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Maximum likelihood estimation is applied to the determination of an unknown quantum measurement. The measuring apparatus performs measurements on many different quantum states and the positive operator-valued measures governing the…
The quantum formalism permits one to discriminate sometimes between any set of linearly-independent pure states with certainty. We obtain the maximum probability with which a set of equally-likely, symmetric, linearly-independent states can…
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…
Quantum mechanics predicts the existence of intrinsically random processes. Contrary to classical randomness, this lack of predictability can not be attributed to ignorance or lack of control. Here we find the optimal method to quantify the…
Measurements approaching the ultimate quantum limits of sensitivity are central in quantum information processing, quantum metrology, and communication. Quantum measurements to discriminate multiple states at the single-photon level are…
Since quantum coherence is an undoubted characteristic trait of quantum physics, the quantification and application of quantum coherence has been one of the long-standing central topics in quantum information science. Within the framework…
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…
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 introduce sequential analysis in quantum information processing, by focusing on the fundamental task of quantum hypothesis testing. In particular our goal is to discriminate between two arbitrary quantum states with a prescribed error…
If only limited control over a multiparticle quantum system is available, a viable method to characterize correlations is to perform random measurements and consider the moments of the resulting probability distribution. We present…
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…
Quantum measurements, alongside quantum states and processes, form a cornerstone of quantum information processing. However, unlike states and processes, their efficient characterisation remains relatively unexplored. We resolve this…
In this paper we investigate the connection between quantum information theory and machine learning. In particular, we show how quantum state discrimination can represent a useful tool to address the standard classification problem in…
We investigate the role of symmetric quantum cloning machines (QCMs) in quantifying the mutual incompatibility of quantum observables. Specifically, we identify a cloning-based incompatibility measure whereby the incompatibility of a set of…
We study the optimization of any quantum process by minimizing the "randomness" in the measurement result at the output of that quantum process. We conceptualize and propose a measure of such randomness and inquire whether an optimization…
The onset of the era of fully-programmable error-corrected quantum computers will be marked by major breakthroughs in all areas of science and engineering. These devices promise to have significant technological and societal impact, notable…
We consider the problem of discriminating qubit states that are sent over a quantum channel and derive a necessary and sufficient condition for an optimal measurement to be preserved by the channel. We apply the result to the…
We derive general discrimination of quantum states chosen from a certain set, given initial $M$ copies of each state, and obtain the matrix inequality, which describe the bound between the maximum probability of correctly determining and…
We analyze the optimal measurements accessing classical correlations in arbitrary two-qubit states. Two-qubit states can be transformed into the canonical forms via local unitary operations. For the canonical forms, we investigate the…
When performing maximum-likelihood quantum-state tomography, one must find the quantum state that maximizes the likelihood of the state given observed measurements on identically prepared systems. The optimization is usually performed with…