Related papers: On a conjecture regarding quantum hypothesis testi…
In the problem of composite hypothesis testing, identifying the potential uniformly most powerful (UMP) unbiased test is of great interest. Beyond typical hypothesis settings with exponential family, it is usually challenging to prove the…
The fidelity of two pure states (also known as transition probability) is a symmetric function of two operators, and well-founded operationally as an event probability in a certain preparation-test pair. Motivated by the idea that the…
A theorem of Davies states that for symmetric quantum states there exists a symmetric POVM maximizing the mutual information. To apply this theorem the representation of the symmetry group has to be irreducible. We obtain a similar yet…
Given a quantum system consisting of many parts, we show that symmetry of the system's state, i.e., invariance under swappings of the subsystems, implies that almost all of its parts are virtually identical and independent of each other.…
In this paper for a class of symmetric multiparty pure states we consider a conjecture related to the geometric measure of entanglement: 'for a symmetric pure state, the closest product state in terms of the fidelity can be chosen as a…
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 nonparametric testing in a non-asymptotic framework. Our statistical guarantees are exact in the sense that Type I and II errors are controlled for any finite sample size. Meanwhile, one proposed test is shown to achieve minimax…
Classical probability theory is based on assumptions which are often violated in practice. Therefore quantum probability is a proposed alternative not only in quantum physics, but also in other sciences. However, so far it mostly criticizes…
Correlation self-testing of quantum theory involves identifying a task or set of tasks whose optimal performance can be achieved only by theories that can realise the same set of correlations as quantum theory in every causal structure.…
One of the key tasks in physics is to perform measurements in order to determine the state of a system. Often, measurements are aimed at determining the values of physical parameters, but one can also ask simpler questions, such as "is the…
We present a theoretical study of minimum error probability discrimination, using quantum- optical probe states, of M optical phase shifts situated symmetrically on the unit circle. We assume ideal lossless conditions and full freedom for…
We study incompatibility of measurements and its relation to steering and nonlocality in a class of finite dimensional general probabilistic theories (GPT).The basic idea is to represent finite collections of measurements as affine maps of…
We consider the classical sequential binary hypothesis testing problem in which there are two hypotheses governed respectively by distributions $P_0$ and $P_1$ and we would like to decide which hypothesis is true using a sequential test. It…
We develop an asymptotic theory of estimation of a shift parameter in a pure quantum state to study the relation between entangled and unentangled covariant estimates in the analytically most transparent way. After recollecting basics of…
When preparing a pure state with a quantum circuit, there is an unavoidable approximation error due to the compilation error in fault-tolerant implementation. A recently proposed approach called probabilistic state synthesis, where the…
In the simple quantum hypothesis testing problem, upper bound with asymmetric setting is shown by using a quite useful inequality by Audenaert et al, quant-ph/0610027, which was originally invented for symmetric setting. Using this upper…
We consider an ideal experiment in which unlimited nonprojective quantum measurements are sequentially performed on a system that is initially entangled with a distant one. At each step of the sequence, the measurements are randomly chosen…
Quantum illumination is a technique for detecting the presence of a target in a noisy environment by means of a quantum probe. We prove that the two-mode squeezed vacuum state is the optimal probe for quantum illumination in the scenario of…
The symmetric subpace has many applications in quantum information theory. This review article begins by explaining key background facts about the symmetric subspace from a quantum information perspective. Then we review, and in some places…
Measurement incompatibility is one of the basic aspects of quantum theory. Here we study the structure of the set of compatible -- i.e. jointly measurable -- measurements. We are interested in whether or not there exist compatible…