Related papers: Conditional probabilities and density operators in…
We characterize the extremal points of the convex set of quantum measurements that are covariant under a finite-dimensional projective representation of a compact group, with action of the group on the measurement probability space which is…
In this work, the definition of the density operator on quantum states in Hilbert spaces and some of its aspects relevant in thermodynamics and information-theoretical entropy calculations are given. In this framework, a physical model…
We discuss relations between several relativistic spin observables and derive a Lorentz-invariant characteristic of a reduced spin density matrix.A relativistic position operator that satisfies all the properties of its nonrelativistic…
In this Letter, we interpret the Husimi function as the conditional probability density of continuously measuring a stream of constant position and momentum outcomes, indefinitely. This gives rise to an alternative definition that naturally…
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…
We present a parallel between commutative and non-commutative polymorphisms. Our emphasis is the applications to conditional distributions from stochastic processes. In the classical case, both the measures and the positive definite kernels…
Two types of states are widely used in quantum mechanics, namely (deterministic-coefficient) pure states and statistical mixtures. A density operator can be associated with each of them. We here address a third type of states, that we…
Coherent-state representations are a standard tool to deal with continuous-variable systems, as they allow one to efficiently visualize quantum states in phase space. Here, we work out an alternative basis consisting of monomials on the…
This article introduces operator on operator regression in quantum probability. Here in the regression model, the response and the independent variables are certain operator valued observables, and they are linearly associated with unknown…
We provide the most general forms of covariant and normalized time operators and their probability densities, with applications to quantum clocks, the time of arrival, and Lyapunov quantum operators. Examples are discussed of the profusion…
We construct a density matrix whose elements are written in terms of expectation values of non-Hermitian operators and their products for arbitrary dimensional bipartite states. We then show that any expression which involves matrix…
Causality imposes strong restrictions on the type of operators that may be observables in relativistic quantum theories. In fact, causal violations arise when computing conditional probabilities for certain partial causally connected…
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…
We discuss a possibility to build a programmable quantum measurement device (a "quantum multimeter"). That is, a device that would be able to perform various desired generalized, positive operator value measure (POVM) measurements depending…
Contrary to general relativity, quantum theory treats space and time in fundamentally different ways. In particular, while joint probabilities associated with spacelike separated measurements are defined in terms of the Born rule, joint…
Quantum states that possess negative conditional von Neumann entropy provide quantum advantage in several information-theoretic protocols including superdense coding, state merging, distributed private randomness distillation and one-way…
Starting from a new principle inspired by quantum tomography rather than from Born's rule, this paper gives a self-contained deductive approach to quantum mechanics and quantum measurement. A suggestive notion for what constitutes a quantum…
We demonstrate in this paper that the probabilities for sequential measurements have features very different from those of single-time measurements. First, they cannot be modelled by a classical stochastic process. Second, they are…
As has already been pointed out by Birkhoff and von Neumann, quantum logic can be formulated in terms of projective geometry. In three-dimensional Hilbert space, elementary logical propositions are associated with one-dimensional subspaces,…
This article is concerned with crossed products and their applications to random operators. We study the von Neumann algebra of a dynamical system using the underlying Hilbert algebra structure. This gives a particularly easy way to…