Entanglement Negativity Spectrum of Random Mixed States: A Diagrammatic Approach

Page curve for entanglement negativity through geometric evaporation

“…In this article we address this significant issue by computing the entanglement negativity of various mixed state configurations in a bath coupled to a two dimensional non-extremal JT black hole obtained by a partial dimensional reduction of a three dimensional BTZ black hole as described in [20]. We will demonstrate that the entanglement negativity of various bipartite systems in a bath coupled to a non-extremal JT black hole exactly reproduces the analogues of the Page curve for the entanglement negativity of random mixed states which were obtained in [70]. Furthermore we interpret the results we derived in terms of the Hawking quanta collected in various subsystems in the bath and their respective islands.…”

“…Quite inter-estingly, several such techniques involving Harr random unitaries have been utilized to gain insight into the black hole evaporation and the information loss paradox (see [63][64][65][66][67][68][69] and references therein). More recently, very interesting developments have led to the computation of various measures such as the entanglement negativity, mutual information, relative entropy to obtain analogues of the Page curve for these measures in Harr random states [70,71]. In [70] the authors have developed a systematic diagrammatic technique to obtain the entanglement negativity of a a bipartite system in a random mixed state chosen from the Wishart ensemble.…”

“…More recently, very interesting developments have led to the computation of various measures such as the entanglement negativity, mutual information, relative entropy to obtain analogues of the Page curve for these measures in Harr random states [70,71]. In [70] the authors have developed a systematic diagrammatic technique to obtain the entanglement negativity of a a bipartite system in a random mixed state chosen from the Wishart ensemble. This led them to determine the analogues of Page curves for the entanglement negativity for bipartite systems in random mixed states.…”

“…The analogues of such Page curves for the entanglement negativity thus obtained for various configurations of the random states is expected to shed new light on the structure of mixed state entanglement in Hawking radiation. Hence, the discussion above raises the crucial issue of obtaining the analogues of the Page curve for the entanglement negativity in the context of black hole evaporation and compare them to the corresponding results obtained through random matrix technique in [70].…”

“…In section 2 we review the model involving the partial dimensional reduction described in [20] to obtain the Page curve for the entanglement entropy of the entire bath/radiation coupled to a JT black hole. Following this we briefly review [70] where the authors obtain the entanglement negativity of a random bipartite mixed state and then go on to describe the holographic entanglement negativity construction proposed in [43,45]. In section 3 we describe our computation of the entanglement negativity of the pure and mixed state configurations involving disjoint, adjacent and single intervals in a bath C F T 2 coupled to an evaporating non-extremal JT gravity obtained through the partial dimensional reduction of the BTZ black hole.…”