Abstract

Due to the restrictions on quantum measurement imposed by relativistic causality, it is not easy to perform a nonlocal measurement on spacelike separated systems instantaneously. Here we design an experiment in an optical system to perform the nonlocal measurement of a product observable on a two-qubit system, where a maximally-entangled two-qubit state, acting as an ancillary meter, and three identical Kerr media are used to couple the system under consideration and the target meter. It is shown that the nonlocal measurement of the product observable, σzAσzB, which has two degenerate eigenvalues, could be implemented in a deterministic way without violating relativistic causality.

© 2016 Optical Society of America

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References

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2016 (3)

A. Brodutch and E. Cohen, “Nonlocal Measurements via Quantum Erasure,” Phys. Rev. Lett. 116, 070404 (2016).
[Crossref] [PubMed]

K. Joulain, J. Drevillon, Y. Ezzahri, and J. Ordonez-Miranda, “Quantum Thermal Transistor,” Phys. Rev. Lett. 116, 200601 (2016).
[Crossref] [PubMed]

D. J. Brod and J. Combes, “Passive CPHASE Gate via Cross-Kerr Nonlinearities,” Phys. Rev. Lett. 117, 080502 (2016).
[Crossref] [PubMed]

2015 (1)

Y. Q. He, D. Ding, F. L. Yan, and T. Gao, “Exploration of photon-number entangled states using weak nonlinearities,” Opt. Express, 23 (17), 21671–21677 (2015).
[Crossref]

2012 (2)

J. S. Tang, Y. L. Li, X. Y. Xu, G. Y. Xiang, C. F. Li, and G. C. Guo, “Realization of quantum Wheeler’s delayed-choice experiment,” Nat. Photonics 6, 600–604 (2012).
[Crossref]

F. Kaiser, T. Coudreau, P. Milman, D. B. Ostrowsky, and S. Tanzilli, “Entanglement-Enabled Delayed-Choice Experiment,” Science 338, 637–640 (2012).
[Crossref] [PubMed]

2010 (1)

S. R. Clark, A. J. Connor, D. Jaksch, and S. Popescu, “Entanglement consumption of instantaneous nonlocal quantum measurements,” New J. Phys. 12, 083034 (2010).
[Crossref]

2008 (2)

2007 (2)

2006 (1)

G. Lüders, “Concerning the state-change due to the measurement process,” Ann. Phys. (Leipzig) 15, 663–670 (2006).
[Crossref]

2005 (2)

H. Rokhsari and K. J. Vahala, “Observation of Kerr nonlinearity in microcavities at room temperature,” Opt. Lett. 30, 427–429 (2005).
[Crossref] [PubMed]

W. J. Munro, Kae Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[Crossref]

2004 (1)

K. J. Resch and A. M. Steinberg, “Extracting Joint Weak Values with Local, Single-Particle Measurements,” Phys. Rev. Lett. 92, 130402 (2004).
[Crossref] [PubMed]

2003 (2)

H. Kang and Y. F. Zhu, “Observation of Large Kerr Nonlinearity at Low Light Intensities,” Phys. Rev. Lett. 91, 093601 (2003).
[Crossref] [PubMed]

L. Vaidman, “Instantaneous Measurement of Nonlocal Variables,” Phys. Rev. Lett. 90, 010402 (2003).
[Crossref] [PubMed]

2002 (2)

B. Groisman and B. Reznik, “Measurements of semilocal and nonmaximally entangled states,” Phys. Rev. A 66, 022110 (2002).
[Crossref]

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Double-slit quantum eraser,” Phys. Rev. A 65, 033818 (2002).
[Crossref]

2001 (2)

C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, “High-efficiency entangled photon pair collection in type-II parametric fluorescence,” Phys. Rev. A 64, 023802 (2001).
[Crossref]

B. Groisman and L. Vaidman, “Nonlocal variables with product-state eigenstates,” J. Phys. A: Math. Gen. 34(35), 6881–6889 (2001).
[Crossref]

2000 (1)

Y. H. Kim, R. Yu, S. P. Kulik, Y. H. Shih, and M. O. Scully, “Delayed “Choice” Quantum Eraser,” Phys. Rev. Lett. 84, 1–5 (2000).
[Crossref] [PubMed]

1999 (2)

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, “Quantum nonlocality without entanglement,” Phys. Rev. A 59, 1070–1091 (1999).
[Crossref]

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[Crossref]

1997 (1)

T. E. Keller and M. H. Rubin, “Theory of two-photon entanglement for spontaneous parametric down-conversion driven by a narrow pump pulse,” Phys. Rev. A 56, 1534–1541 (1997).
[Crossref]

1996 (1)

1995 (2)

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

T. J. Herzog, P. G. Kwiat, H. Weinfurter, and A. Zeilinger, “Complementarity and the Quantum Eraser,” Phys. Rev. Lett. 75, 3034–3037 (1995).
[Crossref] [PubMed]

1994 (2)

S. Popescu and L. Vaidman, “Causality constraints on nonlocal quantum measurements,” Phys. Rev. A 49, 4331–4338 (1994).
[Crossref] [PubMed]

Y. H. Shih, A. V. Sergienko, Morton H. Rubin, T. E. Kiess, and C. O. Alley, “Two-photon entanglement in type-II parametric down-conversion,” Phys. Rev. A 50, 23–28 (1994).
[Crossref] [PubMed]

1991 (1)

M. O. Scully, B. G. Englert, and H. Walther, “Quantum optical tests of complementarity,” Nature 351, 111–116 (1991).
[Crossref]

1990 (1)

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[Crossref] [PubMed]

1988 (1)

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60, 1351–1354 (1988).
[Crossref] [PubMed]

1986 (2)

R. Ghosh, C. K. Hong, Z. Y. Ou, and L. Mandel, “Interference of two photons in parametric down conversion,” Phys. Rev. A 34, 3962–3968 (1986).
[Crossref]

Y. Aharonov, D. Z. Albert, and L. Vaidman, “Measurement process in relativistic quantum theory,” Phys. Rev. D 34, 1805–1813 (1986).
[Crossref]

1985 (2)

C. K. Hong and L. Mandel, “Theory of parametric frequency down conversion of light,” Phys. Rev. A 31, 2409–2418 (1985).
[Crossref]

N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32, 2287–2292 (1985).
[Crossref]

1982 (1)

M. O. Scully and K. Drühl, “Quantum eraser: A proposed photon correlation experiment concerning observation and “delayed choice” in quantum mechanics,” Phys. Rev. A 25, 2208–2213 (1982).
[Crossref]

1981 (1)

Y. Aharonov and D. Z. Albert, “Can we make sense out of the measurement process in relativistic quantum mechanics,” Phys. Rev. D 24, 359–370 (1981).
[Crossref]

1980 (1)

Y. Aharonov and D. Z. Albert, “States and observables in relativistic quantum field theories,” Phys. Rev. D 21, 3316–3324 (1980).
[Crossref]

1969 (1)

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Phys. Rev. Lett. 23, 880–884 (1969).
[Crossref]

1951 (1)

G. Lüders, “Über die Zustandsänderung durch den Meßprozeß (German),” Ann. Phys. (Leipzig) 8, 322–328 (1951).

1931 (1)

L. Landau and R. Peierls, “Erweiterung des Unbestimmtheitsprinzips für die relativistische Quantentheorie,” Z. Phys. 69, 56–69 (1931).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

Aharonov, Y.

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60, 1351–1354 (1988).
[Crossref] [PubMed]

Y. Aharonov, D. Z. Albert, and L. Vaidman, “Measurement process in relativistic quantum theory,” Phys. Rev. D 34, 1805–1813 (1986).
[Crossref]

Y. Aharonov and D. Z. Albert, “Can we make sense out of the measurement process in relativistic quantum mechanics,” Phys. Rev. D 24, 359–370 (1981).
[Crossref]

Y. Aharonov and D. Z. Albert, “States and observables in relativistic quantum field theories,” Phys. Rev. D 21, 3316–3324 (1980).
[Crossref]

Albert, D. Z.

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60, 1351–1354 (1988).
[Crossref] [PubMed]

Y. Aharonov, D. Z. Albert, and L. Vaidman, “Measurement process in relativistic quantum theory,” Phys. Rev. D 34, 1805–1813 (1986).
[Crossref]

Y. Aharonov and D. Z. Albert, “Can we make sense out of the measurement process in relativistic quantum mechanics,” Phys. Rev. D 24, 359–370 (1981).
[Crossref]

Y. Aharonov and D. Z. Albert, “States and observables in relativistic quantum field theories,” Phys. Rev. D 21, 3316–3324 (1980).
[Crossref]

Alley, C. O.

Y. H. Shih, A. V. Sergienko, Morton H. Rubin, T. E. Kiess, and C. O. Alley, “Two-photon entanglement in type-II parametric down-conversion,” Phys. Rev. A 50, 23–28 (1994).
[Crossref] [PubMed]

Appelbaum, I.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[Crossref]

Battle, P.

Beausoleil, R. G.

M. Fiorentino, S. M. Spillane, R. G. Beausoleil, T. D. Roberts, P. Battle, and M. W. Munro, “Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals,” Opt. Express,  15 (12), 7479–7488 (2007).
[Crossref] [PubMed]

W. J. Munro, Kae Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[Crossref]

Bennett, C. H.

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, “Quantum nonlocality without entanglement,” Phys. Rev. A 59, 1070–1091 (1999).
[Crossref]

Brod, D. J.

D. J. Brod and J. Combes, “Passive CPHASE Gate via Cross-Kerr Nonlinearities,” Phys. Rev. Lett. 117, 080502 (2016).
[Crossref] [PubMed]

Brodutch, A.

A. Brodutch and E. Cohen, “Nonlocal Measurements via Quantum Erasure,” Phys. Rev. Lett. 116, 070404 (2016).
[Crossref] [PubMed]

Clark, S. R.

S. R. Clark, A. J. Connor, D. Jaksch, and S. Popescu, “Entanglement consumption of instantaneous nonlocal quantum measurements,” New J. Phys. 12, 083034 (2010).
[Crossref]

Clauser, J. F.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Phys. Rev. Lett. 23, 880–884 (1969).
[Crossref]

Cohen, E.

A. Brodutch and E. Cohen, “Nonlocal Measurements via Quantum Erasure,” Phys. Rev. Lett. 116, 070404 (2016).
[Crossref] [PubMed]

Combes, J.

D. J. Brod and J. Combes, “Passive CPHASE Gate via Cross-Kerr Nonlinearities,” Phys. Rev. Lett. 117, 080502 (2016).
[Crossref] [PubMed]

Connor, A. J.

S. R. Clark, A. J. Connor, D. Jaksch, and S. Popescu, “Entanglement consumption of instantaneous nonlocal quantum measurements,” New J. Phys. 12, 083034 (2010).
[Crossref]

Coudreau, T.

F. Kaiser, T. Coudreau, P. Milman, D. B. Ostrowsky, and S. Tanzilli, “Entanglement-Enabled Delayed-Choice Experiment,” Science 338, 637–640 (2012).
[Crossref] [PubMed]

Ding, D.

Y. Q. He, D. Ding, F. L. Yan, and T. Gao, “Exploration of photon-number entangled states using weak nonlinearities,” Opt. Express, 23 (17), 21671–21677 (2015).
[Crossref]

DiVincenzo, D. P.

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, “Quantum nonlocality without entanglement,” Phys. Rev. A 59, 1070–1091 (1999).
[Crossref]

Dong, C. H.

Drevillon, J.

K. Joulain, J. Drevillon, Y. Ezzahri, and J. Ordonez-Miranda, “Quantum Thermal Transistor,” Phys. Rev. Lett. 116, 200601 (2016).
[Crossref] [PubMed]

Drühl, K.

M. O. Scully and K. Drühl, “Quantum eraser: A proposed photon correlation experiment concerning observation and “delayed choice” in quantum mechanics,” Phys. Rev. A 25, 2208–2213 (1982).
[Crossref]

Eberhard, P. H.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[Crossref]

Englert, B. G.

M. O. Scully, B. G. Englert, and H. Walther, “Quantum optical tests of complementarity,” Nature 351, 111–116 (1991).
[Crossref]

Ezzahri, Y.

K. Joulain, J. Drevillon, Y. Ezzahri, and J. Ordonez-Miranda, “Quantum Thermal Transistor,” Phys. Rev. Lett. 116, 200601 (2016).
[Crossref] [PubMed]

Field, J. E.

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[Crossref] [PubMed]

Fiorentino, M.

Fuchs, C. A.

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, “Quantum nonlocality without entanglement,” Phys. Rev. A 59, 1070–1091 (1999).
[Crossref]

Gaddam, V.

Gao, T.

Y. Q. He, D. Ding, F. L. Yan, and T. Gao, “Exploration of photon-number entangled states using weak nonlinearities,” Opt. Express, 23 (17), 21671–21677 (2015).
[Crossref]

Gerry, C. C.

C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge University, 2005).

Ghosh, R.

R. Ghosh, C. K. Hong, Z. Y. Ou, and L. Mandel, “Interference of two photons in parametric down conversion,” Phys. Rev. A 34, 3962–3968 (1986).
[Crossref]

Groisman, B.

B. Groisman and B. Reznik, “Measurements of semilocal and nonmaximally entangled states,” Phys. Rev. A 66, 022110 (2002).
[Crossref]

B. Groisman and L. Vaidman, “Nonlocal variables with product-state eigenstates,” J. Phys. A: Math. Gen. 34(35), 6881–6889 (2001).
[Crossref]

Guo, G. C.

J. S. Tang, Y. L. Li, X. Y. Xu, G. Y. Xiang, C. F. Li, and G. C. Guo, “Realization of quantum Wheeler’s delayed-choice experiment,” Nat. Photonics 6, 600–604 (2012).
[Crossref]

Harris, S. E.

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[Crossref] [PubMed]

Haus, H. A.

N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32, 2287–2292 (1985).
[Crossref]

He, Y. Q.

Y. Q. He, D. Ding, F. L. Yan, and T. Gao, “Exploration of photon-number entangled states using weak nonlinearities,” Opt. Express, 23 (17), 21671–21677 (2015).
[Crossref]

Herzog, T. J.

T. J. Herzog, P. G. Kwiat, H. Weinfurter, and A. Zeilinger, “Complementarity and the Quantum Eraser,” Phys. Rev. Lett. 75, 3034–3037 (1995).
[Crossref] [PubMed]

Holt, R. A.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Phys. Rev. Lett. 23, 880–884 (1969).
[Crossref]

Hong, C. K.

R. Ghosh, C. K. Hong, Z. Y. Ou, and L. Mandel, “Interference of two photons in parametric down conversion,” Phys. Rev. A 34, 3962–3968 (1986).
[Crossref]

C. K. Hong and L. Mandel, “Theory of parametric frequency down conversion of light,” Phys. Rev. A 31, 2409–2418 (1985).
[Crossref]

Horne, M. A.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Phys. Rev. Lett. 23, 880–884 (1969).
[Crossref]

Imamoglu, A.

H. Schmidt and A. Imamoğlu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21(23), 1936–1938 (1996).
[Crossref] [PubMed]

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[Crossref] [PubMed]

Imoto, N.

Jaksch, D.

S. R. Clark, A. J. Connor, D. Jaksch, and S. Popescu, “Entanglement consumption of instantaneous nonlocal quantum measurements,” New J. Phys. 12, 083034 (2010).
[Crossref]

Joulain, K.

K. Joulain, J. Drevillon, Y. Ezzahri, and J. Ordonez-Miranda, “Quantum Thermal Transistor,” Phys. Rev. Lett. 116, 200601 (2016).
[Crossref] [PubMed]

Kaiser, F.

F. Kaiser, T. Coudreau, P. Milman, D. B. Ostrowsky, and S. Tanzilli, “Entanglement-Enabled Delayed-Choice Experiment,” Science 338, 637–640 (2012).
[Crossref] [PubMed]

Kang, H.

H. Kang and Y. F. Zhu, “Observation of Large Kerr Nonlinearity at Low Light Intensities,” Phys. Rev. Lett. 91, 093601 (2003).
[Crossref] [PubMed]

Keller, T. E.

T. E. Keller and M. H. Rubin, “Theory of two-photon entanglement for spontaneous parametric down-conversion driven by a narrow pump pulse,” Phys. Rev. A 56, 1534–1541 (1997).
[Crossref]

Kiess, T. E.

Y. H. Shih, A. V. Sergienko, Morton H. Rubin, T. E. Kiess, and C. O. Alley, “Two-photon entanglement in type-II parametric down-conversion,” Phys. Rev. A 50, 23–28 (1994).
[Crossref] [PubMed]

Kim, Y. H.

Y. H. Kim, R. Yu, S. P. Kulik, Y. H. Shih, and M. O. Scully, “Delayed “Choice” Quantum Eraser,” Phys. Rev. Lett. 84, 1–5 (2000).
[Crossref] [PubMed]

Knight, P. L.

C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge University, 2005).

Korolkova, N.

G. F. Sinclair and N. Korolkova, “Effective cross-Kerr Hamiltonian for a nonresonant four-level atom,” Phys. Rev. A 77, 033843 (2008).
[Crossref]

G. F. Sinclair and N. Korolkova, “Cross-Kerr interaction in a four-level atomic system,” Phys. Rev. A 76, 033803 (2007).
[Crossref]

Kulik, S. P.

Y. H. Kim, R. Yu, S. P. Kulik, Y. H. Shih, and M. O. Scully, “Delayed “Choice” Quantum Eraser,” Phys. Rev. Lett. 84, 1–5 (2000).
[Crossref] [PubMed]

Kurtsiefer, C.

C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, “High-efficiency entangled photon pair collection in type-II parametric fluorescence,” Phys. Rev. A 64, 023802 (2001).
[Crossref]

Kwiat, P. G.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[Crossref]

T. J. Herzog, P. G. Kwiat, H. Weinfurter, and A. Zeilinger, “Complementarity and the Quantum Eraser,” Phys. Rev. Lett. 75, 3034–3037 (1995).
[Crossref] [PubMed]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

Landau, L.

L. Landau and R. Peierls, “Erweiterung des Unbestimmtheitsprinzips für die relativistische Quantentheorie,” Z. Phys. 69, 56–69 (1931).
[Crossref]

Li, C. F.

J. S. Tang, Y. L. Li, X. Y. Xu, G. Y. Xiang, C. F. Li, and G. C. Guo, “Realization of quantum Wheeler’s delayed-choice experiment,” Nat. Photonics 6, 600–604 (2012).
[Crossref]

Li, Y. L.

J. S. Tang, Y. L. Li, X. Y. Xu, G. Y. Xiang, C. F. Li, and G. C. Guo, “Realization of quantum Wheeler’s delayed-choice experiment,” Nat. Photonics 6, 600–604 (2012).
[Crossref]

Lüders, G.

G. Lüders, “Concerning the state-change due to the measurement process,” Ann. Phys. (Leipzig) 15, 663–670 (2006).
[Crossref]

G. Lüders, “Über die Zustandsänderung durch den Meßprozeß (German),” Ann. Phys. (Leipzig) 8, 322–328 (1951).

Mandel, L.

R. Ghosh, C. K. Hong, Z. Y. Ou, and L. Mandel, “Interference of two photons in parametric down conversion,” Phys. Rev. A 34, 3962–3968 (1986).
[Crossref]

C. K. Hong and L. Mandel, “Theory of parametric frequency down conversion of light,” Phys. Rev. A 31, 2409–2418 (1985).
[Crossref]

Mattle, K.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

Milman, P.

F. Kaiser, T. Coudreau, P. Milman, D. B. Ostrowsky, and S. Tanzilli, “Entanglement-Enabled Delayed-Choice Experiment,” Science 338, 637–640 (2012).
[Crossref] [PubMed]

Monken, C. H.

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Double-slit quantum eraser,” Phys. Rev. A 65, 033818 (2002).
[Crossref]

Mor, T.

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, “Quantum nonlocality without entanglement,” Phys. Rev. A 59, 1070–1091 (1999).
[Crossref]

Munro, M. W.

Munro, W. J.

W. J. Munro, Kae Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[Crossref]

Nemoto, Kae

W. J. Munro, Kae Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[Crossref]

Oberparleiter, M.

C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, “High-efficiency entangled photon pair collection in type-II parametric fluorescence,” Phys. Rev. A 64, 023802 (2001).
[Crossref]

Ordonez-Miranda, J.

K. Joulain, J. Drevillon, Y. Ezzahri, and J. Ordonez-Miranda, “Quantum Thermal Transistor,” Phys. Rev. Lett. 116, 200601 (2016).
[Crossref] [PubMed]

Ostrowsky, D. B.

F. Kaiser, T. Coudreau, P. Milman, D. B. Ostrowsky, and S. Tanzilli, “Entanglement-Enabled Delayed-Choice Experiment,” Science 338, 637–640 (2012).
[Crossref] [PubMed]

Ou, Z. Y.

R. Ghosh, C. K. Hong, Z. Y. Ou, and L. Mandel, “Interference of two photons in parametric down conversion,” Phys. Rev. A 34, 3962–3968 (1986).
[Crossref]

Özdemir, S. K.

Pádua, S.

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Double-slit quantum eraser,” Phys. Rev. A 65, 033818 (2002).
[Crossref]

Peierls, R.

L. Landau and R. Peierls, “Erweiterung des Unbestimmtheitsprinzips für die relativistische Quantentheorie,” Z. Phys. 69, 56–69 (1931).
[Crossref]

Popescu, S.

S. R. Clark, A. J. Connor, D. Jaksch, and S. Popescu, “Entanglement consumption of instantaneous nonlocal quantum measurements,” New J. Phys. 12, 083034 (2010).
[Crossref]

S. Popescu and L. Vaidman, “Causality constraints on nonlocal quantum measurements,” Phys. Rev. A 49, 4331–4338 (1994).
[Crossref] [PubMed]

Rains, E.

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, “Quantum nonlocality without entanglement,” Phys. Rev. A 59, 1070–1091 (1999).
[Crossref]

Resch, K. J.

K. J. Resch and A. M. Steinberg, “Extracting Joint Weak Values with Local, Single-Particle Measurements,” Phys. Rev. Lett. 92, 130402 (2004).
[Crossref] [PubMed]

Reznik, B.

B. Groisman and B. Reznik, “Measurements of semilocal and nonmaximally entangled states,” Phys. Rev. A 66, 022110 (2002).
[Crossref]

Roberts, T. D.

Rokhsari, H.

Rubin, M. H.

T. E. Keller and M. H. Rubin, “Theory of two-photon entanglement for spontaneous parametric down-conversion driven by a narrow pump pulse,” Phys. Rev. A 56, 1534–1541 (1997).
[Crossref]

Rubin, Morton H.

Y. H. Shih, A. V. Sergienko, Morton H. Rubin, T. E. Kiess, and C. O. Alley, “Two-photon entanglement in type-II parametric down-conversion,” Phys. Rev. A 50, 23–28 (1994).
[Crossref] [PubMed]

Schmidt, H.

Scully, M. O.

Y. H. Kim, R. Yu, S. P. Kulik, Y. H. Shih, and M. O. Scully, “Delayed “Choice” Quantum Eraser,” Phys. Rev. Lett. 84, 1–5 (2000).
[Crossref] [PubMed]

M. O. Scully, B. G. Englert, and H. Walther, “Quantum optical tests of complementarity,” Nature 351, 111–116 (1991).
[Crossref]

M. O. Scully and K. Drühl, “Quantum eraser: A proposed photon correlation experiment concerning observation and “delayed choice” in quantum mechanics,” Phys. Rev. A 25, 2208–2213 (1982).
[Crossref]

Sergienko, A. V.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

Y. H. Shih, A. V. Sergienko, Morton H. Rubin, T. E. Kiess, and C. O. Alley, “Two-photon entanglement in type-II parametric down-conversion,” Phys. Rev. A 50, 23–28 (1994).
[Crossref] [PubMed]

Shih, Y.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

Shih, Y. H.

Y. H. Kim, R. Yu, S. P. Kulik, Y. H. Shih, and M. O. Scully, “Delayed “Choice” Quantum Eraser,” Phys. Rev. Lett. 84, 1–5 (2000).
[Crossref] [PubMed]

Y. H. Shih, A. V. Sergienko, Morton H. Rubin, T. E. Kiess, and C. O. Alley, “Two-photon entanglement in type-II parametric down-conversion,” Phys. Rev. A 50, 23–28 (1994).
[Crossref] [PubMed]

Shimony, A.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Phys. Rev. Lett. 23, 880–884 (1969).
[Crossref]

Shor, P. W.

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, “Quantum nonlocality without entanglement,” Phys. Rev. A 59, 1070–1091 (1999).
[Crossref]

Sinclair, G. F.

G. F. Sinclair and N. Korolkova, “Effective cross-Kerr Hamiltonian for a nonresonant four-level atom,” Phys. Rev. A 77, 033843 (2008).
[Crossref]

G. F. Sinclair and N. Korolkova, “Cross-Kerr interaction in a four-level atomic system,” Phys. Rev. A 76, 033803 (2007).
[Crossref]

Smolin, J. A.

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, “Quantum nonlocality without entanglement,” Phys. Rev. A 59, 1070–1091 (1999).
[Crossref]

Spillane, S. M.

Spiller, T. P.

W. J. Munro, Kae Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[Crossref]

Steinberg, A. M.

K. J. Resch and A. M. Steinberg, “Extracting Joint Weak Values with Local, Single-Particle Measurements,” Phys. Rev. Lett. 92, 130402 (2004).
[Crossref] [PubMed]

Tang, J. S.

J. S. Tang, Y. L. Li, X. Y. Xu, G. Y. Xiang, C. F. Li, and G. C. Guo, “Realization of quantum Wheeler’s delayed-choice experiment,” Nat. Photonics 6, 600–604 (2012).
[Crossref]

Tanzilli, S.

F. Kaiser, T. Coudreau, P. Milman, D. B. Ostrowsky, and S. Tanzilli, “Entanglement-Enabled Delayed-Choice Experiment,” Science 338, 637–640 (2012).
[Crossref] [PubMed]

Terra Cunha, M. O.

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Double-slit quantum eraser,” Phys. Rev. A 65, 033818 (2002).
[Crossref]

Vahala, K. J.

Vaidman, L.

L. Vaidman, “Instantaneous Measurement of Nonlocal Variables,” Phys. Rev. Lett. 90, 010402 (2003).
[Crossref] [PubMed]

B. Groisman and L. Vaidman, “Nonlocal variables with product-state eigenstates,” J. Phys. A: Math. Gen. 34(35), 6881–6889 (2001).
[Crossref]

S. Popescu and L. Vaidman, “Causality constraints on nonlocal quantum measurements,” Phys. Rev. A 49, 4331–4338 (1994).
[Crossref] [PubMed]

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60, 1351–1354 (1988).
[Crossref] [PubMed]

Y. Aharonov, D. Z. Albert, and L. Vaidman, “Measurement process in relativistic quantum theory,” Phys. Rev. D 34, 1805–1813 (1986).
[Crossref]

von Neumann, J.

J. von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton University, 1955).

Waks, E.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[Crossref]

Walborn, S. P.

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Double-slit quantum eraser,” Phys. Rev. A 65, 033818 (2002).
[Crossref]

Walther, H.

M. O. Scully, B. G. Englert, and H. Walther, “Quantum optical tests of complementarity,” Nature 351, 111–116 (1991).
[Crossref]

Weinfurter, H.

C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, “High-efficiency entangled photon pair collection in type-II parametric fluorescence,” Phys. Rev. A 64, 023802 (2001).
[Crossref]

T. J. Herzog, P. G. Kwiat, H. Weinfurter, and A. Zeilinger, “Complementarity and the Quantum Eraser,” Phys. Rev. Lett. 75, 3034–3037 (1995).
[Crossref] [PubMed]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

White, A. G.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[Crossref]

Wootters, W. K.

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, “Quantum nonlocality without entanglement,” Phys. Rev. A 59, 1070–1091 (1999).
[Crossref]

Xiang, G. Y.

J. S. Tang, Y. L. Li, X. Y. Xu, G. Y. Xiang, C. F. Li, and G. C. Guo, “Realization of quantum Wheeler’s delayed-choice experiment,” Nat. Photonics 6, 600–604 (2012).
[Crossref]

Xiao, Y. F.

Xu, X. Y.

J. S. Tang, Y. L. Li, X. Y. Xu, G. Y. Xiang, C. F. Li, and G. C. Guo, “Realization of quantum Wheeler’s delayed-choice experiment,” Nat. Photonics 6, 600–604 (2012).
[Crossref]

Yamamoto, Y.

N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32, 2287–2292 (1985).
[Crossref]

Yan, F. L.

Y. Q. He, D. Ding, F. L. Yan, and T. Gao, “Exploration of photon-number entangled states using weak nonlinearities,” Opt. Express, 23 (17), 21671–21677 (2015).
[Crossref]

Yang, L.

Yu, R.

Y. H. Kim, R. Yu, S. P. Kulik, Y. H. Shih, and M. O. Scully, “Delayed “Choice” Quantum Eraser,” Phys. Rev. Lett. 84, 1–5 (2000).
[Crossref] [PubMed]

Zeilinger, A.

T. J. Herzog, P. G. Kwiat, H. Weinfurter, and A. Zeilinger, “Complementarity and the Quantum Eraser,” Phys. Rev. Lett. 75, 3034–3037 (1995).
[Crossref] [PubMed]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

Zhu, Y. F.

H. Kang and Y. F. Zhu, “Observation of Large Kerr Nonlinearity at Low Light Intensities,” Phys. Rev. Lett. 91, 093601 (2003).
[Crossref] [PubMed]

Ann. Phys. (Leipzig) (2)

G. Lüders, “Über die Zustandsänderung durch den Meßprozeß (German),” Ann. Phys. (Leipzig) 8, 322–328 (1951).

G. Lüders, “Concerning the state-change due to the measurement process,” Ann. Phys. (Leipzig) 15, 663–670 (2006).
[Crossref]

J. Phys. A: Math. Gen. (1)

B. Groisman and L. Vaidman, “Nonlocal variables with product-state eigenstates,” J. Phys. A: Math. Gen. 34(35), 6881–6889 (2001).
[Crossref]

Nat. Photonics (1)

J. S. Tang, Y. L. Li, X. Y. Xu, G. Y. Xiang, C. F. Li, and G. C. Guo, “Realization of quantum Wheeler’s delayed-choice experiment,” Nat. Photonics 6, 600–604 (2012).
[Crossref]

Nature (1)

M. O. Scully, B. G. Englert, and H. Walther, “Quantum optical tests of complementarity,” Nature 351, 111–116 (1991).
[Crossref]

New J. Phys. (1)

S. R. Clark, A. J. Connor, D. Jaksch, and S. Popescu, “Entanglement consumption of instantaneous nonlocal quantum measurements,” New J. Phys. 12, 083034 (2010).
[Crossref]

Opt. Express (2)

Opt. Express, (1)

Y. Q. He, D. Ding, F. L. Yan, and T. Gao, “Exploration of photon-number entangled states using weak nonlinearities,” Opt. Express, 23 (17), 21671–21677 (2015).
[Crossref]

Opt. Lett. (2)

Phys. Rev. A (15)

N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32, 2287–2292 (1985).
[Crossref]

W. J. Munro, Kae Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum-nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[Crossref]

Y. H. Shih, A. V. Sergienko, Morton H. Rubin, T. E. Kiess, and C. O. Alley, “Two-photon entanglement in type-II parametric down-conversion,” Phys. Rev. A 50, 23–28 (1994).
[Crossref] [PubMed]

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Double-slit quantum eraser,” Phys. Rev. A 65, 033818 (2002).
[Crossref]

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[Crossref]

C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, “High-efficiency entangled photon pair collection in type-II parametric fluorescence,” Phys. Rev. A 64, 023802 (2001).
[Crossref]

B. Groisman and B. Reznik, “Measurements of semilocal and nonmaximally entangled states,” Phys. Rev. A 66, 022110 (2002).
[Crossref]

S. Popescu and L. Vaidman, “Causality constraints on nonlocal quantum measurements,” Phys. Rev. A 49, 4331–4338 (1994).
[Crossref] [PubMed]

C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, “Quantum nonlocality without entanglement,” Phys. Rev. A 59, 1070–1091 (1999).
[Crossref]

M. O. Scully and K. Drühl, “Quantum eraser: A proposed photon correlation experiment concerning observation and “delayed choice” in quantum mechanics,” Phys. Rev. A 25, 2208–2213 (1982).
[Crossref]

C. K. Hong and L. Mandel, “Theory of parametric frequency down conversion of light,” Phys. Rev. A 31, 2409–2418 (1985).
[Crossref]

R. Ghosh, C. K. Hong, Z. Y. Ou, and L. Mandel, “Interference of two photons in parametric down conversion,” Phys. Rev. A 34, 3962–3968 (1986).
[Crossref]

T. E. Keller and M. H. Rubin, “Theory of two-photon entanglement for spontaneous parametric down-conversion driven by a narrow pump pulse,” Phys. Rev. A 56, 1534–1541 (1997).
[Crossref]

G. F. Sinclair and N. Korolkova, “Cross-Kerr interaction in a four-level atomic system,” Phys. Rev. A 76, 033803 (2007).
[Crossref]

G. F. Sinclair and N. Korolkova, “Effective cross-Kerr Hamiltonian for a nonresonant four-level atom,” Phys. Rev. A 77, 033843 (2008).
[Crossref]

Phys. Rev. D (3)

Y. Aharonov and D. Z. Albert, “States and observables in relativistic quantum field theories,” Phys. Rev. D 21, 3316–3324 (1980).
[Crossref]

Y. Aharonov and D. Z. Albert, “Can we make sense out of the measurement process in relativistic quantum mechanics,” Phys. Rev. D 24, 359–370 (1981).
[Crossref]

Y. Aharonov, D. Z. Albert, and L. Vaidman, “Measurement process in relativistic quantum theory,” Phys. Rev. D 34, 1805–1813 (1986).
[Crossref]

Phys. Rev. Lett. (12)

L. Vaidman, “Instantaneous Measurement of Nonlocal Variables,” Phys. Rev. Lett. 90, 010402 (2003).
[Crossref] [PubMed]

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Figures (1)

Fig. 1
Fig. 1 A schematic setup for performing the nonlocal measurement σ z A σ z B. Two photons A and B generated from PDC are sent to two interferometers hold by Alice and Bob, who are separated very far. The nonlocal measurement σ z A σ z B on the two photons can be turned to local measurement on the photon in the meter , where an ancillary meter �� initially prepared in a maximally entangled state and three identical Kerr media (shade rectangles) are used to generate the quantum correlation between the AB two-photon system and the meter . The polarization of the photon can be adjusted by the half wave plate (grey oval).

Equations (15)

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| ψ 0 A B = α 1 | H A H B + α 2 | H A V B + α 3 | V A H B + α 4 | V A V B ,
U = P ^ A B ( + 1 ) | + + | P ^ A B ( 1 ) | 1 | ,
| ψ 0 = 1 2 ( | 0 + | 1 ) ,
| ψ f = U ( | ψ 0 A B | ψ 0 ) = 1 2 ( c + | ψ A B ( + 1 ) | + c | ψ A B ( 1 ) | ) ,
| ψ 0 𝒩 = 1 2 [ | 1 𝒩 A ( | 1 + | 0 ) 𝒩 B + | 0 𝒩 A ( | 1 | 0 ) 𝒩 B ] ,
H = g a 1 a 1 a 2 a 2 ,
| ψ = 1 2 [ ( α 1 | H A H B + α 2 | H A V B + α 3 | V A H B + α 4 | V A V B ) | 1 𝒩 A ( | 1 + | 0 ) 𝒩 B + e i ϕ ( α 1 | H A H B + α 2 | H A V B ) | 0 𝒩 A ( | 1 | 0 ) 𝒩 B + ( α 3 | V A H B + α 4 | V A V B ) | 0 𝒩 A ( | 1 | 0 ) 𝒩 B ] | ψ 0 ,
| ψ 2 = [ ( α 1 | H A H B + α 2 | H A V B ) | 1 𝒩 B + ( α 3 | V A H B + α 4 | V A V B ) | 0 𝒩 B ] | ψ 0 | 𝒩 A ,
| ψ 2 = [ ( α 1 | H A H B + α 2 | H A V B ) | 0 𝒩 B + ( α 3 | V A H B + α 4 | V A V B ) | 1 𝒩 B ] | ψ 0 | 𝒩 A ,
| ψ 3 = 1 2 { [ [ ( α 1 | H A H B + α 2 | H A V B ) | 1 𝒩 B + ( α 3 | V A H B + α 4 | V A V B ) | 0 𝒩 B ] | 0 + [ ( α 1 | H A H B + α 2 | H A V B ) | 1 𝒩 B + ( α 3 | V A H B + α 4 | V A V B ) | 0 𝒩 B ] | 1 } | 𝒩 A ,
| ψ 3 = 1 2 { [ ( α 1 | H A H B + α 2 | H A V B ) | 0 𝒩 B + ( α 3 | V A H B + α 4 | V A V B ) | 1 𝒩 B ] | 0 + [ ( α 1 | H A H B + α 2 | H A V B ) | 0 𝒩 B ( α 3 | V A H B + α 4 | V A V B ) | 1 𝒩 B ] | 1 } | 𝒩 A .
| ψ 4 ( ± ) = 1 2 [ ( α 1 | H A H B + α 2 | H A V B α 3 | V A H B + α 4 | V A V B ) | 0 ± ( α 1 | H A H B + α 2 | H A V B α 3 | V A H B α 4 | V A V B ) | 1 ] | + 𝒩 B | ± 𝒩 A ,
| ψ 4 ( ) = 1 2 [ ( α 1 | H A H B + α 2 | H A V B + α 3 | V A H B α 4 | V A V B ) | 0 ± ( α 1 | H A H B + α 2 | H A V B + α 3 | V A H B + α 4 | V A V B ) | 1 ] | 𝒩 B | ± 𝒩 A ,
| ψ 4 ( + ) = ( c | ψ A B ( ) | + c ± | ψ A B ( ± ) | ) | + 𝒩 B | + 𝒩 A ,
| ψ 4 ( ) = ( c | ϕ A B ( ) | + c ± | ϕ A B ( ± ) | ) | 𝒩 B | ± 𝒩 A .

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