Related papers: On the error exponents of binary state discriminat…
It is known that probabilistically mixing an arbitrary pair of pure quantum states, one of which is entangled and the other product, in any bipartite quantum system, one always obtains an entangled state, provided the entangled state of the…
We study the binary hypothesis testing problem where an adversary may potentially corrupt a fraction of the samples. The detector is, however, permitted to abstain from making a decision if (and only if) the adversary is present. We…
We investigate a state discrimination problem in operationally the most general framework to use a probability, including both classical, quantum theories, and more. In this wide framework, introducing closely related family of ensembles…
There are two common settings in a quantum-state discrimination problem. One is minimum-error discrimination where a wrong guess (error) is allowed and the discrimination success probability is maximized. The other is unambiguous…
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…
We consider the multiple hypothesis testing problem for symmetric quantum state discrimination between r given states \sigma_1,...,\sigma_r. By splitting up the overall test into multiple binary tests in various ways we obtain a number of…
This paper studies distributed binary test of statistical independence under communication (information bits) constraints. While testing independence is very relevant in various applications, distributed independence test is particularly…
We consider two different optimized measurement strategies for the discrimination of nonorthogonal quantum states. The first is conclusive discrimination with a minimum probability of inferring an erroneous result, and the second is…
We introduce a class of states of a composite quantum system, the so-called cross states, that turn out to play a major role in the theory of entanglement for a genuinely infinite-dimensional bipartite system. In the case where at least one…
Error probability is a popular and well-studied optimization criterion in discriminating non-orthogonal quantum states. It captures the threat from an adversary who can only query the actual state once. However, when the adversary is able…
In this paper we present the solution to the problem of optimally discriminating among quantum states, i.e., identifying the states with maximum probability of success when a certain fixed rate of inconclusive answers is allowed. By varying…
This paper investigates symmetric composite binary quantum hypothesis testing (QHT), where the goal is to determine which of two uncertainty sets contains an unknown quantum state. While asymptotic error exponents for this problem are…
One possibility of defining a quantum R\'enyi $\alpha$-divergence of two quantum states is to optimize the classical R\'enyi $\alpha$-divergence of their post-measurement probability distributions over all possible measurements (measured…
The achievable error-exponent pairs for the type I and type II errors are characterized in a hypothesis testing setup where the observation consists of independent and identically distributed samples from either a known joint probability…
We consider the problem of estimating the state of a large but finite number $N$ of identical quantum systems. In the limit of large $N$ the problem simplifies. In particular the only relevant measure of the quality of the estimation is the…
Error bounds are central objects in optimization theory and its applications. They were for a long time restricted only to the theory before becoming over the course of time a field of itself. This paper is devoted to the study of error…
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 discuss the uniqueness of quantum states compatible with given results for measuring a set of observables. For a given pure state, we consider two different types of uniqueness: (1) no other pure state is compatible with the same…
We have determined numerically the maximum quantum violation of over 100 tight bipartite Bell inequalities with two-outcome measurements by each party on systems of up to four dimensional Hilbert spaces. We have found several cases,…
We present a generic study of unambiguous discrimination between two mixed quantum states. We derive operational optimality conditions and show that the optimal measurements can be classified according to their rank. In Hilbert space…