Related papers: Negative probabilities
The evolution of the discrete Wigner function is formally similar to a probabilistic process, but the transition probabilities, like the discrete Wigner function itself, can be negative. We investigate these transition probabilities, as…
We show, in a formal way, how a class of complex quasiprobability distribution functions may be introduced by using the fractional Fourier transform. This leads to the Fresnel transform of a characteristic function instead of the usual…
An observation space $\mathcal S$ is a family of probability distributions $\langle P_i: i\in I \rangle$ sharing a common sample space $\Omega$ in a consistent way. A \emph{grounding} for $\mathcal S$ is a signed probability distribution…
We extend the random characteristics approach to Wigner matrices whose entries are not required to have a normal distribution. As an application, we give a simple and fully dynamical proof of the weak local semicircle law in the bulk.
This contribution derives from a rather extensive study on the foundations of probability. We start by discussing critically the two main models of the random event in Probability Theroy and cast light over a number of incongruities. We…
We introduce an experimental test for ruling out classical explanations for the statistics obtained when measuring arbitrary observables at arbitrary times using individual detectors. This test requires some trust in the measurements,…
We introduce a quantum phase space representation for the orientation state of extended quantum objects, using the Euler angles and their conjugate momenta as phase space coordinates. It exhibits the same properties as the standard Wigner…
It is common knowledge that the Wigner function of a quantum state may admit negative values, so that it cannot be viewed as a genuine probability density. Here, we examine the difficulty in finding an entropy-like functional in phase space…
The quasi likelihood analysis is generalized to the partial quasi likelihood analysis. Limit theorems for the quasi likelihood estimators, especially the quasi Bayesian estimator, are derived in the situation where existence of a slow…
I describe a method of inferring the past of quantum observables given the initial state and the subsequent measurement results using Wigner quasi-probability representations. The method is proved to be compatible with logic for large…
We develop a general framework to investigate fluctuations of non-commuting observables. To this end, we consider the Keldysh quasi-probability distribution (KQPD). This distribution provides a measurement-independent description of the…
In this short note we discuss the time-reversal of a quasiprobability distribution of work.
We study the weak values of a quantum observable from the point of view of the Wigner formalism. The main actor is here the cross-Wigner transform of two functions, which is in disguise the cross-ambiguity function familiar from radar…
We analyze quasi probability distributions in discrete phase space related to the discrete Heisenberg-Weyl group. In particular, we discuss the relation between the Discrete Wigner and Q- functions.
We introduce a quasi-probability phase space distribution with two pairs of azimuthal-angular coordinates. This representation is well adapted to describe quantum systems with discrete symmetry. Quantum error correction of states encoded in…
An example shows that weak decoherence is more restrictive than the minimal logical decoherence structure that allows probabilities to be used consistently for quantum histories. The probabilities in the sum rules that define minimal…
We study a generalization of the Wigner function to arbitrary tuples of hermitian operators, which is a distribution uniquely characterized by the property that the marginals for all linear combinations of the given operators agree with the…
In reverse mathematics, is is possible to have a curious situation where we know that an implication does not reverse, but appear to have no information on on how to weaken the assumption while preserving the conclusion. A main cause of…
Given a choice of an ordered, orthonormal basis for a $D$-dimensional Hilbert space, one can define a discrete version of the Wigner function -- a quasi-probability distribution which represents any quantum state as a real, normalized…
Cahill-Glauber C(s)-correspondence is employed to construct Quasi-Probability Distribution Functions (QPDFs) for optical-polarization in phase space following equivalent description of polarization in Classical Optics. The proposed scheme…