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Kluwer Academic Publishers eBooks

Entropy and Information Gain in Quantum Continual Measurements

Alberto Barchielli

Published Feb 24, 2006• 10 citations
Publisher

Abstract

'Entropy and Information Gain in Quantum Continual Measurements' published in 'Quantum Communication, Computing, and Measurement 3'
DOI
10.1007/0-306-47114-0_10

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The theory of measurements continuous in time in quantum mechanics (quantum continual measurements) has been formulated by using the notions of instrument, positive operator valued measure, etc., by using quantum stochastic differential equations and by using classical stochastic differential equations (SDE's) for vectors in Hilbert spaces or for trace-class operators. In the same times Ozawa made developments in the theory of instruments and introduced the related notions of a posteriori states and of information gain [1]. In this paper we introduce a simple class of SDE's relevant to the theory of continual measurements and we recall how they are related to instruments and a posteriori states and, so, to the general formulation of quantum mechanics. Then we introduce and use the notion of information gain and the other results of the paper [1] inside the theory of continual measurements. [1] M. Ozawa, On information gain by quantum measurements of continuous observables, J. Math. Phys. 27 (1986) 759-763.

arXiv:quant-ph/0012115•Dec 21, 2000•2 citations
We derive a thermodynamic uncertainty relation (TUR) under quantum continuous measurement and feedback control. By incorporating the quantum-classical-transfer entropy, which quantifies the information gained by continuous measurement, we show that the precision of currents is constrained by information-thermodynamic costs such as the entropy production and information gain. Our result shows that information gain has the potential to enhance the precision of currents beyond the bounds set by the conventional TUR. We illustrate the bound with a driven two-level system under continuous measurement and feedback, demonstrating that feedback achieves higher precision of currents while suppressing the entropy production.
Abstract The present paper is devoted to the investigation of the entropy reduction and entanglement-assisted classical capacity (information gain) of continuous variable quantum measurements. These quantities are computed explicitly for multimode Gaussian measurement channels. For this we establish a fundamental property of the entropy reduction of a measurement: under a restriction on the second moments of the input state it is maximized by a Gaussian state (providing an analytical expression for the maximum). In the case of one mode, the gain of entanglement assistance is investigated in detail.
The theory of measurements continuous in time in quantum mechanics (quantum continual measurements) has been formulated by using the notions of instrument, positive operator valued measure, etc., by using quantum stochastic differential equations and by using classical stochastic differential equations (SDE's) for vectors in Hilbert spaces or for trace-class operators. In the same times Ozawa made developments in the theory of instruments and introduced the related notions of a posteriori states and of information gain [1]. In this paper we introduce a simple class of SDE's relevant to the theory of continual measurements and we recall how they are related to instruments and a posteriori states and, so, to the general formulation of quantum mechanics. Then we introduce and use the notion of information gain and the other results of the paper [1] inside the theory of continual measurements. [1] M. Ozawa, On information gain by quantum measurements of continuous observables, J. Math. Phys. 27 (1986) 759-763.