相关论文: Robust generalized quantum Stein's lemma
The quantum Stein's lemma is a fundamental result of quantum hypothesis testing in the context of distinguishing two quantum states. A recent conjecture, known as the ``generalized quantum Stein's lemma", asserts that this result is true in…
The generalized quantum Stein's lemma characterizes the optimal asymptotic exponent of the type-II error in quantum hypothesis testing for an independent and identically distributed (IID) null hypothesis against a composite alternative…
We solve the generalised quantum Stein's lemma, proving that the Stein exponent associated with entanglement testing, namely, the quantum hypothesis testing task of distinguishing between $n$ copies of an entangled state $\rho_{AB}$ and a…
We present a generalization of quantum Stein's Lemma to the situation in which the alternative hypothesis is formed by a family of states, which can moreover be non-i.i.d.. We consider sets of states which satisfy a few natural properties,…
We show that the proof of the generalised quantum Stein's lemma [Brand\~ao & Plenio, Commun. Math. Phys. 295, 791 (2010)] is not correct due to a gap in the argument leading to Lemma III.9. Hence, the main achievability result of Brand\~ao…
Recall the classical hypothesis testing setting with two convex sets of probability distributions P and Q. One receives either n i.i.d. samples from a distribution p in P or from a distribution q in Q and wants to decide from which set the…
We consider the manipulation of multipartite entangled states in the limit of many copies under quantum operations that asymptotically cannot generate entanglement. As announced in [Brandao and Plenio, Nature Physics 4, 8 (2008)], and in…
We extend quantum Stein's lemma in asymmetric quantum hypothesis testing to composite null and alternative hypotheses. As our main result, we show that the asymptotic error exponent for testing convex combinations of quantum states…
Quantum Stein's Lemma is a cornerstone of quantum statistics and concerns the problem of correctly identifying a quantum state, given the knowledge that it is one of two specific states ($\rho$ or $\sigma$). It was originally derived in the…
The Generalized Quantum Stein's Lemma is a theorem in quantum hypothesis testing that provides an operational meaning to the relative entropy within the context of quantum resource theories. Its original proof was found to have a gap, which…
The trade-offs between error probabilities in quantum hypothesis testing are by now well-understood in the centralized setting, but much less is known for distributed settings. Here, we study a distributed binary hypothesis testing problem…
The asymptotic equipartition property (AEP) states that in the limit of a large number of independent and identically distributed (i.i.d.) random experiments, the output sequence is virtually certain to come from the typical set, each…
The problem of testing two simple hypotheses in a general probability space is considered. For a fixed type-I error probability, the best exponential decay rate of the type-II error probability is investigated. In regular asymptotic cases…
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…
We show finite-size bounds on the deviation of the optimal type II error from its asymptotic value in the quantum hypothesis testing problem of Stein's lemma with composite null-hypothesis. The proof is based on some simple properties of a…
The second law of thermodynamics is the cornerstone of physics, characterizing the convertibility between thermodynamic states through a single function, entropy. Given the universal applicability of thermodynamics, a fundamental question…
In the asymptotic theory of quantum hypothesis testing, the minimal error probability of the first kind jumps sharply from zero to one when the error exponent of the second kind passes by the point of the relative entropy of the two states…
We consider the task of distinguishing whether a quantum system is prepared in a state from one of several sets of quantum states. Assuming their convexity and stability under tensor product, we prove that the optimal error exponent for…
A novel measure, quantumness of correlations is introduced here for bipartite states, by incorporating the required measurement scheme crucial in defining any such quantity. Quantumness coincides with the previously proposed measures in…
Given two families of quantum states $A$ and $B$, called the null and the alternative hypotheses, quantum hypothesis testing is the task of determining whether an unknown quantum state belongs to $A$ or $B$. Mistaking $A$ for $B$ is a type…