Related papers: The optimal positive operator-valued measure for s…
We consider the problem of discrimination between two pure quantum states. It is well known that the optimal measurement under both the error-probability and log-loss criteria is a projection, while under an ``erasure-distortion'' criterion…
We show that information gain in a qubit measurement is optimal under a Von Neumann measurement. For an initially mixed apparatus kept in touch with a qubit, the conditions for achieving the equality sign of Holevo bound on the information…
Every sufficiently rich set of measurements on a fixed quantum system defines a statistical norm on the states of that system via the optimal bias that can be achieved in distinguishing the states using measurements from that set (assuming…
In the signal-processing literature, a frame is a mechanism for performing analysis and reconstruction in a Hilbert space. By contrast, in quantum theory, a positive operator-valued measure (POVM) decomposes a Hilbert-space vector for the…
We introduce positive operator-valued measure (POVM) generated by the projective unitary representation of a direct product of locally compact Abelian group $G$ with its dual $\hat G$. The method is based upon the Pontryagin duality…
We consider the optimal discrimination of nonorthogonal qubit states with post-measurement information and provide an analytic structure of the optimal measurements. We also show that there is always a null optimal measurement when…
We consider measurements, described by a positive-operator-valued measure (POVM), whose outcome probabilities determine an arbitrary pure state of a D-dimensional quantum system. We call such a measurement a pure-state informationally…
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…
It is a fundamental property of quantum mechanics that information is lost as a result of performing measurements. Indeed, with every quantum measurement one can associate a number -- its POVM norm constant -- that quantifies how much the…
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…
We compare several instances of pure-state Belavkin weighted square-root measurements from the standpoint of minimum-error discrimination of quantum states. The quadratically weighted measurement is proven superior to the so-called "pretty…
Quantum state tomography is a fundamental problem in quantum computing. Given $n$ copies of an unknown $N$-qubit state $\rho \in \mathbb{C}^{d \times d},d=2^N$, the goal is to learn the state up to an accuracy $\epsilon$ in trace distance,…
We present a technique for performing quantum detector tomography (QDT) of phase insensitive quantum detectors, a category under which many detectors of interest fall under, using gradient descent-based optimization to learn the positive…
The problem of non-orthogonal state discrimination underlies crucial quantum information tasks, such as cryptography and computing protocols. Therefore, it is decisive to find optimal scenarios for discrimination among quantum states. We…
We derive the optimal measurement for quantum state discrimination without a priori probabilities, i.e. in a minimax strategy instead of the usually considered Bayesian one. We consider both minimal-error and unambiguous discrimination…
Informationally complete measurements on a quantum system allow to estimate the expectation value of any arbitrary operator by just averaging functions of the experimental outcomes. We show that such kind of measurements can be achieved…
We present a local-hidden-variable model for positive-operator-valued measurements (an LHVPOV model) on a class of entangled generalized Werner states, thus demonstrating that such measurements do not always violate a Bell-type inequality.…
A suitable generalized measurement described by a 4-element positive operator-valued measure (POVM) on each particle of a two-qubit system in the singlet state is, from the point of view of Einstein, Podolsky, and Rosen's (EPR's) criterion…
Self-testing represents the strongest form of certification of a quantum system. Here we investigate theoretically and experimentally the question of self-testing non-projective quantum measurements. That is, how can one certify, from…
Distinguishing assigned quantum states with assigned probabilities via quantum measurements is a crucial problem for the transmission of classical information through quantum channels. Measurement operators maximizing the probability of…