Abstract
Quantum systems generally exhibit different kinds of correlations. In order to compare them on equal footing, one uses the so-called distance-based approach where different types of correlations are captured by the distance to different sets of states. However, these quantifiers are usually hard to compute as their definition involves optimization aiming to find the closest states within the set. On the other hand, negativity is one of the few computable entanglement monotones, but its comparison with other correlations required further justification. Here we place negativity as part of a family of correlation measures that has a distance-based construction. We introduce a suitable distance, discuss the emerging measures and their applications, and compare them to relative entropy-based correlation quantifiers. This work is a step towards correlation measures that are simultaneously comparable and computable.
Highlights
A common answer to this question is to define the amount of correlation as a distance to a set of uncorrelated states [7, 8], in the same spirit as monotones introduced in the framework of resource theories [9]
As an upper bound to this task, we expect that the partial transpose distance is contractive under PPT operations
We introduced partial transpose distance and explored its connection to negativity — a computable entanglement monotone
Summary
In the simplest case of bipartite systems, we typically distinguish classical correlations, quantum discord, quantum entanglement, quantum steering, and Bell nonlocality [1] These correlations form a hierarchical structure [2], can be measured by a variety of quantifiers [3, 4], which even for entanglement are generally not comparable as they lead to different ordering of entangled states [5, 6]. The distance from a given state to the set of separable states quantifies the amount of quantum entanglement, the distance to the so-called classical states defines quantum discord, and the distance to product states gives rise to total correlation. These quantifiers are comparable because the same distance measure is used and one only modifies the set of uncorrelated states. We present exact expressions of the resulting quantifiers for certain classes of states and discuss their applications to detection of non-decomposability and non-Markovianity of dynamics
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