Related papers: Unambiguous pure state identification without clas…
The problem of quantum state classification asks how accurately one can identify an unknown quantum state that is promised to be drawn from a known set of pure states. In this work, we introduce the notion of $k$-learnability, which…
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 problem of discriminating the state of a quantum system among a number of hypothetical states is usually addressed under the assumption that one has perfect knowledge of the possible states of the system. In this thesis, I analyze the…
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…
Quantum state discrimination is a fundamental task that is meaningful in quantum information theory. In this manuscript, we consider a revised unambiguous discrimination of quantum resources. First, we present an upper bound of the success…
We study an optimum measurement for quantum state discrimination, which maximizes the probability of correct results when the probability of inconclusive results is fixed at a given value. The measurement describes minimum-error…
In this paper, we discuss the problem of determining whether a quantum system is in a pure state, or in a mixed state. We apply two strategies to settle this problem: the unambiguous discrimination and the maximum confidence discrimination.…
We prove that the states secretly chosen from a mixed state set can be perfectly discriminated if and only if these states are orthogonal. The sufficient and necessary condition when nonorthogonal quantum mixed states can be unambiguously…
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…
In this article, we study the problem of comparing mixed quantum states: given $n$ unknown mixed quantum states, can one determine whether they are identical or not with an unambiguous quantum measurement? We first study universal…
Suppose you receive a sequence of qubits where each qubit is guaranteed to be in one of two pure states, but you do not know what those states are. Your task is to determine the states. This can be viewed as a kind of quantum state learning…
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 present a solution of the problem of the optimal unambiguous comparison of two ensembles of unknown quantum states (psi_1)^k and (psi_2)^l. We consider two cases: 1) The two unknown states psi_1 and psi_2 are arbitrary states of qudits.…
We analyze the optimal unambiguous discrimination of two arbitrary mixed quantum states. We show that the optimal measurement is unique and we present this optimal measurement for the case where the rank of the density operator of one of…
We establish a sharp quantum advantage in determining the parity (even/odd) of an unknown permutation applied to any number $n \ge 3$ of particles. Classically, this is impossible with fewer than $n$ labels, being that the success is…
Two unknown states can be unambiguously distinguished by a universal programmable discriminator, which has been widely discussed in previous works and the optimal solution has also been obtained. In this paper, we investigate the…
A bipartite state which is secretly chosen from a finite set of known entangled pure states cannot be immediately useful in standard quantum information processing tasks. To effectively make use of the entanglement contained in this unknown…
We investigate the performance of discrimination strategy in the comparison task of known quantum states. In the discrimination strategy, one infers whether or not two quantum systems are in the same state on the basis of the outcomes of…
We discuss the problem of designing an unambiguous programmable discriminator for mixed quantum states. We prove that there does not exist such a universal unambiguous programmable discriminator for mixed quantum states that has two program…
We extend the concept of probabilistic unambiguous discrimination of quantum states to quantum state estimation. We consider a scenario where the measurement device can output either an estimate of the unknown input state or an inconclusive…