Related papers: Minimum-error discrimination between a pure and a …
Quantum hypothesis testing (QHT) provides an effective method to discriminate between two quantum states using a two-outcome positive operator-valued measure (POVM). Two types of decision errors in a QHT can occur. In this paper we focus on…
We study the discrimination of N mixed quantum states in an optimal measurement that maximizes the probability of correct results while the probability of inconclusive results is fixed at a given value. After considering the discrimination…
The discrimination of non-orthogonal quantum states with reduced or without errors is a fundamental task in quantum measurement theory. In this work, we investigate a quantum measurement strategy capable of discriminating two coherent…
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…
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…
We consider the problem of designing an optimal quantum detector that distinguishes unambiguously between a collection of mixed quantum states. Using arguments of duality in vector space optimization, we derive necessary and sufficient…
Based on our previous publication [U. Herzog and J. A. Bergou, Phys.Rev. A 71, 050301(R) (2005)] we investigate the optimum measurement for the unambiguous discrimination of two mixed quantum states that occur with given prior…
We relate the the distinguishability of quantum states with their robustness of the entanglement, where the robustness of any resource quantifies how tolerant it is to noise. In particular, we identify upper and lower bounds on the…
The necessary and sufficient conditions for minimization of the generalized rate error for discriminating among $N$ pure qubit states are reformulated in terms of Bloch vectors representing the states. For the direct optimization problem an…
Quantum state elimination measurements tell us what states a quantum system does not have. This is different from state discrimination, where one tries to determine what the state of a quantum system is, rather than what it is not. Apart…
In this paper, we consider the problem of unambiguous discrimination between a set of mixed quantum states. We first divide the density matrix of each mixed state into two parts by the fact that it comes from ensemble of pure quantum…
The distinction between pure states and mixed states is a kernel ingredient of what is considered to be the standard formulation of quantum mechanics and plays today a kernel role in foundational debates about the meaning of quantum…
There are fundamental limits to the accuracy with which one can determine the state of a quantum system. I give an overview of the main approaches to quantum state discrimination. Several strategies exist. In quantum hypothesis testing, a…
The minimum-error probability of ambiguous discrimination for two quantum states is the well-known {\it Helstrom limit} presented in 1976. Since then, it has been thought of as an intractable problem to obtain the minimum-error probability…
In this thesis we study the problem of unambiguously discriminating two mixed quantum states. We first present reduction theorems for optimal unambiguous discrimination of two generic density matrices. We show that this problem can be…
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…
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…
The problem of optimally discriminating between two completely unknown qubit states is generalized by allowing an error margin. It is visualized as a device---the programmable discriminator---with one data and two program ports, each fed…
We investigate the discrimination of pure-mixed (quantum filtering) and mixed-mixed states and compare their optimal success probability with the one for discriminating other pairs of pure states superposed by the vectors included in the…