Abstract

Hyper-encoding enables storing several qubits in a single photon using its different degrees of freedom like polarization and spatial ones. This approach enables feasible implementation of multi-qubit operations. One of the basic manipulations of two or more qubits is to swap their quantum state. Here we report on feasible and stable experimental implementation of a deterministic single photon two-qubit SWAP gate that interchanges path and polarization qubits. We discuss the principle of its operation and give detailed information about experimental demonstration employing two Mach-Zehnder interferometers with one common arm. The gate characterization is done by full quantum process tomography using photons produced by heralded single-photon source. The achieved quantum process fidelity reached more than 0.94 with an effective phase uncertainty of the whole setup, evaluated by means of Allan deviation, below 2.5 deg for 2.5 h without any active stabilization. Our design provides a contribution to the hyper-encoded linear quantum optics toolbox.

© 2018 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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2017 (2)

T. Ono, R. Okamoto, M. Tanida, H. F. Hofmann, and S. Takeuchi, “Implementation of a quantum controlled-SWAP gate with photonic circuits,” Sci. Rep. 7, 45353 (2017).
[Crossref] [PubMed]

K. Wang, G. C. Knee, X. Zhan, Z. Bian, J. Li, and P. Xue, “Optimal experimental demonstration of error-tolerant quantum witnesses,” Phys. Rev. A 95, 032122 (2017).
[Crossref]

2016 (3)

R. Stárek, M. Mičuda, I. Straka, M. Miková, M. Ježek, R. Filip, and J. Fiurašek, “Control and enhancement of interferometric coupling between two photonic qubits,” Phys. Rev. A 93, 042321 (2016).
[Crossref]

R. Stárek, M. Mičuda, M. Miková, I. Straka, M. Dušek, M. Ježek, and J. Fiurášek, “Experimental investigation of a four-qubit linear-optical quantum logic circuit,” Sci. Rep. 6, 33475 (2016).
[Crossref] [PubMed]

R. Patel, J. Ho, F. Ferreyrol, T. C. Ralph, and G. J. Pryde, “A quantum Fredkin gate,” Sci. Adv. 2 (3), e1501531 (2016).
[Crossref] [PubMed]

2015 (2)

T. M. Graham, H. J. Bernstein, T.-C. Wei, M. Junge, and P. G. Kwiat, “Superdense teleportation using hyperentangled photons,” Nat. Commun. 6, 7185 (2015).
[Crossref] [PubMed]

Y.-y. Zhao, N.-k. Yu, P. Kurzyński, G.-y. Xiang, C.-F. Li, and G.-C. Guo, “Experimental realization of generalized qubit measurements based on quantum walks,” Phys. Rev. A 91, 042101 (2015).
[Crossref]

2014 (3)

S. K. Goyal, P. E. Boukama-Dzoussi, S. Ghosh, F. S. Roux, and T. Konrad, “Qudit-teleportation for photons with linear optics”, Sci. Rep. 4, 4543 (2014).
[Crossref] [PubMed]

S. Barz, I. Kassal, M. Ringbauer, Y. O. Lipp, B.- Dakič, A. Aspuru-Guzik, and P. Walther, “A two-qubit photonic quantum processor and its application to solving systems of linear equations,” Sci. Rep. 4, 6115 (2014).
[Crossref] [PubMed]

G. Corrielli, A. Crespi, R. Geremia, R. Ramponi, L. Sansoni, A. Santinelli, P. Mataloni, F. Sciarrino, and R. Osellame, “Rotated waveplates in integrated waveguide optics,” Nat. Commun. 5, 4249 (2014).
[Crossref] [PubMed]

2013 (5)

C. Vitelli, N. Spagnolo, L. Aparo, F. Sciarrino, E. Santamato, and L. Marrucci, “Joining the quantum state of two photon into one,” Nat. Photonics 7, 521–526 (2013).
[Crossref]

S. K. Goyal and T. Konrad, “Teleporting photonic qudits using multimode quantum scissors”, Sci. Rep. 3, 3548 (2013).
[Crossref] [PubMed]

M.-Z. Zhu and L. Ye, “Implementation of SWAP gate and Fredkin gate using linear optical elements,” Int. J. Quantum Inf. 11, 1350031 (2013).
[Crossref]

J. C. Garcia-Escartin and P. Chamorro-Posada, “A SWAP gate for qudits,” Quantum Inf. Process. 12, 3625–3631 (2013).
[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]

2012 (3)

A. Aspuru-Guzik and P. Walther, “Photonic quantum simulators,” Nat. Phys. 8, 285–291 (2012).
[Crossref]

E. Martín-López, A. Laing, T. Lawson, R. Alvarez, X.-Q. Zhou, and J. L. O’Brien, “Experimental realization of Shor’s quantum factoring algorithm using qubit recycling,” Nat. Photonics 6, 773–776 (2012).
[Crossref]

D. Bonneau, M. Lobino, P. Jiang, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, M. G. Thompson, and J. L. O’Brien, “Fast path and polarization manipulation of telecom wavelength single photons in lithium niobate waveguide devices,” Phys. Rev. Lett. 107, 053601 (2012).
[Crossref]

2011 (5)

W.-A. Li, “Quantum SWAP gate with atomic ensembles in two distant cavities,” Opt. Commun. 284, 685–690 (2011).
[Crossref]

A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits,” Nat. Commun. 2, 566 (2011).
[Crossref] [PubMed]

H. W. Li, S. Przeslak, A. O. Niskanen, J. C. F. Matthews, A. Politi, P. Shadbolt, A. Laing, M. Lobino, M. G. Thompson, and J. L. O’Brien, “Reconfigurable controlled two-qubit operation on a quantum photonic chip,” New J. Phys. 13, 115009 (2011).
[Crossref]

M. Ježek, I. Straka, M. Mičuda, M. Dušek, J. Fiurášek, and R. Filip, “Experimental test of the quantum non-gaussian character of a heralded single-photon state,” Phys. Rev. Lett. 107, 213602 (2011).
[Crossref]

X.-Q. Zhou, T. C. Ralph, P. Kalasuwan, M. Zhang, A. Peruzzo, B. P. Lanyon, and J. L. O’Brien, “Adding control to arbitrary unknown quantum operations,” Nat. Commun. 2, 413 (2011).
[Crossref] [PubMed]

2010 (2)

H.-F. Wang, X.-Q. Shao, Y.-F. Zhao, S. Zhang, and K.-H. Yeon, “Linear optical implementation of an ancilla-free quantum SWAP gate,” Phys. Scripta 81, 015011 (2010).
[Crossref]

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] [PubMed]

2009 (2)

A. Politi, J. C. F. Matthews, and J. L. O’Brien, “Shor’s quantum factoring algorithm on a photonic chip,” Science 325 (5945), 1221 (2009).
[Crossref] [PubMed]

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]

2007 (3)

B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barberi, D. F. V. James, A. Gilchrist, and A. G. White, “Experimental demonstration of a compiled version of Shor’s algorithm with quantum entanglement,” Phys. Rev. Lett. 99, 250505 (2007).
[Crossref]

C. Y. Lu, D. E. Brown, T. Yang, and J.-W. Pan, “Demonstration of a compiled version of Shor’s quantum factoring algorithm using photonic qubits,” Phys. Rev. Lett. 99, 250504 (2007).
[Crossref]

J. L. O’Brien, “Optical Quantum Computing,” Science 318 (5856), 1567–1570 (2007).
[Crossref]

2006 (2)

J. H. Shapiro and F. N. C. Wong, “Attacking quantum key distribution with single-photon two-qubit quantum logic,” Phys. Rev. A 73, 012315 (2006).
[Crossref]

L. Bartůšková, A. Černoch, R. Filip, J. Fiurášek, J. Soubusta, and M. Dušek, “Optical implementation of the encoding of two qubits to a single qutrit,” Phys. Rev. A 76, 022325 (2006).
[Crossref]

2005 (5)

L.-m. Liang and C.-z. Li, “Realization of quantum SWAP gate between flying and stationary qubits,” Phys. Rev. A 72, 024303 (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] [PubMed]

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] [PubMed]

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210506 (2005).
[Crossref]

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Demonstration of quantum error correction using linear optics,” Phys. Rev. A 71, 052332 (2005).
[Crossref]

2004 (2)

M. Fiorentino and F. N. C. Wong, “Deterministic controlled-not gate for single-photon two-qubit quantum logic,” Phys. Rev. Lett. 93, 070502 (2004).
[Crossref] [PubMed]

A. G. Fowler, S. J. Devitt, and L. C. L. Hollenberg, “Implementation of Shor’s algorithm on a linear nearest neighbour qubit array,” Quantum Inf. Comput. 4, 237–251 (2004).

2003 (2)

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]

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

2001 (1)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref] [PubMed]

1998 (1)

P. G. Kwiat and H. Weinfurter, “Embedded Bell-state analysis,” Phys. Rev. A 58, R2623–R2626 (1998).
[Crossref]

1994 (1)

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
[Crossref] [PubMed]

1975 (1)

M.-D. Choi, “Completely positive linear maps on complex matrices,” Linear Algebra Appl. 10, 285–290 (1975).
[Crossref]

1974 (1)

A. Jamiołkowski, “An effective method of investigation of positive maps on the set of positive definite operators,” Rep. Math. Phys. 5, 415–424 (1974).
[Crossref]

1970 (1)

D. C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
[Crossref]

1966 (1)

D. W. Allan, “Statistics of atomic frequency standards,” Proc. IEEE 54 (2), 221–230 (1966).
[Crossref]

Allan, D. W.

D. W. Allan, “Statistics of atomic frequency standards,” Proc. IEEE 54 (2), 221–230 (1966).
[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] [PubMed]

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]

Alvarez, R.

E. Martín-López, A. Laing, T. Lawson, R. Alvarez, X.-Q. Zhou, and J. L. O’Brien, “Experimental realization of Shor’s quantum factoring algorithm using qubit recycling,” Nat. Photonics 6, 773–776 (2012).
[Crossref]

Aparo, L.

C. Vitelli, N. Spagnolo, L. Aparo, F. Sciarrino, E. Santamato, and L. Marrucci, “Joining the quantum state of two photon into one,” Nat. Photonics 7, 521–526 (2013).
[Crossref]

Aspuru-Guzik, A.

S. Barz, I. Kassal, M. Ringbauer, Y. O. Lipp, B.- Dakič, A. Aspuru-Guzik, and P. Walther, “A two-qubit photonic quantum processor and its application to solving systems of linear equations,” Sci. Rep. 4, 6115 (2014).
[Crossref] [PubMed]

A. Aspuru-Guzik and P. Walther, “Photonic quantum simulators,” Nat. Phys. 8, 285–291 (2012).
[Crossref]

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M. Ježek, I. Straka, M. Mičuda, M. Dušek, J. Fiurášek, and R. Filip, “Experimental test of the quantum non-gaussian character of a heralded single-photon state,” Phys. Rev. Lett. 107, 213602 (2011).
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L. Bartůšková, A. Černoch, R. Filip, J. Fiurášek, J. Soubusta, and M. Dušek, “Optical implementation of the encoding of two qubits to a single qutrit,” Phys. Rev. A 76, 022325 (2006).
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R. Stárek, M. Mičuda, M. Miková, I. Straka, M. Dušek, P. Marek, M. Ježek, and J. Fiurášek, “Experimental characterization of the photonic quantum Fredkin gate,” 2017 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC), Munich, Germany, 25–29 June 2017.

R. Stárek, M. Mičuda, M. Miková, I. Straka, M. Dušek, P. Marek, M. Ježek, R. Filip, and J. Fiurášek, Department of Optics, Palacký University, 17. listopadu 12, Olomouc, are preparing manuscript to be called “Nondestructive detector for exchange-symmetry of photonic qubits”.

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L. Bartůšková, A. Černoch, R. Filip, J. Fiurášek, J. Soubusta, and M. Dušek, “Optical implementation of the encoding of two qubits to a single qutrit,” Phys. Rev. A 76, 022325 (2006).
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R. Stárek, M. Mičuda, M. Miková, I. Straka, M. Dušek, P. Marek, M. Ježek, R. Filip, and J. Fiurášek, Department of Optics, Palacký University, 17. listopadu 12, Olomouc, are preparing manuscript to be called “Nondestructive detector for exchange-symmetry of photonic qubits”.

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L. Bartůšková, A. Černoch, R. Filip, J. Fiurášek, J. Soubusta, and M. Dušek, “Optical implementation of the encoding of two qubits to a single qutrit,” Phys. Rev. A 76, 022325 (2006).
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R. Stárek, M. Mičuda, M. Miková, I. Straka, M. Dušek, P. Marek, M. Ježek, R. Filip, and J. Fiurášek, Department of Optics, Palacký University, 17. listopadu 12, Olomouc, are preparing manuscript to be called “Nondestructive detector for exchange-symmetry of photonic qubits”.

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Z. Hradil, J. Řeháček, J. Fiurášek, and M. Ježek, “Maximum-likelihood methods in quantum mechanics,” in Quantum State Estimation, Lect. Notes Phys. 649, M. G. A. Paris and J. Řeháček, eds. (Springer, 2004)
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R. Stárek, M. Mičuda, M. Miková, I. Straka, M. Dušek, P. Marek, M. Ježek, R. Filip, and J. Fiurášek, Department of Optics, Palacký University, 17. listopadu 12, Olomouc, are preparing manuscript to be called “Nondestructive detector for exchange-symmetry of photonic qubits”.

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X.-Q. Zhou, T. C. Ralph, P. Kalasuwan, M. Zhang, A. Peruzzo, B. P. Lanyon, and J. L. O’Brien, “Adding control to arbitrary unknown quantum operations,” Nat. Commun. 2, 413 (2011).
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B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barberi, D. F. V. James, A. Gilchrist, and A. G. White, “Experimental demonstration of a compiled version of Shor’s algorithm with quantum entanglement,” Phys. Rev. Lett. 99, 250505 (2007).
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H. W. Li, S. Przeslak, A. O. Niskanen, J. C. F. Matthews, A. Politi, P. Shadbolt, A. Laing, M. Lobino, M. G. Thompson, and J. L. O’Brien, “Reconfigurable controlled two-qubit operation on a quantum photonic chip,” New J. Phys. 13, 115009 (2011).
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R. Stárek, M. Mičuda, M. Miková, I. Straka, M. Dušek, P. Marek, M. Ježek, and J. Fiurášek, “Experimental characterization of the photonic quantum Fredkin gate,” 2017 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC), Munich, Germany, 25–29 June 2017.

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R. Stárek, M. Mičuda, M. Miková, I. Straka, M. Dušek, P. Marek, M. Ježek, R. Filip, and J. Fiurášek, Department of Optics, Palacký University, 17. listopadu 12, Olomouc, are preparing manuscript to be called “Nondestructive detector for exchange-symmetry of photonic qubits”.

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R. Stárek, M. Mičuda, M. Miková, I. Straka, M. Dušek, P. Marek, M. Ježek, and J. Fiurášek, “Experimental characterization of the photonic quantum Fredkin gate,” 2017 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC), Munich, Germany, 25–29 June 2017.

R. Stárek, M. Mičuda, M. Miková, I. Straka, M. Dušek, P. Marek, M. Ježek, R. Filip, and J. Fiurášek, Department of Optics, Palacký University, 17. listopadu 12, Olomouc, are preparing manuscript to be called “Nondestructive detector for exchange-symmetry of photonic qubits”.

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J. H. Shapiro and F. N. C. Wong, “Attacking quantum key distribution with single-photon two-qubit quantum logic,” Phys. Rev. A 73, 012315 (2006).
[Crossref]

Soubusta, J.

L. Bartůšková, A. Černoch, R. Filip, J. Fiurášek, J. Soubusta, and M. Dušek, “Optical implementation of the encoding of two qubits to a single qutrit,” Phys. Rev. A 76, 022325 (2006).
[Crossref]

Spagnolo, N.

C. Vitelli, N. Spagnolo, L. Aparo, F. Sciarrino, E. Santamato, and L. Marrucci, “Joining the quantum state of two photon into one,” Nat. Photonics 7, 521–526 (2013).
[Crossref]

Stárek, R.

R. Stárek, M. Mičuda, I. Straka, M. Miková, M. Ježek, R. Filip, and J. Fiurašek, “Control and enhancement of interferometric coupling between two photonic qubits,” Phys. Rev. A 93, 042321 (2016).
[Crossref]

R. Stárek, M. Mičuda, M. Miková, I. Straka, M. Dušek, M. Ježek, and J. Fiurášek, “Experimental investigation of a four-qubit linear-optical quantum logic circuit,” Sci. Rep. 6, 33475 (2016).
[Crossref] [PubMed]

R. Stárek, M. Mičuda, M. Miková, I. Straka, M. Dušek, P. Marek, M. Ježek, R. Filip, and J. Fiurášek, Department of Optics, Palacký University, 17. listopadu 12, Olomouc, are preparing manuscript to be called “Nondestructive detector for exchange-symmetry of photonic qubits”.

R. Stárek, M. Mičuda, M. Miková, I. Straka, M. Dušek, P. Marek, M. Ježek, and J. Fiurášek, “Experimental characterization of the photonic quantum Fredkin gate,” 2017 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC), Munich, Germany, 25–29 June 2017.

Straka, I.

R. Stárek, M. Mičuda, M. Miková, I. Straka, M. Dušek, M. Ježek, and J. Fiurášek, “Experimental investigation of a four-qubit linear-optical quantum logic circuit,” Sci. Rep. 6, 33475 (2016).
[Crossref] [PubMed]

R. Stárek, M. Mičuda, I. Straka, M. Miková, M. Ježek, R. Filip, and J. Fiurašek, “Control and enhancement of interferometric coupling between two photonic qubits,” Phys. Rev. A 93, 042321 (2016).
[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, I. Straka, M. Mičuda, M. Dušek, J. Fiurášek, and R. Filip, “Experimental test of the quantum non-gaussian character of a heralded single-photon state,” Phys. Rev. Lett. 107, 213602 (2011).
[Crossref]

R. Stárek, M. Mičuda, M. Miková, I. Straka, M. Dušek, P. Marek, M. Ježek, and J. Fiurášek, “Experimental characterization of the photonic quantum Fredkin gate,” 2017 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC), Munich, Germany, 25–29 June 2017.

R. Stárek, M. Mičuda, M. Miková, I. Straka, M. Dušek, P. Marek, M. Ježek, R. Filip, and J. Fiurášek, Department of Optics, Palacký University, 17. listopadu 12, Olomouc, are preparing manuscript to be called “Nondestructive detector for exchange-symmetry of photonic qubits”.

Takeuchi, S.

T. Ono, R. Okamoto, M. Tanida, H. F. Hofmann, and S. Takeuchi, “Implementation of a quantum controlled-SWAP gate with photonic circuits,” Sci. Rep. 7, 45353 (2017).
[Crossref] [PubMed]

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210506 (2005).
[Crossref]

Tanida, M.

T. Ono, R. Okamoto, M. Tanida, H. F. Hofmann, and S. Takeuchi, “Implementation of a quantum controlled-SWAP gate with photonic circuits,” Sci. Rep. 7, 45353 (2017).
[Crossref] [PubMed]

Tanner, M. G.

D. Bonneau, M. Lobino, P. Jiang, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, M. G. Thompson, and J. L. O’Brien, “Fast path and polarization manipulation of telecom wavelength single photons in lithium niobate waveguide devices,” Phys. Rev. Lett. 107, 053601 (2012).
[Crossref]

Thompson, M. G.

D. Bonneau, M. Lobino, P. Jiang, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, M. G. Thompson, and J. L. O’Brien, “Fast path and polarization manipulation of telecom wavelength single photons in lithium niobate waveguide devices,” Phys. Rev. Lett. 107, 053601 (2012).
[Crossref]

H. W. Li, S. Przeslak, A. O. Niskanen, J. C. F. Matthews, A. Politi, P. Shadbolt, A. Laing, M. Lobino, M. G. Thompson, and J. L. O’Brien, “Reconfigurable controlled two-qubit operation on a quantum photonic chip,” New J. Phys. 13, 115009 (2011).
[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] [PubMed]

Vallone, G.

A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits,” Nat. Commun. 2, 566 (2011).
[Crossref] [PubMed]

Vitelli, C.

C. Vitelli, N. Spagnolo, L. Aparo, F. Sciarrino, E. Santamato, and L. Marrucci, “Joining the quantum state of two photon into one,” Nat. Photonics 7, 521–526 (2013).
[Crossref]

Walther, P.

S. Barz, I. Kassal, M. Ringbauer, Y. O. Lipp, B.- Dakič, A. Aspuru-Guzik, and P. Walther, “A two-qubit photonic quantum processor and its application to solving systems of linear equations,” Sci. Rep. 4, 6115 (2014).
[Crossref] [PubMed]

A. Aspuru-Guzik and P. Walther, “Photonic quantum simulators,” Nat. Phys. 8, 285–291 (2012).
[Crossref]

Wang, H.-F.

H.-F. Wang, X.-Q. Shao, Y.-F. Zhao, S. Zhang, and K.-H. Yeon, “Linear optical implementation of an ancilla-free quantum SWAP gate,” Phys. Scripta 81, 015011 (2010).
[Crossref]

Wang, K.

K. Wang, G. C. Knee, X. Zhan, Z. Bian, J. Li, and P. Xue, “Optimal experimental demonstration of error-tolerant quantum witnesses,” Phys. Rev. A 95, 032122 (2017).
[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] [PubMed]

Wei, T.-C.

T. M. Graham, H. J. Bernstein, T.-C. Wei, M. Junge, and P. G. Kwiat, “Superdense teleportation using hyperentangled photons,” Nat. Commun. 6, 7185 (2015).
[Crossref] [PubMed]

Weinberg, D. L.

D. C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
[Crossref]

Weinfurter, H.

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] [PubMed]

P. G. Kwiat and H. Weinfurter, “Embedded Bell-state analysis,” Phys. Rev. A 58, R2623–R2626 (1998).
[Crossref]

Weinhold, T. J.

B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barberi, D. F. V. James, A. Gilchrist, and A. G. White, “Experimental demonstration of a compiled version of Shor’s algorithm with quantum entanglement,” Phys. Rev. Lett. 99, 250505 (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] [PubMed]

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] [PubMed]

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]

B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barberi, D. F. V. James, A. Gilchrist, and A. G. White, “Experimental demonstration of a compiled version of Shor’s algorithm with quantum entanglement,” Phys. Rev. Lett. 99, 250505 (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] [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]

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] [PubMed]

Wong, F. N. C.

J. H. Shapiro and F. N. C. Wong, “Attacking quantum key distribution with single-photon two-qubit quantum logic,” Phys. Rev. A 73, 012315 (2006).
[Crossref]

M. Fiorentino and F. N. C. Wong, “Deterministic controlled-not gate for single-photon two-qubit quantum logic,” Phys. Rev. Lett. 93, 070502 (2004).
[Crossref] [PubMed]

Xiang, G.-y.

Y.-y. Zhao, N.-k. Yu, P. Kurzyński, G.-y. Xiang, C.-F. Li, and G.-C. Guo, “Experimental realization of generalized qubit measurements based on quantum walks,” Phys. Rev. A 91, 042101 (2015).
[Crossref]

Xue, P.

K. Wang, G. C. Knee, X. Zhan, Z. Bian, J. Li, and P. Xue, “Optimal experimental demonstration of error-tolerant quantum witnesses,” Phys. Rev. A 95, 032122 (2017).
[Crossref]

Yang, T.

C. Y. Lu, D. E. Brown, T. Yang, and J.-W. Pan, “Demonstration of a compiled version of Shor’s quantum factoring algorithm using photonic qubits,” Phys. Rev. Lett. 99, 250504 (2007).
[Crossref]

Ye, L.

M.-Z. Zhu and L. Ye, “Implementation of SWAP gate and Fredkin gate using linear optical elements,” Int. J. Quantum Inf. 11, 1350031 (2013).
[Crossref]

Yeon, K.-H.

H.-F. Wang, X.-Q. Shao, Y.-F. Zhao, S. Zhang, and K.-H. Yeon, “Linear optical implementation of an ancilla-free quantum SWAP gate,” Phys. Scripta 81, 015011 (2010).
[Crossref]

Yu, N.-k.

Y.-y. Zhao, N.-k. Yu, P. Kurzyński, G.-y. Xiang, C.-F. Li, and G.-C. Guo, “Experimental realization of generalized qubit measurements based on quantum walks,” Phys. Rev. A 91, 042101 (2015).
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Zeilinger, A.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
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Zhan, X.

K. Wang, G. C. Knee, X. Zhan, Z. Bian, J. Li, and P. Xue, “Optimal experimental demonstration of error-tolerant quantum witnesses,” Phys. Rev. A 95, 032122 (2017).
[Crossref]

Zhang, M.

X.-Q. Zhou, T. C. Ralph, P. Kalasuwan, M. Zhang, A. Peruzzo, B. P. Lanyon, and J. L. O’Brien, “Adding control to arbitrary unknown quantum operations,” Nat. Commun. 2, 413 (2011).
[Crossref] [PubMed]

Zhang, S.

H.-F. Wang, X.-Q. Shao, Y.-F. Zhao, S. Zhang, and K.-H. Yeon, “Linear optical implementation of an ancilla-free quantum SWAP gate,” Phys. Scripta 81, 015011 (2010).
[Crossref]

Zhao, Y.-F.

H.-F. Wang, X.-Q. Shao, Y.-F. Zhao, S. Zhang, and K.-H. Yeon, “Linear optical implementation of an ancilla-free quantum SWAP gate,” Phys. Scripta 81, 015011 (2010).
[Crossref]

Zhao, Y.-y.

Y.-y. Zhao, N.-k. Yu, P. Kurzyński, G.-y. Xiang, C.-F. Li, and G.-C. Guo, “Experimental realization of generalized qubit measurements based on quantum walks,” Phys. Rev. A 91, 042101 (2015).
[Crossref]

Zhou, X.-Q.

E. Martín-López, A. Laing, T. Lawson, R. Alvarez, X.-Q. Zhou, and J. L. O’Brien, “Experimental realization of Shor’s quantum factoring algorithm using qubit recycling,” Nat. Photonics 6, 773–776 (2012).
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X.-Q. Zhou, T. C. Ralph, P. Kalasuwan, M. Zhang, A. Peruzzo, B. P. Lanyon, and J. L. O’Brien, “Adding control to arbitrary unknown quantum operations,” Nat. Commun. 2, 413 (2011).
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Zhu, M.-Z.

M.-Z. Zhu and L. Ye, “Implementation of SWAP gate and Fredkin gate using linear optical elements,” Int. J. Quantum Inf. 11, 1350031 (2013).
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D. Bonneau, M. Lobino, P. Jiang, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, M. G. Thompson, and J. L. O’Brien, “Fast path and polarization manipulation of telecom wavelength single photons in lithium niobate waveguide devices,” Phys. Rev. Lett. 107, 053601 (2012).
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Int. J. Quantum Inf. (1)

M.-Z. Zhu and L. Ye, “Implementation of SWAP gate and Fredkin gate using linear optical elements,” Int. J. Quantum Inf. 11, 1350031 (2013).
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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).
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Nat. Commun. (4)

T. M. Graham, H. J. Bernstein, T.-C. Wei, M. Junge, and P. G. Kwiat, “Superdense teleportation using hyperentangled photons,” Nat. Commun. 6, 7185 (2015).
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X.-Q. Zhou, T. C. Ralph, P. Kalasuwan, M. Zhang, A. Peruzzo, B. P. Lanyon, and J. L. O’Brien, “Adding control to arbitrary unknown quantum operations,” Nat. Commun. 2, 413 (2011).
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A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits,” Nat. Commun. 2, 566 (2011).
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C. Vitelli, N. Spagnolo, L. Aparo, F. Sciarrino, E. Santamato, and L. Marrucci, “Joining the quantum state of two photon into one,” Nat. Photonics 7, 521–526 (2013).
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E. Martín-López, A. Laing, T. Lawson, R. Alvarez, X.-Q. Zhou, and J. L. O’Brien, “Experimental realization of Shor’s quantum factoring algorithm using qubit recycling,” Nat. Photonics 6, 773–776 (2012).
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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).
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A. Aspuru-Guzik and P. Walther, “Photonic quantum simulators,” Nat. Phys. 8, 285–291 (2012).
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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).
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New J. Phys. (1)

H. W. Li, S. Przeslak, A. O. Niskanen, J. C. F. Matthews, A. Politi, P. Shadbolt, A. Laing, M. Lobino, M. G. Thompson, and J. L. O’Brien, “Reconfigurable controlled two-qubit operation on a quantum photonic chip,” New J. Phys. 13, 115009 (2011).
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J. H. Shapiro and F. N. C. Wong, “Attacking quantum key distribution with single-photon two-qubit quantum logic,” Phys. Rev. A 73, 012315 (2006).
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Y.-y. Zhao, N.-k. Yu, P. Kurzyński, G.-y. Xiang, C.-F. Li, and G.-C. Guo, “Experimental realization of generalized qubit measurements based on quantum walks,” Phys. Rev. A 91, 042101 (2015).
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K. Wang, G. C. Knee, X. Zhan, Z. Bian, J. Li, and P. Xue, “Optimal experimental demonstration of error-tolerant quantum witnesses,” Phys. Rev. A 95, 032122 (2017).
[Crossref]

R. Stárek, M. Mičuda, I. Straka, M. Miková, M. Ježek, R. Filip, and J. Fiurašek, “Control and enhancement of interferometric coupling between two photonic qubits,” Phys. Rev. A 93, 042321 (2016).
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[Crossref]

Phys. Rev. Lett. (11)

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
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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]

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] [PubMed]

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).
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R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210506 (2005).
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B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barberi, D. F. V. James, A. Gilchrist, and A. G. White, “Experimental demonstration of a compiled version of Shor’s algorithm with quantum entanglement,” Phys. Rev. Lett. 99, 250505 (2007).
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C. Y. Lu, D. E. Brown, T. Yang, and J.-W. Pan, “Demonstration of a compiled version of Shor’s quantum factoring algorithm using photonic qubits,” Phys. Rev. Lett. 99, 250504 (2007).
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M. Ježek, I. Straka, M. Mičuda, M. Dušek, J. Fiurášek, and R. Filip, “Experimental test of the quantum non-gaussian character of a heralded single-photon state,” Phys. Rev. Lett. 107, 213602 (2011).
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D. Bonneau, M. Lobino, P. Jiang, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, M. G. Thompson, and J. L. O’Brien, “Fast path and polarization manipulation of telecom wavelength single photons in lithium niobate waveguide devices,” Phys. Rev. Lett. 107, 053601 (2012).
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M. Fiorentino and F. N. C. Wong, “Deterministic controlled-not gate for single-photon two-qubit quantum logic,” Phys. Rev. Lett. 93, 070502 (2004).
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H.-F. Wang, X.-Q. Shao, Y.-F. Zhao, S. Zhang, and K.-H. Yeon, “Linear optical implementation of an ancilla-free quantum SWAP gate,” Phys. Scripta 81, 015011 (2010).
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T. Ono, R. Okamoto, M. Tanida, H. F. Hofmann, and S. Takeuchi, “Implementation of a quantum controlled-SWAP gate with photonic circuits,” Sci. Rep. 7, 45353 (2017).
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[Crossref] [PubMed]

Other (4)

R. Stárek, M. Mičuda, M. Miková, I. Straka, M. Dušek, P. Marek, M. Ježek, and J. Fiurášek, “Experimental characterization of the photonic quantum Fredkin gate,” 2017 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC), Munich, Germany, 25–29 June 2017.

R. Stárek, M. Mičuda, M. Miková, I. Straka, M. Dušek, P. Marek, M. Ježek, R. Filip, and J. Fiurášek, Department of Optics, Palacký University, 17. listopadu 12, Olomouc, are preparing manuscript to be called “Nondestructive detector for exchange-symmetry of photonic qubits”.

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

Z. Hradil, J. Řeháček, J. Fiurášek, and M. Ježek, “Maximum-likelihood methods in quantum mechanics,” in Quantum State Estimation, Lect. Notes Phys. 649, M. G. A. Paris and J. Řeháček, eds. (Springer, 2004)
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 An illustrative scheme depicting the essence of our SWAP gate implementation for two photonic qubits encoded in path and polarization modes of a single photon. The different optical modes are denoted by the different colors and line styles to distinguish them.
Fig. 2
Fig. 2 Experimental setup of the photonic two-qubit SWAP gate based on two coupled MZ interferometers. QWP – quarter-wave plate, HWP – half-wave plate, BD – beam displacer, GP – glass plate, PBS – polarizing beam splitter, APD – avalanche photodiode. See text for more details.
Fig. 3
Fig. 3 The truth table of the realized SWAP gate in the computation basis (|H〉 and the upper interferometer arm form logical 0, |V〉 and the lower interferometer arm form logical 1) estimated from experimental data.
Fig. 4
Fig. 4 Reconstructed process matrices χ of the SWAP gate after phase compensation. The 16 × 16 matrices are written in the polarization and spatial basis of the input and output Hilbert spaces (|H〉 and the upper interferometer arm form logical 0, |V〉 and the lower interferometer arm form logical 1). a) the theoretical process matrix χth, b) the real and c) imaginary part of the reconstructed process matrix χ, respectively. Note that the theoretical process matrix has only real values.
Fig. 5
Fig. 5 Comparison of the phase evolution of single MZ interferometer (red dots) and the whole setup (blue dots). Dashed lines correspond to linear fit used to estimated a slope of the phase evolution. See text for more details.
Fig. 6
Fig. 6 Allan deviation of the measured phase - comparison of a single MZ interferometer (red) and the whole setup stability (blue).

Equations (6)

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U swap = | 00 00 | + | 01 10 | + | 10 01 | + | 11 11 | ,
ρ out = ( ρ in ) = Tr in [ ρ in T 𝟙 out χ ]
| Ψ = j , k = 0 1 | j k | j k ,
χ th = ( 𝟙 U swap ) | Ψ Ψ | ( 𝟙 U swap ) = | Ψ swap Ψ swap | ,
F χ = Tr [ χ χ th ] Tr [ χ ] Tr [ χ th ] ,
σ ( τ ) = 1 2 N n = 1 N 1 ( y ¯ n + 1 y ¯ n ) 2 ,

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