Entropy inequalities and Bell inequalities for two-qubit systems

Abstract

Sufficient conditions for the non-violation of the Bell-CHSH inequalities in a mixed state of a two-qubit system are: 1) The linear entropy of the state is not smaller than 1/2, 2) The sum of the conditional linear entropies is not negative, 3) The von Neumann entropy is not smaller than 0.833, 4) The sum of the conditional von Neumann entropies is not smaller than 0.280.

The quantum moment problem and bounds on entangled multi-prover games

“…the Bell-CH inequality), or a Bell correlation inequality, we will collapse each block matrix and write it as a single number. 12 The other tight Bell inequalities are trivial in the sense that they either require probabilities to be non-negative or not larger than unity. 13 Hereafter, we will drop the arguments of S LHV for brevity of notation.…”

“…12 The other tight Bell inequalities are trivial in the sense that they either require probabilities to be non-negative or not larger than unity. 13 Hereafter, we will drop the arguments of S LHV for brevity of notation.…”

Introduction to Quantum Entanglement

“…Thus the entanglement witness is difficult to use. Construction a entanglement witnesses for different classes of entangled states are described in [21,23,22].…”

Many body localization in Heisenberg XXZ magnet in a random field

“…This indicates that the system probably displays the same kind of localization also for smaller magnetic field strength. If this is the case, transition in level spacing statistics observed in 12,13 might be just due to finite size effects (localization length being larger than the system size).…”

“…Later, the influence of the disorder on the entanglement has been studied for single particle states 10 and for quantum computer simulating single particle localization 11 . Disordered Heisenberg model and entanglement properties of its eigenstates has been studied in 12 where a transition in level spacing distribution from Poissonian for no disorder, to Wigner-Dyson distribution of random matrix theory, and back to Poissonian in the case of localization, has been observed as the disorder amplitude is increased. Spectral statistics for interacting disordered system has been also studied in 13 , sugesting the existence of localization for sufficiently strong disorder.…”