Related papers: Barycentric decomposition of quantum measurements …
In many a traditional physics textbook, a quantum measurement is defined as a projective measurement represented by a Hermitian operator. In quantum information theory, however, the concept of a measurement is dealt with in complete…
We propose a scheme that can realize a class of positive-operator-valued measures (POVMs) by performing a sequence of projective measurements on the original system, in the sense that for an arbitrary input state the probability…
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,…
To mitigate dissipative effects from environmental interactions and efficiently stabilize quantum states, time-optimal control has emerged as an effective strategy for open quantum systems. This paper extends the framework by incorporating…
We show that a partition of the unity (or POVM) on a Hilbert space that is almost orthogonal is close to an orthogonal POVM in the same von Neumann algebra. This generalizes to infinite dimension previous results in matrix algebras by…
It is well-known in quantum information theory that a positive operator valued measure (POVM) is the most general kind of quantum measurement. Mathematically, a quantum probability is a normalised POVM, namely a function on certain subsets…
We present an operationally motivated treatment of quantum reference frames in the setting that the frame is a covariant positive operator valued measure (POVM) on a finite homogeneous space, generalising the principal homogeneous spaces…
Here we propose an implementation of all possible Positive Operator Value Measures (POVMs) of two-photon polarization states. POVMs are the most general class of quantum measurements. Our setup requires linear optics, Bell State…
We consider positive operator valued measures whose image is the bounded operators acting on an infinite-dimensional Hilbert space, and we relax, when possible, the usual assumption of positivity of the operator valued measure seen in 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…
This paper presents an overview of close parallels that exist between the theory of positive operator-valued measures (POVMs) associated with a separable Hilbert space and the theory of frames on that space, including its most important…
In quantum estimation for a $d$-parameter family of density operators on a finite-dimensional Hilbert space $\mathcal{H}$, an estimator is specified by a pair $\left(M,\hat{\theta}\right)$, where $M$ is a POVM with a finite outcome set…
The notion of Symmetric Informationally Complete Positive Operator-Valued Measures (SIC-POVMs) arose in physics as a kind of optimal measurement basis for quantum systems. However the question of their existence is equivalent to that of the…
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…
A solution to the second measurement problem, determining what prior microscopic properties can be inferred from measurement outcomes ("pointer positions"), is worked out for projective and generalized (POVM) measurements, using consistent…
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…
In a previous paper we have presented a general scheme for the implementation of symmetric generalized measurements (POVMs) on a quantum computer. This scheme is based on representation theory of groups and methods to decompose matrices…
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…
We introduce several notions of random positive operator valued measures (POVMs), and we prove that some of them are equivalent. We then study statistical properties of the effect operators for the canonical examples, obtaining limiting…
Concentrating on finite dimensional systems, we show that one can limit to extremal rank-1 POVMs if two simple procedures of mixing and relabeling are permitted. We demonstrate that any finite outcome POVM can be obtained from extremal…