Quantum bath statistics tagging

Abstract

The possibility of discriminating the statistics of a thermal bath using indirect measurements performed on quantum probes is presented. The scheme relies on the fact that, when weakly coupled with the environment of interest, the transient evolution of the probe toward its final thermal configuration, is strongly affected by the fermionic or bosonic nature of the bath excitations. Using figures of merit taken from quantum metrology such as the Holevo-Helstrom probability of error and the Quantum Chernoff bound, we discuss how to achieve the greatest precision in this statistics tagging procedure, analyzing different models of probes and different initial preparations and by optimizing over the time of exposure of the probe. arXiv:1907.04704v1 [quant-ph]

Discrimination of thermal baths by single-qubit probes

“…As in Ref. [15], we will attempt to discriminate between the two alternatives by only performing measurements on the reduced final stateρ(t ) of A, which hence encodes all the information about the nature of E one can access. This allows us to describe the whole scheme as a standard hypothesis testing problem [23] where one has to determine whetherρ(t ) corresponds to the density matrix ρ b (t ) of A, which one would have obtained by evolvingρ(0) under the influence of the bosonic bath of temperature 1/β b , or toρ f (t ), which instead one would have obtained by evolving the sameρ(0) under the influence of the fermionic bath of temperature 1/β f .…”

“…Relying on these observations, in Ref. [15] a statistics tagging scheme was presented, allowing the determination of the fermionic or bosonic character of a thermal bath E by detecting the modifications induced on a quantum probing system A put in thermal contact with E for some proper interaction time t. The analysis was conducted assuming the temperature of the bath to be known and, most importantly, equal in the two alternative scenarios. Under this condition, waiting for the complete thermalization of A (i.e., setting t → ∞) is clearly not a viable option to get useful information on the nature of the bath.…”

“…As a consequence, the optimal discrimination performances in Ref. [15] were obtained at times t where the evolved state of A was explicitly in a nonequilibrium condition. Superiority of nonequilibrium conditions for measurement purposes is not unique to the statistics tagging procedure discussed in [15]; similar behavior can be observed in thermometric tasks, when we want to infer the temperature of a bosonic bath by the same interaction with a probe.…”

“…[15] were obtained at times t where the evolved state of A was explicitly in a nonequilibrium condition. Superiority of nonequilibrium conditions for measurement purposes is not unique to the statistics tagging procedure discussed in [15]; similar behavior can be observed in thermometric tasks, when we want to infer the temperature of a bosonic bath by the same interaction with a probe. Even if the thermalized states corresponding to different temperatures can be distinguished, there is an advantage when measuring the probe at earlier times [16][17][18].…”

“…In an effort to check the generality of these observations (i.e., the optimality of using nonequilibrium observation times t and energy diagonal input states of the probe), here we cast the problem studied in Ref. [15] in a more complex framework by looking at the discrimination between two alternative thermal baths models which differ both in terms of their statistical properties and in terms of their associated temperatures. The analysis relies on information-theoretic quantities which admit clear operational interpretations in quantum metrology [19][20][21][22].…”