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
Phys. Rev. D, 24, 359 (1981)

[3] Y. Aharonov, D. Z. Albert and L. Vaidman
Phys. Rev. D, 34, 1805 (1986)

[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)