Related papers: The Converse Part of The Theorem for Quantum Hoeff…
Hypothesis testing is a fundamental issue in statistical inference and has been a crucial element in the development of information sciences. The Chernoff bound gives the minimal Bayesian error probability when discriminating two hypotheses…
In this paper we develop the theory of quantum reverse hypercontractivity inequalities and show how they can be derived from log-Sobolev inequalities. Next we prove a generalization of the Stroock-Varopoulos inequality in the…
Quantum query complexity is known to be characterized by the so-called quantum adversary bound. While this result has been proved in the standard discrete-time model of quantum computation, it also holds for continuous-time (or…
We prove a limit theorem for quantum stochastic differential equations with unbounded coefficients which extends the Trotter-Kato theorem for contraction semigroups. From this theorem, general results on the convergence of approximations…
An approach to the foundations of quantum theory is advertised that proceeds by "reverse engineering" quantum field theory. As a concrete instance of this approach, the general boundary formulation of quantum theory is outlined.
We give a novel derivation of Holevo's bound using an important result from nonequilibrium statistical physics, the fluctuation theorem. To do so we develop a general formalism of quantum fluctuation theorems for two-time measurements,…
We present two general approaches to obtain the strong converse rate of quantum hypothesis testing for correlated quantum states. One approach requires that the states satisfy a certain factorization property; typical examples of such…
In this paper, we provide a simple framework for deriving one-shot achievable bounds for some problems in quantum information theory. Our framework is based on the joint convexity of the exponential of the collision relative entropy, and is…
We consider a distributed quantum hypothesis testing problem with communication constraints, in which the two hypotheses correspond to two different states of a bipartite quantum system, multiple identical copies of which are shared between…
The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of unknown parameters of a quantum system. In this work, we prove lower bounds on the size of confidence regions reported…
The direct part of Stein's lemma in quantum hypothesis testing is revisited based on a key operator inequality between a density operator and its pinching. The operator inequality is used to show a simple proof of the direct part of Stein's…
Alternative exact expressions are derived for the minimum error probability of a hypothesis test discriminating among $M$ quantum states. The first expression corresponds to the error probability of a binary hypothesis test with certain…
The notion of the quantum angle is introduced. The quantum angle turns out to be a metric on the set of physical states of a quantum system. Its kinematics and dynamics is studied. The certainty principle for quantum systems is formulated…
Measurement-induced back action, a direct consequence of the Heisenberg Uncertainty Principle, is the defining feature of quantum measurements. We use quantum measurement theory to analyze the recent experiment of Safavi-Naeini et al.…
We consider the problem of detecting the true quantum state among $r$ possible ones, based of measurements performed on $n$ copies of a finite-dimensional quantum system. A special case is the problem of discriminating between $r$…
We evaluate a Gaussian distance-type degree of nonclassicality for a single-mode Gaussian state of the quantum radiation field by use of the recently discovered quantum Chernoff bound. The general properties of the quantum Chernoff overlap…
Quantum theory is notoriously counterintuitive, and yet remains entirely self-consistent when applied universally. Here we uncover a new manifestation of its unusual consequences. We demonstrate, theoretically and experimentally (by means…
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…
We extend Einstein's hole argument into the quantum domain, and argue that quantum observables for quasiclassical superpositional states of gravitational fields require additional information to be well-defined, namely, relative positions…
The asymptotic state discrimination problem with simple hypotheses is considered for a cubic lattice of bosons. A complete solution is provided for the problems of the Chernoff and the Hoeffding bounds and Stein's lemma in the case when…