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Notes on nonlocal projective measurements in relativistic systems. (English) Zbl 1360.81096

Summary: In quantum mechanical bipartite systems, naive extensions of von Neumann’s projective measurement to nonlocal variables can produce superluminal signals and thus violate causality. We analyze the projective quantum nondemolition state-verification in a two-spin system and see how the projection introduces nonlocality without entanglement. For the ideal measurements of “R-nonlocal” variables, we argue that causality violation can be resolved by introducing further restrictions on the post-measurement states, which makes the measurement “Q-nonlocal”. After we generalize these ideas to quantum mechanical harmonic oscillators, we look into the projective measurements of the particle number of a single mode or a wave-packet of a relativistic quantum field in Minkowski space. It turns out that the causality-violating terms in the expectation values of the local operators, generated either by the ideal measurement of the “R-nonlocal” variable or the quantum nondemolition verification of a Fock state, are all suppressed by the IR and UV cutoffs of the theory. Thus relativistic quantum field theories with such projective measurements are effectively causal.

MSC:

81P45 Quantum information, communication, networks (quantum-theoretic aspects)
81P15 Quantum measurement theory, state operations, state preparations
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