Related papers: Informationally Overcomplete POVMs for Quantum Sta…
Recently, it has been argued that quantum mechanics is complete, and that quantum states vectors are necessarily in one-to-one correspondence with the elements of reality, under the assumptions that quantum theory is correct and that…
In this paper we shall introduce the mathematical framework for the description of measurements of quantum processes. Using this framework the process estimation problems can be treated in the similar way as the state estimation problems,…
Many prominent quantum computing algorithms with applications in fields such as chemistry and materials science require a large number of measurements, which represents an important roadblock for future real-world use cases. We introduce a…
Wigner functions provide a way to do quantum physics using quasiprobabilities, that is, "probability" distributions that can go negative. Informationally complete POVMs, a much younger subject than phase space formulations of quantum…
Informationally overcomplete POVMs are known to outperform minimally complete measurements in many tomography and estimation tasks, and they also leave a purely classical freedom in shadow tomography: the same observable admits infinitely…
We report an optical detector with tunable positive operator-valued measures (POVMs). The device is based on a combination of weak-field homodyne techniques and photon-number-resolving detection. The resulting POVMs can be continuously…
The expectation value <O> of an arbitrary operator O can be obtained via a universal measuring apparatus that is independent of O, by changing only the data-processing of the outcomes. Such a ``universal detector'' performs a joint…
In information fusion, one is often confronted with the following problem: given a preexisting set of measurements about an unknown quantity, what new measurements should one collect in order to accomplish a given fusion task with optimal…
We show how an upper bound for the ability to discriminate any number N of candidates for the Hamiltonian governing the evolution of an open quantum system may be calculated by numerically efficient means. Our method applies an effective…
The tight frames can be regarded as a particular case of POVMs (positive operator-valued measures describing generalized measurements), namely the case when all the operators are rank-one. Each orthonormal basis is a tight frame, and every…
We consider a protocol to perform the optimal quantum state discrimination of $N$ linearly independent non-orthogonal pure quantum states and present a computational code. Through the extension of the original Hilbert space, it is possible…
We address the problem of constructing positive operator-valued measures (POVMs) in finite dimension $n$ consisting of $n^2$ operators of rank one which have an inner product close to uniform. This is motivated by the related question of…
The development of quantum information theory has renewed interest in the idea that the state vector does not represent the state of a quantum system, but rather the knowledge or information that we may have on the system. I argue that this…
In quantum-state tomography on sources with quantum degrees of freedom of large Hilbert spaces, inference of quantum states of light for instance, a complete characterization of the quantum states for these sources is often not feasible…
We celebrate this year hundred years of quantum mechanics but there is still no consensus regarding its interpretation and limitations. In this article we advocate the statistical contextual interpretation which is free of paradoxes. State…
We characterize the asymptotic performance of a class of positive operator valued measurements (POVMs) where the only task is to make measurements on independent and identically distributed quantum states on finite-dimensional systems. The…
Quantum coherence is a fundamental feature of quantum physics and plays a significant role in quantum information processing. By generalizing the resource theory of coherence from von Neumann measurements to positive operator-valued…
Quantum coherence is a fundamental feature of quantum mechanics and an underlying requirement for most quantum information tasks. In the resource theory of coherence, incoherent states are diagonal with respect to a fixed orthonormal basis,…
We present a universal algorithm for the optimal quantum state estimation of an arbitrary finite dimensional system. The algorithm specifies a physically realizable positive operator valued measurement (POVM) on a finite number of…
Generalized quantum measurements, described by positive operator-valued measures (POVMs), are essential for modeling realistic processes in open quantum systems. While quantum process tomography can fully characterize a POVM, it is…