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arXiv:quant-ph/0111124 · Physical Review Letters

Instantaneous Measurement of Nonlocal Variables

Lev Vaidman A

Published Jan 2, 2003• 92 citations
arXivHTMLPDF

Abstract

It is shown, under the assumption of the possibility to perform an arbitrary local operation, that all nonlocal variables related to two or more separate sites can be measured instantaneously, except for a finite time required for bringing to one location the classical records from these sites which yield the result of the measurement. It is a verification measurement: it yields reliably the eigenvalues of the nonlocal variables, but it does not prepare the eigenstates of the system.

DOI
10.1103/physrevlett.90.010402

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It is shown, under the assumption of the possibility to perform an arbitrary local operation, that all nonlocal variables related to two or more separate sites can be measured instantaneously, except for a finite time required for bringing to one location the classical records from these sites which yield the result of the measurement. It is a verification measurement: it yields reliably the eigenvalues of the nonlocal variables, but it does not prepare the eigenstates of the system.
We report results of an investigation of relativistic causality constraints on the measurability of nonlocal variables. We show that measurability of certain nondegenerate variables with entangled eigenstates contradicts the principle of causality, but that there are other, certainly nonlocal, variables which can be measured without breaking causality. We show that any causal measurement of nonlocal variables must erase certain local information. For example, for a system of two spin-1/2 particles, even if we take the weakest possible definition of verification measurement, verification of an entangled state must erase all local information.
With reference to a system of n spin‐1/2 particles which are distributed between two space‐like separated parties, we present two procedures to perform an instantaneous and local measurement of any nondegenerate observable having as its eigenstates the orthonormal basis of n‐partite entangled states introduced in [S. Bose, V. Vedral, and P. L. Knight, Phys. Rev. A 57, 822 (1998)], whose vectors reduce to the Bell states for n = 2 and to the GHZ states for n = 3. The first procedure implements a genuine nondemolition measurement by resorting to two n‐particle entangled states as an additional resource. The second one distinguishes between those eigenstates, though without preserving them (i.e., it is a demolition measurement), but it requires only a single couple of additional particles in a (maximally entangled) Bell state. Both methods are instantaneous, in the sense that the outcome of the measurement process is completely determined as soon as the local operations, whose duration can be made as short as one wishes, have been independently performed in the two distant regions where the particles are located.
Although for some nonlocal variables the standard quantum measurements which are reliable, instantaneous, and nondemolition, are impossible, demolition reliable instantaneous measurements of all variables are possible. It is shown that this is correct also in the framework of the time-symmetric quantum formalism, i.e. nonlocal variables of composite quantum systems with quantum states evolving both forward and backward in time are measurable in a demolition way. The result follows from the possibility to reverse with certainty the time direction of backward evolving quantum states.