidelity of linear optical quantum Toffoli gate,” Phys. Rev. Lett. 111, 160407 (2013).
[Crossref]

A. Peres, “Separability criterion for density matrices,” Phys. Rev. Lett. 77, 1413–1415 (1996).
[Crossref]

B. Jungnitsch, T. Moroder, and O. Gühne, “Taming multiparticle entanglement,” Phys. Rev. Lett. 106, 190502 (2011).
[Crossref]

Rev. Mod. Phys. (1)

L. Amico, R. Fazio, A. Osterloh, and V. Vedral, “Entanglement in many-body systems,” Rev. Mod. Phys. 80, 517–576 (2008).
[Crossref]

Science (2)

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306, 1330–1336 (2004).
[Crossref]

P. W. Anderson, “More is different,” Science 177, 393–396 (1972).
[Crossref]

SIAM Rev. (1)

L. Vandenberghe and S. Boyd, “Semidefinite programming,” SIAM Rev. 38, 49–95 (1996).
[Crossref]

Other (5)

J. Löfberg, “YALMIP: a toolbox for modeling and optimization in MATLAB,” in Proceedings of the CACSD Conference (2004).

MOSEK ApS, “MOSEK optimization toolbox for MATLAB manual 8.1.0.80,” 2017, http://docs.mosek.com/8.1/toolbox/index.html .

https://www.mathworks.com/matlabcentral/fileexchange/30968-pptmixer-a-tool-to-detect-genuine-multipartite-entanglement .

D. M. Greenberger, M. Horne, and A. Zeilinger, Bell’s Theorem, Quantum Theory, and Conceptions of the Universe, M. Kafatos, ed. (Kluwer, 1989), p. 69.

M. Paris and J. Řeháček, Quantum State Estimation, Vol. 649 of Lecture Notes in Physics (Springer, 2004).

Supplementary Material (1)

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Figures (2)

Fig. 1.
Fig. 1. Symbolic circuit diagram and experimental scheme of photonic circuit producing three-qubit quantum state ρp, Eq. (7). Red line denotes photon’s path. HWP, half-wave plate (the ring variant is used in cnot and swap blocks); QWP, quarter-wave plate; BD, calcite beam displacer; PPBS partially polarizing beam splitter; PBS, polarizing beam splitter; SPAD, collimator and single-mode optical fiber connected to single-photon avalanche photodiode. See text for details.
Fig. 2.
Fig. 2. Dependence of the theoretical lowest eigenvalue min[eig(ρp,BCTB)] (dashed blue line), the experimental lowest eigenvalue min{eig[(ρp,BCexp)TB]} (blue squares), the theoretical mean value Tr(ρpW) (dashed red line) for state (7) and the experimental mean value Tr(ρpexpW) (red squares) for the experimental state ρpexp as a function of the mixing parameter p. See text for details.

Tables (1)

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Table 1. Minimal Eigenvalue βexp(jk):=min{eig[(ρ0.868,jkexp)Tj]} with One Standard Deviation of the Partial Transpose with Respect to Qubit j of the Reduced Density Matrix ρ0.868,jkexp of Qubits j and k

Equations (11)

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ρABCbisep=p1ρA|BCsep+p2ρB|ACsep+p3ρC|ABsep,
ρ=23|ξξ|+13|W¯W¯|,
|ξ=13|W+23|111,
|W=13(eiπ3|001+eiπ3|010|100),
|W¯=13(|011+|101+|110).
minimizeW,PM,QMTr(ρW)subjecttoTr(W)=1,whereW=i,j=03wij(AB)σi(A)σj(B)1(C)+permutations,and for all bipartitionsM|M¯,W=PM+QMTM,PM0,QM0.
ρp=pρ+(1p)81,0p1,
[23|11AC+132(eiπ3+6eiπ3)|00AC+12(ei2π36)|01AC]|0B,
UC=12(1eiπ3eiπ31).
F=Tr[(ρ1/2ρexpρ1/2)1/2]2,
13(|01AC+2|1A|+C)|0B