Related papers: POVM Quantization
We investigate the following generalisation of the entropy of quantum measurement. Let H be an infinite-dimensional separable Hilbert space with a 'density' operator {\rho}, tr {\rho}=1. Let I(P)\in R be defined for any partition P =…
It is proposed a possible new approach of quantum measurements (QMS), disconnected of the traditional interpretation of uncertainty relations and independent of any appeal to the strange idea of collapse (reduction) of wave functions. The…
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 Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties…
Hilbert space combines the properties of two fundamentally different types of mathematical spaces: vector space and metric space. While the vector-space aspects of Hilbert space, such as formation of linear combinations of state vectors,…
Quantum systems with real energies generated by an apparently non-Hermitian Hamiltonian may re-acquire the consistent probabilistic interpretation via an ad hoc metric which specifies the set of observables in the updated Hilbert space of…
The fundamental principles of complementarity and uncertainty are shown to be related to the possibility of joint unsharp measurements of pairs of noncommuting quantum observables. A new joint measurement scheme for complementary…
Quantum measurements play a fundamental role in quantum information. Therefore, increasing efforts are being made to construct symmetric measurement operators for qudit systems. A wide class of projective measurements corresponds to complex…
Recently foundational issues of applicability of the formalism of quantum mechanics (QM) to cognitive psychology, decision making, and psychophysics attracted a lot of interest. In particular, in \cite{DKBB} the possibility to use of the…
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,…
Randomness is a central feature of quantum mechanics and an invaluable resource for both classical and quantum technologies. Commonly, in Device-Independent and Semi-Device-Independent scenarios, randomness is certified using projective…
Observables and instruments have played significant roles in recent studies on the foundations of quantum mechanics. Sequential products of effects and conditioned observables have also been introduced. After an introduction in Section~1,…
The concept of quantum coherence and its possible use as a resource are currently the subject of active researches. Uncertainty and complementarity relations for quantum coherence allow one to study its changes with respect to other…
We address the class of positive operator-valued measures (POVMs) for qubit systems that are obtained by coupling the signal qubit with a probe qubit and then performing a projective measurement on the sole probe system. These POVMs, which…
According to the Kolmogorovian Censorship Hypothesis, everything that quantum theory says about the world in the language of the quantum mechanical Hilbert space formalism is actually about relationships between ordinary relative…
Several quantities of interest in quantum information, including entanglement and purity, are nonlinear functions of the density matrix and cannot, even in principle, correspond to proper quantum observables. Any method aimed to determine…
The positive operator valued measure (POVM) for a photon counting array detector is derived and found to equal photon flux density integrated over pixel area and measurement time. Since photon flux density equals number density multiplied…
The goal of comparison is to reveal the difference of compared objects as fast and reliably as possible. In this paper we formulate and investigate the unambiguous comparison of unknown quantum measurements represented by non-degenerate…
Modal interpretations have the ambition to construe quantum mechanics as an objective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but…
We propose a scheme to implement general quantum measurements, also known as Positive Operator Valued Measures (POVMs) in dimension $d$ using only classical resources and a single ancillary qubit. Our method is based on the probabilistic…