A model for the macroscopic description and continual observations in quantum mechanics

Barchielli, Alberto; Lanz, L.; Prosperi, G. M.

doi:10.1007/bf02894935

Cited by 256 publications

(159 citation statements)

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“…Therefore, we can reconstruct the instruments associated to our measurement by means of (0.7). As in [28,39], we shall do this by using the notion of characteristic operator, a concept introduced in [10]- [13], and Itô formula for counting processes.…”

Section: Counting Processesmentioning

confidence: 99%

“…The same was true in the case of counting processes, but in that case this difference was irrelevant, because we had the natural initial condition N j (0) = 0. Second, (3.16) can be interpreted by saying that y j (t) is the output of a continuous measurement of the quantum observables (selfadjoint operators) f j (t) * Z j (t) + f j (t)Z j (t) † , which are in general noncommuting [10]- [12,22]- [25].…”

Section: Diffusion Processesmentioning

confidence: 99%

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Measurements continuous in time and a posteriori states in quantum mechanics

Barchielli¹,

Belavkin²

1991

J. Phys. A: Math. Gen.

280

283

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Measurements continuous in time were consistently introduced in quantum mechanics and applications worked out, mainly in quantum optics. In this context a quantum filtering theory has been developed giving the reduced state after the measurement when a certain trajectory of the measured observables is registered (the a posteriori states). In this paper a new derivation of filtering equations is presented, in the cases of counting processes and of measurement processes of diffusive type. It is also shown that the equation for the a posteriori dynamics in the diffusive case can be obtained, by a suitable limit, from that one in the counting case. Moreover, the paper is intended to clarify the meaning of the various concepts involved and to discuss the connections among them. As an illustration of the theory, simple models are worked out.

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Section: Counting Processesmentioning

confidence: 99%

Section: Diffusion Processesmentioning

confidence: 99%

Measurements continuous in time and a posteriori states in quantum mechanics

Barchielli¹,

Belavkin²

1991

J. Phys. A: Math. Gen.

280

283

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show abstract

“…The original paper formulates the problem in very general way, but only proves for projective measurements, which prevails negligibly small time evolution during the time t/n when the number of repetitions n → ∞. The theory of continuous quantum measurement is built up from sequence of unsharp measurements, such that each measurement is increasingly weak by the increase of 8 the repetition n. This construction [26,27] allows QZE only for measurement strength γ → ∞. In order to investigate the effect, let us consider the case that our system is initially in the spin up state.…”

Section: Resultsmentioning

confidence: 99%

Double detected spin-dependent quantum dot

Bernád

2012

Physica B: Condensed Matter

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We study the dynamics of a spin-dependent quantum dot system, where an unsharp and a sharp detection scenario is introduced. The back-action of the unsharp detection related to the magnetization, proposed in terms of the continuous quantum measurement theory, is observed via the von Neumann measurement (sharp detection) of the electric charge current. The behavior of the average electron charge current is studied as a function of the unsharp detection strength γ, and features of measurement back-action are discussed. The achieved equations reproduce the quantum Zeno effect. Considering magnetic leads, we demonstrate that the measurement process may freeze the system in its initial state. We show that the continuous observation may enhance the transition between spin states, in contradiction with rapidly repeated projective observations, when it slows down. Experimental issue, such as the accuracy of the electric current measurement, is analyzed.

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“…Repeating this procedure n times, we get a classical output sequence (y 1 , y 2 , · · · , y n ) and the collapsed state |Ψ n (y 1 , y 2 , · · · , y n ) S of the system, given by the same expression as in (10). Furthermore, U n (see (5)), followed by a measurement on the reservoir yielding a classical output (y 1 , y 2 , · · · , y n ) and a post measured state |Ψ n (y 1 , y 2 , · · · y n ) S of the system.…”

Section: The Case Of Irreversible Discrete Time Dynamics Of Finitmentioning

confidence: 99%

From quantum stochastic differential equations to Gisin-Percival state diffusion

Parthasarathy

Devi

2017

Journal of Mathematical Physics

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Starting from the quantum stochastic differential equations of Hudson and Parthasarathy (Comm. Math. Phys. 93, 301 (1984)) and exploiting the Wiener-Itô-Segal isomorphism between the Boson Fock reservoir space Γ(L 2 (R + ) ⊗ (C n ⊕ C n )) and the Hilbert space L 2 (µ), where µ is the Wiener probability measure of a complex n-dimensional vector-valued standard Brownian motion {B(t), t ≥ 0}, we derive a non-linear stochastic Schrödinger equation describing a classical diffusion of states of a quantum system, driven by the Brownian motion B. Changing this Brownian motion by an appropriate Girsanov transformation, we arrive at the Gisin-Percival state diffusion equation (J. Phys. A 167, 315 (1992)). This approach also yields an explicit solution of the GisinPercival equation, in terms of the Hudson-Parthasarathy unitary process and a radomized Weyl displacement process. Irreversible dynamics of system density operators described by the wellknown Gorini-Kossakowski-Sudarshan-Lindblad master equation is unraveled by coarse-graining over the Gisin-Percival quantum state trajectories.

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A model for the macroscopic description and continual observations in quantum mechanics

Cited by 256 publications

References 0 publications

Measurements continuous in time and a posteriori states in quantum mechanics

Measurements continuous in time and a posteriori states in quantum mechanics

Double detected spin-dependent quantum dot

From quantum stochastic differential equations to Gisin-Percival state diffusion

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