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arXiv:0704.3179

Measurement-induced manipulation of the quantum-classical border

Sabrina Maniscalco, Jyrki Piilo, Kalle‐Antti Suominen

Published Apr 24, 2007• 0 citations
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Abstract

We demonstrate the possibility of controlling the border between the quantum and the classical world by performing nonselective measurements on quantum systems. We consider a quantum harmonic oscillator initially prepared in a Schroedinger cat state and interacting with its environment. We show that the environment induced decoherence transforming the cat state into a statistical mixture can be strongly inhibited by means of appropriate sequences of measurements.

DOI
10.48550/arxiv.0704.3179

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We demonstrate the possibility of controlling the border between the quantum and the classical world by performing nonselective measurements on quantum systems. We consider a quantum harmonic oscillator initially prepared in a Schroedinger cat state and interacting with its environment. We show that the environment induced decoherence transforming the cat state into a statistical mixture can be strongly inhibited by means of appropriate sequences of measurements.
We study the dynamics of classical and quantum systems linearly interacting with a classical environment represented by an infinite set of harmonic oscillators. The environment induces a dynamical localization of the quantum state into a generalized coherent state for which the ℏ→0\hbar \to 0ℏ→0 limit always exists and reproduces the classical motion. We describe the consequences of this localization on the behavior of a macroscopic system by considering the example of a Schroedinger cat.
We investigate two techniques for controlling decoherence, focusing on the crucial role played by the environmental spectrum. We show how environments with different spectra lead to very different dynamical behaviors. Our study clearly proves that such differences must be taken into account when designing decoherence control schemes. The two techniques we consider are reservoir engineering and quantum Zeno control. We focus on a quantum harmonic oscillator initially prepared in a nonclassical state and derive analytically its non-Markovian dynamics in the presence of different bosonic thermal environments. On the one hand, we show how, by modifying the spectrum of the environment, it is possible to prolong or reduce the life of a Schr\"odinger cat state. On the other hand, we study the effect of nonselective energy measurements on the degradation of quantumness of initial Fock states. In this latter case, we see that the crossover between quantum Zeno and anti-Zeno effects, discussed by Maniscalco et al. [Phys. Rev. Lett. 97, 130402 (2006)], is highly sensitive to the details of the spectrum. In particular, for certain types of spectra, even very small variations of the system frequency may cause a measurement-induced acceleration of decoherence rather than its inhibition.
The manner in which states of some quantum systems become effectively classical is of great significance for the foundations of quantum physics, as well as for problems of practical interest such as quantum engineering. In the past two decades it has become increasingly clear that many (perhaps all) of the symptoms of classicality can be induced in quantum systems by their environments. Thus decoherence is caused by the interaction in which the environment in effect monitors certain observables of the system, destroying coherence between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly nonlocal ``Schr\"odinger-cat states.'' The classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit. Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation. Only the preferred pointer observable of the apparatus can store information that has predictive power. When the measured quantum system is microscopic and isolated, this restriction on the predictive utility of its correlations with the macroscopic apparatus results in the effective ``collapse of the wave packet.'' The existential interpretation implied by einselection regards observers as open quantum systems, distinguished only by their ability to acquire, store, and process information. Spreading of the correlations with the effectively classical pointer states throughout the environment allows one to understand ``classical reality'' as a property based on the relatively objective existence of the einselected states. Effectively classical pointer states can be ``found out'' without being re-prepared, e.g, by intercepting the information already present in the environment. The redundancy of the records of pointer states in the environment (which can be thought of as their ``fitness'' in the Darwinian sense) is a measure of their classicality. A new symmetry appears in this setting. Environment-assisted invariance or envariance sheds new light on the nature of ignorance of the state of the system due to quantum correlations with the environment and leads to Born's rules and to reduced density matrices, ultimately justifying basic principles of the program of decoherence and einselection.
We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the measured system. Selective and nonselective measurement processes are then introduced according to a selection of or an average over all possible initial configurations of the measurement apparatus. At quantum level, the selective processes are described by a nonlinear stochastic Schrödinger equation whose solutions evolve into properly defined coherent states in the case of linear systems. For arbitrary measured systems, classical behavior is always recovered in the macroscopic limit.