Negative probabilities and measurement disturbance

Andrei Yu. Khrennikov

We study the problem of a simultaneous measurement of incompatible observables in the framework of Prugoveckiis empirical theory of measurement (i.e., the theory where the irreducible errors in individual measurements ought to be taken into account). We propose a solution for the main problem of this theory: negative probability distributions that arise for some states in the probabilistic description of a simultaneous measurement. These probabilities have a meaningful frequency interpretation. However, limits of relative frequencies exist only in a generalized sense and this is only a chaotic oscillation from the ordinary point of view. We present a measurement (i.e., a preparation and determinative measurements) where negative and usual Kolmogorov probabilities might arise. We show that there are two roots of negative probabilities: disturbance effects and the finite exactness of a measurement. Resume : Nous Otudions le problme reliO aux mesures simultanOes diobservables

Klaus Mølmer

D. Aleksandrov, E. Yu. Nikolskii, B.G. Novatskii +1 more

Xue-Min Bai, Jun‐Qi Li, J.-Q. Liang

We investigate in this paper measurement-induced disturbance (MID) and negativity in a two-spin-qutrit model by considering the influence of the external magnetic field, nonlinear coupling parameter, the uniaxial field and temperature. It is shown that all of these parameters play a significant role in negativity and MID. We make an explicit comparison between the negativity and MID and disclose some interesting results. By the way, we find that negativity is a better measure than MID to detect the sudden point in a finite temperature, which is obviously different from the previous findings.

CHRISTOF WETTERICH

Jing Yang, Qi-Xiong Mu, Yanxia Huang

The dynamics of the tripartite thermal entanglement measured by Negativity (N) and the tripartite quantum correlation described by measurement-induced disturbance (MID) under Ornstein–Uhlenbeck noise are investigated. This study has found that the tripartite N and MID can be preserved more effectively in the non-Markovian environment than in the short-time limit and the Markov limit cases. The short-time limit is a better approximation than the Markov limit. MID vanishes only in the asymptotic limit, while entanglement sudden death may occur, and the decreasing duration of MID far outweighs entanglement. This implies that MID is more robust than Negativity. As the noise bandwidth increases, the disentanglement time and the decay time of MID are significantly shorter. The increase of XZX[Formula: see text]+[Formula: see text]YZY three-site interaction is more effective than XZY−YZX three-site interaction to enhance Negativity and MID as well as the disentanglement time. The magnetic field diminishes Negativity and MID, but has no significant influence on the decreasing durations of both Negativity and MID.