Incompatibility breaking quantum channels

Abstract

Abstract. A typical bipartite quantum protocol, such as EPRsteering, relies on two quantum features, entanglement of states and incompatibility of measurements. Noise can delete both of these quantum features. In this work we study the behavior of incompatibility under noisy quantum channels. The starting point for our investigation is the observation that compatible measurements cannot become incompatible by the action of any channel. We focus our attention to channels which completely destroy the incompatibility of various relevant sets of measurements. We call such channels incompatibility breaking, in analogy to the concept of entanglement breaking channels. This notion is relevant especially for the understanding of noise-robustness of the local measurement resources for steering.

Dynamics of incompatibility of quantum measurements in open systems

“…Hence one expects that the incompatibility function (14) will eventually decrease to zero under the assumption (15). The purpose of the present paper is to study the behaviour of the function (14) for certain concrete choices of the dynamical map Λ t on two-level systems, using the incompatibility monotone (7).…”

“…One should notice the following important observation [6,8,15]: the nonexistence of the hidden state model for the correlations P(i, j|a, b) is equivalent to incompatibility of Alice's noisy local observables…”

“…Our starting point was the general result on incompatibility breaking channels [15], which says that sudden death of initially maximal entanglement always implies sudden death of all incompatibility, while the converse is not true. We investigated this phenomenon in the specific physically relevant settings.…”

Unsharp Measurements and Joint Measurability

“…In addition to bringing out the fact that measurement compatibility is not synonymous with commutativity of the observables, these research efforts highlight the quantum resource nature of incompatible measurements. There are ongoing investigations recently, which focus towards developing a resource theory of measurement incompatibility 16,17 .…”

“…While sharp values for non-commuting observables can not be assigned jointly via their PV measurements, their unsharp joint values could be perceived when compatible POVMs are employed. Active research efforts are dedicated to investigate operationally significant criteria of joint measurability (compatibility) of two or more POVMs and also to develop a resource theory of measurement incompatibility [5][6][7][8][9][10][11][12][13][14][15][16][17] . In this paper, we review the notion of compatible POVMs in the generalized measurement setting.…”