### 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)*

**Instantaneous measurement of non-local variables is possible**

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*

*J. Phys. A: Math. Gen.***34, 6881 (2001).****Methods for reliable teleportation**

Lev Vaidman and Nadav Yoran

*Phys. Rev. A***59**, 116 (1999)**Causality, Memory Erasing and Delayed Choice Experiments**

Y. Aharonov, S. Popsecu and L. Vaidman

*Phys. Rev. A***52**, 4984 (1995)

*quant-ph/9501006***Nonlocality of a Single Photon Revisited Again**

Lev Vaidman

*Phys. Rev. Lett.***75**, 2063 (1995)

*quant-ph/9501003***Nonlocal Measurements and Teleportation of Quantum States**

L. Vaidman

*in Fundamental Problems in Quantum Physics, M. Ferrero and A. van der Merwe (eds.) (Kluwer Academic Publishers, Denver, 1995), 347***Causality Constraints on Nonlocal Quantum Measurements**

S. Popescu and L. Vaidman

*Phys. Rev. A***49**, 4331 (1994)

*hep-th/9306087***Measurement of Nonlocal Variables Without Breaking Causality**

L. Vaidman

*in Quantum Coherence and Reality, J. Anandan and J. Safko (eds.) (World Scientific, 1994), 349*

*hep-th/9306086***Lorentz-Invariant "Elements of Reality" and the Joint Measurability of Commuting Observables**

L. Vaidman

*Phys. Rev. Lett.***70**, 3369 (1993)

*hep-th/9305162***Measurement Process in Relativistic Quantum Theory**

Y. Aharonov, D. Albert and L. Vaidman

*Phys. Rev. D***34**, 1805 (1986)**Further Discussion of Possible Experimental Tests for the Paradox of Einstein, Podolsky and Rosen**

D. Bohm and Y. Aharonov

*Nuovo Cimento***17**, 964 (1960)**Discussion of Experimental Proof for the Paradox of Einstein, Rosen, and Podolsky**

D. Bohm and Y. Aharonov

*Phys. Rev.***108**, 1070 (1957)