arXiv:1505.03056 · Europhysics Letters (EPL)

Parametric description of the quantum measurement process

Pietro Liuzzo-Scorpo, Alessandro Cuccoli, Paola Verrucchi

Published Aug 1, 2015• 9 citations

Abstract

We present a description of the measurement process based on the parametric representation with environmental coherent states. This representation is specifically tailored for studying quantum systems whose environment needs being considered through the quantum-to-classical crossover. Focusing upon projective measures, and exploiting the connection between large- N quantum theories and the classical limit of related ones, we manage to push our description beyond the pre-measurement step. This allows us to show that the outcome production follows from a global-symmetry breaking, entailing the observed system's state reduction, and that the statistical nature of the process is brought about, together with the Born's rule, by the macroscopic character of the measuring apparatus.

DOI: 10.1209/0295-5075/111/40008

Related papers

Whenever a quantum environment emerges as a classical system, it behaves like a measuring apparatus

Caterina Foti, Teiko Heinosaari, Sabrina Maniscalco +1 more

We study the dynamics of a quantum system Γ with an environment Ξ made of N elementary quantum components. We aim at answering the following questions: can the evolution of Γ be characterized by some general features when N becomes very large, regardless of the specific form of its interaction with each and every component of Ξ ? In other terms: should we expect all quantum systems with a macroscopic environment to undergo a somehow similar evolution? And if yes, of what type? In order to answer these questions we use well established results from large- N quantum field theories, particularly referring to the conditions ensuring a large- N quantum model to be effectively described by a classical theory. We demonstrate that the fulfillment of these conditions, when properly imported into the framework of the open quantum systems dynamics, guarantees that the evolution of Γ is always of the same type of that expected if Ξ were a measuring apparatus, no matter the details of the actual interaction. On the other hand, such details are found to determine the specific basis w.r.t. which Γ undergoes the decoherence dictated by the dynamical description of the quantum measurement process. This result wears two hats: on the one hand it clarifies the physical origin of the formal statement that, under certain conditions, any channel from ρΓ to ρΞ takes the form of a measure-and-prepare map, as recently shown in Ref. \cite{BrandaoPH15}; on the other hand, it formalizes the qualitative argument that the reason why we do not observe state superpositions is the continual measurement performed by the environment.

arXiv:1810.10261QuantumAug 26, 201916 citations

Lectures on dynamical models for quantum measurements

Theo M. Nieuwenhuizen, Martí Perarnau-Llobet, Roger Balian

In textbooks, ideal quantum measurements are described in terms of the tested system only by the collapse postulate and Born's rule. This level of description offers a rather flexible position for the interpretation of quantum mechanics. Here we analyse an ideal measurement as a process of interaction between the tested system S and an apparatus A, so as to derive the properties postulated in textbooks. We thus consider within standard quantum mechanics the measurement of a quantum spin component ŝz by an apparatus A, being a magnet coupled to a bath. We first consider the evolution of the density operator of S + A describing a large set of runs of the measurement process. The approach describes the disappearance of the off-diagonal terms ("truncation") of the density matrix as a physical effect due to A, while the registration of the outcome has classical features due to the large size of the pointer variable, the magnetization. A quantum ambiguity implies that the density matrix at the final time can be decomposed on many bases, not only the one of the measurement. This quantum oddity prevents to connect individual outcomes to measurements, a difficulty known as the "measurement problem". It is shown that it is circumvented by the apparatus as well, since the evolution in a small time interval erases all decompositions, except the one on the measurement basis. Once one can derive the outcome of individual events from quantum theory, the so-called collapse of the wavefunction or the reduction of the state appears as the result of a selection of runs among the original large set. Hence nothing more than standard quantum mechanics is needed to explain features of measurements. The employed statistical formulation is advocated for the teaching of quantum theory.

arXiv:1406.5178International Journal of Modern Physics BJun 23, 20145 citations

Interaction and Measuring Process in Quantum Theory

Frank Kaschluhn

Abstract A statistical law for interaction processes in quantum theory is presented. It states that the final state of the scattered systems, evaluated on the basis of quantum theory, reduces alternatively to different substates provided correlation states are produced by the interaction. Such processes also underlie the measuring process (interaction system‐apparatus). To test the modified scattering theory experiments are proposed. The consequences for the description of the interaction between a system and a macroscopic body, in particular a measuring apparatus, are discussed. The reduction of the wave function needed here comes out quite naturally.

Fortschritte der PhysikJan 1, 19814 citations

Irreversibility, equilibrium and measurement in quantum mechanics

Christopher J. N. Coveney, Peter V. Coveney

Quantum mechanics is widely recognised as being incomplete. It is not consistent with the second law of thermodynamics and does not provide a scientifically credible physical account of the measurement process, the means by which coherence is broken and classically observable states are recorded. This has led to many ad hoc assumptions being used to account for various properties of quantum systems, among which is the coherence time of quantum devices that determines their ability to perform computations. Here, we show that all these properties can be accommodated naturally and consistently in the context of mixing quantum systems which exhibit continuous spectra, as arises in the thermodynamic limit in quantum statistical mechanics and quantum gravity. In particular, for isolated systems we show that the time-reversal symmetry associated with unitary time evolution of the quantum state gives rise to time-symmetry breaking and a semi-group evolution which attains thermodynamic equilibrium at long times. Moreover, the emergence of this non-unitary time-asymmetry leads to microcanonical equilibrium states in which all quantum coherence is lost and is accompanied by the transformation of pure states into mixtures, leading in turn to an increase in entropy. Inclusion of a macroscopic measurement apparatus shows how the outcome of a measurement corresponds to the von Neumann projection postulate, arising with probabilities in conformance with the Born rule. The mathematical structure of the theory which applies to quantum systems with continuous spectra is closely analogous to the classical ergodic theory of dynamical systems and the conditions under which they attain equilibrium states.

quant-pharXiv:2607.19142Jul 22, 20260 citations

On the Theory of Measurement in Quantum Mechanical Systems

Loyal Durand

This paper is concerned with the description of the process of measurement within the context of a quantum theory of the physical world. It is noted that quantum mechanics permits a quasi-classical description (classical in the limited sense implied by the correspondence principle of Bohr) of those macroscopic phenomena in terms of which the observer forms his perceptions. Thus, the process of measurement in quantum mechanics can be understood on the quasi-classical level by transcribing from the strictly classical observables of Newtonian physics to their quasi-classical counterparts the known rules for the measurement of the former. The remaining physical problem is the delineation of the circumstances in which the correlation of a peculiarly quantum mechanical observable A with a classically measurable observable B can result in a significant measurement of A. This is undertaken within the context of quantum theory. The resulting clarification of the process of measurement has important implications relative to the philosophic interpretation of quantum mechanics.

Philosophy of ScienceApr 1, 196010 citations

The quantum measurement process: an exactly solvable model

ARMEN E. ALLAHVERDYAN, Roger Balian, Theo M. Nieuwenhuizen

An exactly solvable model for a quantum measurement is discussed, that integrates quantum measurements with classical measurements. The z-component of a spin-1/2 test spin is measured with an apparatus, that itself consists of magnet of N spin-1/2 particles, coupled to a bath. The initial state of the magnet is a metastable paramagnet, while the bath starts in a thermal, gibbsian state. Conditions are such that the act of measurement drives the magnet in the up or down ferromagnetic state, according to the sign of s_z of the test spin. The quantum measurement goes in two steps. On a timescale 1/\sqrt{N} the collapse takes place due to a unitary evolution of test spin and apparatus spins; on a larger but still short timescale this collapse is made definite by the bath. Then the system is in a `classical' state, having a diagonal density matrix. The registration of that state is basically a classical process, that can already be understood from classical statistical mechanics.

arXiv:cond-mat/0309188Sep 8, 20034 citations