Measurement of quantum states and the Wigner function

Rubens Viana Ramos

In this work, the usage of the disentropy of the Wigner function as order and quantumness measure is investigated. Furthermore, the relative disentropy of the Wigner function as a distance measure between two Wigner functions is also discussed. The numerical calculation of the dynamic of the disentropy and relative disentropy of the Wigner function are realized considering an initially pure quantum state that evolves to a classical mixture and when an initially coherent state evolves to a Schrödinger cat state. It is shown that in all cases the disentropy is minimal for the quantum states with maximal quantumness, and it is maximal for maximally ordered states (pure states with positive Wigner function).

Dan Cristian Marinescu, Gabriela M. Marinescu

Amir Kalev, A. Mann, Pier A. Mello +1 more

We study the possibility of giving a classical interpretation to quantum projective measurements for a particle described by a pure Gaussian state whose Wigner function is non-negative. We analyze the case of a projective measurement which gives rise to a proper Wigner function---i.e., taking on, as its values, the eigenvalues of the projector. We find that, despite having this property, this kind of projector produces a state whose Wigner function ceases to be non-negative and hence precludes its interpretation as a classical probability density. We also study the general case in which the projected state has a non-negative Wigner function, but then we find that the Wigner function of the projector is not a proper one. Thus, we conclude that a non-negative Wigner function is inadequate to serve as a hidden-variable model for quantum processes in which projective measurements take place.

Giacomo Mauro D’Ariano

Robert Raussendorf, Cihan Okay, Michael Zurel +1 more

The scheme of quantum computation with magic states, and in particular the role of the Wigner function as an indicator of quantumness, motivate the question of when Clifford-covariant Wigner functions exist, and when Wigner functions exist that represent Pauli measurements positively. This question has been settled affirmatively for all odd dimensions. Here, we discuss the case of even dimension, for Wigner functions obtained from operator bases. We find that such Clifford-covariant Wigner functions do not exist in any even dimension, and furthermore, Pauli measurement cannot be positively represented by them in any even dimension whenever the number of qudits is n >= 2.

Willi-Hans Steeb