Hi all,
This week, Simon Fuchs will tell us about “A Generalisation of Reflected Entropy”, see below for the abstract. The talk will take place on Thursday at 11:00 in HIT F 13.
Best, Ladina
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Title:
A Generalisation of Reflected Entropy
Abstract:
Holographic theories are quantum field theories for which there exists a dictionary that translates quantum observables into geometrical quantities. This allows us to assign geometrical meaning to correlation measures, in analogy to the black hole entropy. In this context, reflected entropy was introduced and a geometric dual was conjectured. This is enticing as reflected entropy is a witness of non-bipartite correlations, allowing for a geometric indicator of an otherwise elusive phenomenon.
Despite its early success, reflected entropy was found to be non-monotonic: it can increase after tracing out a subsystem. Thus, it cannot make quantitative measurements of correlation, motivating the search for an alternative.
In my semester project, we analyse such a candidate: twofold replica entropy. Based on the replica trick—a technique used in some quantum gravity approaches—it generalises the definition of reflected entropy. Whether this alternative can save the principle of reflected entropy remains uncertain. We find that the version of twofold replica entropy that limits itself to replicas with pure composite state reproduces the main flaw of reflected entropy: non-monotonicity. While many properties of general twofold replica entropy remain unknown due to its more complex definition, we can show that it differs from its pure counterpart.