Non-Local Measurements and Causality
In 1931 L. Landau and R. Peierls [1] claimed, that any nonlocal property of a quantum system at a given time cannot be measured in relativistic quantum theory. However, in 1980 Y. Aharonov and D. Albert showed [2] that this claim is not true and some nonlocal properties can indeed be measured instantaneously. Y Aharonov and coworkers found some explicit methods for performing instantaneous nonlocal measurement [2,3]. In particular, they showed how A+B, (A+B)mod a and Bell-operator can be measured nonlocally. On the other hand, it have been shown in other works that measurement of any variable of the following three different classes: the variables defined by four "one-side twisted" product states as their eigenstates |00>, |01>, |1(0+1)>, |1(0-1)>, the variables which have nonmaximally entangled eigenstates [a|00> + b |11>], where a nonequal b , and 4x4 dimensional "twisted" variables, contradicts relativistic causality [4,5].
[1] L. Landau and R. Peierls
Z. Phys.69, 56 (1931)
[2] Y. Aharonov, D. Z. Albert
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[3] Y. Aharonov, D. Z. Albert and L. Vaidman
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[4] S. Popescu and L. Vaidman
Phys. Rev. A, 49, 4331 (1994)
[5] D. Beckman, D. Gottesman, M.A. Nielsen and J. Preskill
Phys. Rev. A, 64, 052309 (2001)
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Lev Vaidman
quant-ph/0111124 - Measurements of semi-local and non-maximally entangled states
Berry Groisman, Benni Reznik
quant-ph/0111012 - Nonlocal variables with product states eigenstates
B. Groisman and L. Vaidman
quant-ph/0103084
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Lev Vaidman and Nadav Yoran
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Y. Aharonov, S. Popsecu and L. Vaidman
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quant-ph/9501006 - Nonlocality of a Single Photon Revisited Again
Lev Vaidman
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quant-ph/9501003 - Nonlocal Measurements and Teleportation of Quantum States
L. Vaidman
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S. Popescu and L. Vaidman
Phys. Rev. A 49, 4331 (1994)
hep-th/9306087 - Measurement of Nonlocal Variables Without Breaking Causality
L. Vaidman
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L. Vaidman
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Y. Aharonov, D. Albert and L. Vaidman
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D. Bohm and Y. Aharonov
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