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Mardi 14 juin 2016-14:00

Repeated quantum measurements and time direction hypothesis testing

Tristan Benoist (LPT)

par Gabriel LeMarié - 14 juin 2016

The introduction of fluctuation relations in the nineties helped understand the statistics of the transition from a microscopic reversible evolution to an irreversible macroscopic one. In the early 2000’s Kurchan extended the classical fluctuation relations to the quantum realm. He introduced a two time measurement picture that had actually been used in 1964 by Aharonov, Bergmann and Lebowitz to argue that the projection postulate does not introduce an irreversibility if one consider the appropriate statistical ensemble.

Pursuing the investigation of entropy production statistics in quantum physics, with V. Jaksic, Y. Pautrat and C.-A. Pillet we study the entropy production of general repeated measurements. I will present some of our results.

The repeated measurements model is directly inspired by experiments in cavity and circuitry QED, and trapped ions where atoms and oscillators are measured and manipulated by shooting auxiliary atoms or light pulses at them. These auxiliary systems can be measured before and after their interaction with the system being manipulated. The experimenter obtains then a sequence of measurement results. A natural notion of time reversal emerge. Namely, the reversal of the measurement result sequence order. In specific models related to the usual full counting statistics, this reversal is obtained from the time reversal invariance of the underlying unitary dynamic.

Using a sub additive extension of the thermodynamic formalism, we study the statistics of the order reversal entropy production. A local fluctuation relation theorem follows from generic assumptions. We further show that the entropy production converges with probability one to a fixed value. Since the forward and backward distributions of the measurement results are either equal or have non nul values on disjoint sets of measurement sequences, the time direction can be asymptotically read directly from the sequence of measurement results. We quantify further this property using different relative entropies and deduce the corresponding error exponents related to the exponential decay of the errors in the hypothesis testing of the time direction.

Post-scriptum :

contact : G. Lemarié