TY - JOUR

T1 - Notes on nonlocal projective measurements in relativistic systems

AU - Lin, Shih Yuin

N1 - Funding Information:
I thank Jason Doukas and Andrzej Dragan for very helpful discussions. This work is supported by the Ministry of Science and Technology, Taiwan under grant MOST 102-2112-M-018-005-MY3 , and in part by the National Center for Theoretical Sciences, Taiwan .

PY - 2014/12/1

Y1 - 2014/12/1

N2 - 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.

AB - 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.

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U2 - 10.1016/j.aop.2014.08.018

DO - 10.1016/j.aop.2014.08.018

M3 - Article

AN - SCOPUS:84908574608

VL - 351

SP - 773

EP - 786

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

ER -