Related papers: On a conjecture regarding quantum hypothesis testi…
We consider the problem of a state determination for a two-level quantum system which can be in one of two nonorthogonal mixed states. It is proved that for the two independent identical systems the optimal combined measurement (which…
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…
Two types of errors can occur when discriminating pairs of quantum states. Asymmetric state discrimination involves minimizing the probability of one type of error, subject to a constraint on the other. We give explicit expressions bounding…
This expository article gives an overview of the theory of hypothesis testing of quantum states in finite dimensional Hilbert spaces. Optimal measurement strategy for testing binary quantum hypotheses, which result in minimum error…
In this paper, our interest is in the problem of simultaneous hypothesis testing when the test statistics corresponding to the individual hypotheses are possibly correlated. Specifically, we consider the case when the test statistics…
We discuss a general approach to handling "multiple hypotheses" testing in the case when a particular hypothesis states that the vector of parameters identifying the distribution of observations belongs to a convex compact set associated…
We investigate how to determine whether the states of a set of quantum systems are identical or not. This paper treats both error-free comparison, and comparison where errors in the result are allowed. Error-free comparison means that we…
We consider the problem of optimal asymptotically faithful compression for ensembles of mixed quantum states. Although the optimal rate is unknown, we prove upper and lower bounds and describe a series of illustrative examples of…
The task of binary quantum hypothesis testing is to determine the state of a quantum system via measurements on it, given the side information that it is in one of two possible states, say $\rho$ and $\sigma$. This task is generally studied…
Symmetry is a unifying concept in physics. In quantum information and beyond, it is known that quantum states possessing symmetry are not useful for certain information-processing tasks. For example, states that commute with a Hamiltonian…
The classical binary hypothesis testing problem is revisited. We notice that when one of the hypotheses is composite, there is an inherent difficulty in defining an optimality criterion that is both informative and well-justified. For…
We investigate the intermediate permutational symmetries of a system of qubits, that lie in between the perfect symmetric and antisymmetric cases. We prove that, on average, pure states of qubits picked at random with respect to the uniform…
Quantum metrology is a promising practical use case for quantum technologies, where physical quantities can be measured with unprecedented precision. In lieu of quantum error correction procedures, near term quantum devices are expected to…
Human agents happen to judge that a conjunction of two terms is more probable than one of the terms, in contradiction with the rules of classical probabilities---this is the conjunction fallacy. One of the most discussed accounts of this…
In this paper we consider the construction of optimal tests of equivalence hypotheses. Specifically, assume X_1,..., X_n are i.i.d. with distribution P_{\theta}, with \theta \in R^k. Let g(\theta) be some real-valued parameter of interest.…
We pose the question whether the asymptotic equivalence between quantum cloning and quantum state estimation, valid at the single-clone level, still holds when all clones are examined globally. We conjecture that the answer is affirmative…
The asymptotically optimal hypothesis testing problem with the general sources as the null and alternative hypotheses is studied under exponential-type error constraints on the first kind of error probability. Our fundamental philosophy in…
The ultimate limits of quantum state discrimination are often thought to be captured by asymptotic bounds that restrict the achievable error probabilities, notably the quantum Chernoff and Hoeffding bounds. Here we study hypothesis testing…
We propose a new measure of relative incompatibility for a quantum system with respect to two non-commuting observables, and call it quantumness of relative incompatibility. In case of a classical state, order of observation is…
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…