Related papers: Unambiguous discrimination of mixed states
The optimal and minimal measuring strategy is obtained for a two-state system prepared in a mixed state with a probability given by any isotropic a priori distribution. We explicitly construct the specific optimal and minimal generalized…
We present reduction theorems for the problem of optimal unambiguous state discrimination (USD) of two general density matrices. We show that this problem can be reduced to that of two density matrices that have the same rank $n$ and are…
We present three necessary separability criteria for bipartite mixed states, the violation of each of these conditions is a sufficient condition for entanglement. Some ideas on the issue of finding a necessary and sufficient criterion of…
By combining the Minkowski inequality and the quantum Chernoff bound, we derive easy-to-compute upper bounds for the error probability affecting the optimal discrimination of Gaussian states. In particular, these bounds are useful when the…
The necessary and sufficient condition of separability of a mixed state of any systems is presented, which is practical in judging the separability of a mixed state. This paper also presents a method of finding the disentangled…
In this paper we consider the problem of unambiguous discrimination between a set of linearly independent pure quantum states. We show that the design of the optimal measurement that minimizes the probability of an inconclusive result can…
We show that the quantum measurement known as the pretty good measurement can be used to identify an unknown quantum state picked from any set of $n$ mixed states that have pairwise fidelities upper-bounded by a constant below 1, given…
We formulate the necessary and sufficient conditions for the existence of a pair of maximally incompatible two-outcome measurements in a finite dimensional General Probabilistic Theory. The conditions are on the geometry of the state space,…
We present theory and experiment for the task of discriminating two nonorthogonal states, given multiple copies. We implement several local measurement schemes, on both pure states and states mixed by depolarizing noise. We find that…
In the present paper I formulate a framework that accommodates many unambiguous discrimination problems. I show that the prior information about any type of constituent (state, channel, or observable) allows us to reformulate the…
Quantum state discrimination, alongside its other applications, has recently found use as a tool for witnessing generalised contextuality. In this article, we derive noncontextuality inequalities for both conclusive and inconclusive…
We address perfect discrimination of two separable states. When available states are restricted to separable states, we can theoretically consider a larger class of measurements than the class of measurements allowed in quantum theory. The…
Sequential methods for quantum hypothesis testing offer significant advantages over fixed-length approaches, which rely on a predefined number of state copies. Despite their potential, these methods remain underexplored for unambiguous…
The theory of generalised measurements is used to examine the problem of discriminating unambiguously between non-orthogonal pure quantum states. Measurements of this type never give erroneous results, although, in general, there will be a…
It is shown that local distinguishability of orthogonal mixed states can be completely characterized by local distinguishability of their supports irrespective of entanglement and mixedness of the states. This leads to two kinds of upper…
In this paper, we propose a method to discriminate two extremely similar quantum states via a weak measurement. For the two states with equal prior probabilities, the optimum discrimination probability given by Ivanovic-Dieks-Peres limit…
Quantum state discrimination is a fundamental primitive in quantum statistics where one has to correctly identify the state of a system that is in one of two possible known states. A programmable discrimination machine performs this task…
We introduce algebraic sets in the complex projective spaces for the mixed states in bipartite quantum systems as their invariants under local unitary operations. The algebraic sets of the mixed state have to be the union of the linear…
State discrimination with the aim to minimize the error probability is a well studied problem. Instead, here the binary decision problem for operators with a given prior is investigated. A black box containing the unknown operator is probed…
We address the problem of distinguishing among a finite collection of quantum states, when the states are not entirely known. For completely specified states, necessary and sufficient conditions on a quantum measurement minimizing the…