Related papers: When is the Chernoff Exponent for Quantum Operatio…
We study an optimum measurement for quantum state discrimination, which maximizes the probability of correct results when the probability of inconclusive results is fixed at a given value. The measurement describes minimum-error…
We study the error exponents in quantum hypothesis testing between two sets of quantum states, extending the analysis beyond the independent and identically distributed case to encompass composite correlated hypotheses. In particular, we…
Following the result by Skrzypczyk et al., arXiv:1009.0865, that certain self-contained quantum thermal machines can reach Carnot efficiency, we discuss the functioning of self-contained quantum thermal machines and show, in a very general…
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…
In this work, I analyze the quantum fluctuations and the thermal fluctuations in the framework of quantum mechanics. Being recognized as incoherent perturbations with different features, fluctuations of these two types lead to dissipative…
The determination of a quantum observable from the first and second moments of its measurement outcome statistics is investigated. Operational conditions for the moments of a probability measure are given which suffice to determine the…
We uncover the quantum fluctuation-response inequality, which, in the most general setting, establishes a bound for the mean difference of an observable at two different quantum states, in terms of the quantum relative entropy. When the…
The hopes for scalable quantum computing rely on the "threshold theorem": once the error per qubit per gate is below a certain value, the methods of quantum error correction allow indefinitely long quantum computations. The proof is based…
We give a mathematical definition for the notion of inconclusive quantum measurements. In physics, such measurements occur at intermediate stages of a complex measurement procedure, with the final measurement result being operationally…
Lyapunov exponents describe the asymptotic behavior of the singular values of large products of random matrices. A direct computation of these exponents is however often infeasible. By establishing a link between Lyapunov exponents and an…
The quantum version of the Bochkov-Kuzovlev identity is derived on the basis of the appropriate definition of work as the difference of the measured internal energies of a quantum system at the beginning and at the end of an external action…
Giving a universal upper bound on the power output of heat engines is a long-standing open problem. We tackle this problem for generic quantum machines in self-contained formulation by carefully including the switching process of the…
We prove the quantum Zeno effect in open quantum systems whose evolution, governed by quantum dynamical semigroups, is repeatedly and frequently interrupted by the action of a quantum operation. For the case of a quantum dynamical semigroup…
The entropy produced when a system undergoes an infinitesimal quench is directly linked to the work parameter susceptibility, making it sensitive to the existence of a quantum critical point. Its singular behavior at $T=0$, however,…
A physical system is determined by a finite set of initial conditions and "laws" represented by equations. The system is computable if we can solve the equations in all instances using a "finite body of mathematical knowledge". In this…
The consistency of the Shannon entropy, when applied to outcomes of quantum experiments, is analysed. It is shown that the Shannon entropy is fully consistent and its properties are never violated in quantum settings, but attention must be…
The classical Chernoff's theorem is a statement about discrete-time approximations of semigroups, where the approximations are consturcted as products of time-dependent contraction operators strongly differentiable at zero. We generalize…
We consider the problem, where a camera is tasked with determining one of two hypotheses: first with an incoherently-radiating quasi-monochromatic point source and the second with two identical closely spaced point sources. We are given…
We explore a possibility of measuring deviation from the exponential decay law in pure quantum systems. The power law behavior at late times of decay time profile is predicted in quantum mechanics, and has been experimentally attempted to…
In this note the Chernoff Theorem is used to approximate evolution semigroups constructed by the procedure of subordination. The considered semigroups are subordinate to some original, unknown explicitly but already approximated by the same…