High Energy Physics

Primordial black holes (PBHs) can appear from early Universe dynamics. We show that some or all of heavy element abundance from r-process nucleosynthesis can be produced in interactions of tiny primordial black holes with neutron stars (NSs), if PBHs make up a few percent or more of the dark matter. A PBH captured by a NS will eventually consume it. For a rapidly rotating pulsar, the resulting star spin-up will eject significant amount of cold neutron rich material. The ejection, decompression and decay of nuclear matter can produce electromagnetic transients, like kilonovae and fast radio bursts. Beta decay of ejected material yields positron emission consistent with the observed 511 keV-line from the Galactic Center. Lack of accompanying gravity wave (GW) signal and neutrino emission allows to distinguish these events from supernovae and compact object mergers. Finally, if the consumed star was part of a binary system, long after the event a distinct detectable GW signal from the binary merger with an atypically small solar mass BH will carry information about star's destruction.

In quantum theory, there can exist correlations between subsystems of a new kind that are absent in classical systems. These correlations are nowadays called "entanglement".

An entanglement measure is a functional on states quantifying the amount of entanglement across two subsystems (i.e. causally disjoint regions in the context of quantum field theory). A reasonable measure should satisfy certain general properties: for example, it should assign zero entanglement to separable states, and be monotonic under separable, completely positive maps ("LOCC-operations"). The v. Neumann entropy of the "reduced state" (to one of the subsystems) is one such measure if the state for the total system is pure. But for mixed states, it is not, and one has to consider other measures. In particular, one has to consider other measures if the subsystems have a finite non-zero distance.

In this talk I will present several good measures, and in particular analyze the « relative entanglement entropy", $E_R$, defined as the "distance" of the given state to the set of separable states, where "distance" is defined using Araki's relative entropy. I will show several features of this measure for instance: (i) charged states, where the relative entanglement entropy is related to the quantum dimension of the charge, (ii) vacuum states in 1+1 dimensional integrable models, (iii) general upper bounds for certain special regions in general CFTs in d dimensions, (iv) area law type bounds. I will also explain the relationship between $E_R$ and other entanglement measures, such as distillable entropy.

[Based on joint work with Jacobus Sanders.]