### Abstract

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.

Original language | English |
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Pages (from-to) | 773-786 |

Number of pages | 14 |

Journal | Annals of Physics |

Volume | 351 |

DOIs | |

Publication status | Published - 2014 Dec 1 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

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*Annals of Physics*, vol. 351, pp. 773-786. https://doi.org/10.1016/j.aop.2014.08.018

**Notes on nonlocal projective measurements in relativistic systems.** / Lin, Shih Yuin.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Notes on nonlocal projective measurements in relativistic systems

AU - Lin, Shih Yuin

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.

UR - http://www.scopus.com/inward/record.url?scp=84908574608&partnerID=8YFLogxK

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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 -