Past Quantum States of a Monitored System

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Past Quantum States of a Monitored System. / Gammelmark, Søren; Julsgaard, Brian; Mølmer, Klaus.

In: Physical Review Letters, Vol. 111, No. 16, 160401, 15.10.2013.

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Gammelmark, Søren ; Julsgaard, Brian ; Mølmer, Klaus. / Past Quantum States of a Monitored System. In: Physical Review Letters. 2013 ; Vol. 111, No. 16.

Bibtex

@article{18c4d0d020fc4ef986cd9a6e5c039d9a,
title = "Past Quantum States of a Monitored System",
abstract = "A density matrix ρ(t) yields probabilistic information about the outcome of measurements on a quantum system. We introduce here the past quantum state, which, at time T, accounts for the state of a quantum system at earlier times t<T. The past quantum state Ξ(t) is composed of two objects, ρ(t) and E(t), conditioned on the dynamics and the probing of the system until t and in the time interval [t, T], respectively. The past quantum state is characterized by its ability to make better predictions for the unknown outcome of any measurement at t than the conventional quantum state at that time. On the one hand, our formalism shows how smoothing procedures for estimation of past classical signals by a quantum probe [M. Tsang, Phys. Rev. Lett. 102 250403 (2009)] apply also to describe the past state of the quantum system itself. On the other hand, it generalizes theories of pre- and postselected quantum states [Y. Aharonov and L. Vaidman, J. Phys. A 24 2315 (1991)] to systems subject to any quantum measurement scenario, any coherent evolution, and any Markovian dissipation processes. ",
author = "S{\o}ren Gammelmark and Brian Julsgaard and Klaus M{\o}lmer",
year = "2013",
month = oct,
day = "15",
doi = "10.1103/PhysRevLett.111.160401",
language = "English",
volume = "111",
journal = "Physical Review Letters",
issn = "0031-9007",
publisher = "AMER PHYSICAL SOC",
number = "16",

}

RIS

TY - JOUR

T1 - Past Quantum States of a Monitored System

AU - Gammelmark, Søren

AU - Julsgaard, Brian

AU - Mølmer, Klaus

PY - 2013/10/15

Y1 - 2013/10/15

N2 - A density matrix ρ(t) yields probabilistic information about the outcome of measurements on a quantum system. We introduce here the past quantum state, which, at time T, accounts for the state of a quantum system at earlier times t<T. The past quantum state Ξ(t) is composed of two objects, ρ(t) and E(t), conditioned on the dynamics and the probing of the system until t and in the time interval [t, T], respectively. The past quantum state is characterized by its ability to make better predictions for the unknown outcome of any measurement at t than the conventional quantum state at that time. On the one hand, our formalism shows how smoothing procedures for estimation of past classical signals by a quantum probe [M. Tsang, Phys. Rev. Lett. 102 250403 (2009)] apply also to describe the past state of the quantum system itself. On the other hand, it generalizes theories of pre- and postselected quantum states [Y. Aharonov and L. Vaidman, J. Phys. A 24 2315 (1991)] to systems subject to any quantum measurement scenario, any coherent evolution, and any Markovian dissipation processes.

AB - A density matrix ρ(t) yields probabilistic information about the outcome of measurements on a quantum system. We introduce here the past quantum state, which, at time T, accounts for the state of a quantum system at earlier times t<T. The past quantum state Ξ(t) is composed of two objects, ρ(t) and E(t), conditioned on the dynamics and the probing of the system until t and in the time interval [t, T], respectively. The past quantum state is characterized by its ability to make better predictions for the unknown outcome of any measurement at t than the conventional quantum state at that time. On the one hand, our formalism shows how smoothing procedures for estimation of past classical signals by a quantum probe [M. Tsang, Phys. Rev. Lett. 102 250403 (2009)] apply also to describe the past state of the quantum system itself. On the other hand, it generalizes theories of pre- and postselected quantum states [Y. Aharonov and L. Vaidman, J. Phys. A 24 2315 (1991)] to systems subject to any quantum measurement scenario, any coherent evolution, and any Markovian dissipation processes.

U2 - 10.1103/PhysRevLett.111.160401

DO - 10.1103/PhysRevLett.111.160401

M3 - Journal article

C2 - 24182235

VL - 111

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 16

M1 - 160401

ER -