Related papers: On the convex structure of process POVMs
It is the purpose of the present contribution to demonstrate that the generalization of the concept of a quantum mechanical observable from the Hermitian operator of standard quantum mechanics to a positive operator-valued measure is not a…
In this paper, a characterization of maps between quantum states that preserve pure states and strict convex combinations is obtained. Based on this characterization, a structural theorem for maps between multipartite quantum states that…
It is a well-known fact that the optimal POVM for quantum state tomography is the symmetric, informationally complete, positive operator valued measure (SIC-POVM). We investigate the same problem only in the case when there are some a…
We introduce a concept of a minimal sufficient positive-operator valued measure (POVM), which is the least redundant POVM among the POVMs that have the equivalent information about the measured quantum system. Assuming the system Hilbert…
Weighted cone-volume functionals are introduced for the convex polytopes in $\mathbb{R}^n$. For these functionals, geometric inequalities are proved and the equality conditions are characterized. A variety of corollaries are derived,…
State transformations in quantum mechanics are described by completely positive maps which are constructed from quantum channels. We call a finest sharp quantum channel a context. The result of a measurement depends on the context under…
In this paper, we consider the convex set of $d$ dimensional unital quantum channels. In particular, we parametrise a family of maps and through this parametrisation we provide a partial characterisation of the set of unital quantum maps…
A photodetector may be characterized by various figures of merit such as response time, bandwidth, dark count rate, efficiency, wavelength resolution, and photon-number resolution. On the other hand, quantum theory says that any measurement…
Measurements in quantum theory exhibit incompatibility, i.e., they can fail to be jointly measurable. An intuitive way to represent the (in)compatibility relations among a set of measurements is via a hypergraph representing their joint…
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 study the distinguishability norms associated to families of locally restricted POVMs on multipartite systems. These norms (introduced by Matthews, Wehner and Winter) quantify how quantum measurements, subject to locality constraints,…
We determine the extreme points of the convex set of covariant phase observables. Such extremals describe the best phase parameter measurements of laser light - the best in the sense that they are free from classical randomness due to…
Quantum instruments describe outcome probability as well as state change induced by measurement of a quantum system. Incompatibility of two instruments, i. e. the impossibility to realize them simultaneously on a given quantum system,…
In the measurement-based quantum computing, there is a natural "causal cone" among qubits of the resource state, since the measurement angle on a qubit has to depend on previous measurement results in order to correct the effect of…
This paper studies system theoretic properties of the class of difference inclusions of convex processes. We will develop a framework considering eigenvalues and eigenvectors, weakly and strongly invariant cones, and a decomposition of…
The Wigner Phase Operator (WPO) is identified as an operator valued measure (OVM) and its eigen states are obtained. An operator satisfying the canonical commutation relation with the Wigner phase operator is also constructed and this…
We describe a construction of ordered algebraic structures (ordered abelian semigroups, ordered commutative semirings, etc.) and describe applications to codimension-1 laminations. For a suitable ordered semi- algebraic structure $\mathbb…
Generalized quantum measurements play a crucial role in quantum mechanics, and symmetric informationally complete positive operator-valued measurements (SIC POVMs) provide a powerful and flexible framework for extracting information from…
In the device-independent scenario, positive operator-valued measurements (POVMs) can certify more randomness than projective measurements. This paper self-tests a three-outcome extremal qubit POVM in the X-Z plane of the Bloch sphere by…
How much unavoidable randomness is generated by a Positive Operator Valued Measure (POVM)? We address this question using two complementary approaches. First we study the variance of a real variable associated to the POVM outcomes. In this…