Tensor network models of unitary black hole evaporation

Abstract

We introduce a general class of toy models to study the quantum informationtheoretic properties of black hole radiation. The models are governed by a set of isometries that specify how microstates of the black hole at a given energy evolve to entangled states of a tensor product black-hole/radiation Hilbert space. The final state of the black hole radiation is conveniently summarized by a tensor network built from these isometries. We introduce a set of quantities generalizing the Renyi entropies that provide a complete set of bipartite/multipartite entanglement measures, and give a general formula for the average of these over initial black hole states in terms of the isometries defining the model. For models where the dimension of the final tensor product radiation Hilbert space is the same as that of the space of initial black hole microstates, the entanglement structure is universal, independent of the choice of isometries. In the more general case, we find that models which best capture the "information-free" property of black hole horizons are those whose isometries are tensors corresponding to states of tripartite systems with maximally mixed subsystems.

Entanglement features of random Hamiltonian dynamics

“…The randomness in the unitary circuit efficiently removes the basis specific details and allows us to focus on the universal properties of entanglement dynamics. The same philosophy also underlies the recent works [27][28][29][30][31][32][33][34] of using random tensor networks to model entangled many-body states or chaotic unitary evolutions. Due to the lack of time-translation symmetry in the random unitary circuit, energy is not conserved under random unitary dynamics, which obscure its application to problems like energy transport.…”

Quantum information in Hawking radiation

“…Many conceptual models in the literature [11][12][13][14][15][16][17] posit that the quantum degrees of freedom of a black hole are discrete, which leads to an assumption of H BH being finite-dimensional 7 . This suggests that realistic models involving quantised radiation may need hybrid discrete-continuous quantum information techniques 40,41 .…”

“…It inspired a plethora of theoretical models which, for the most part, assume either a fundamental loss of information 5,6 or some form of quantum gravity 7,8 . At variance to the main trends, a conservative approach assuming information retrieval in quantum correlation between Hawking particles was proposed 9, 10 and recently developed within qubit toy-models [11][12][13][14][15][16][17] . Here we leverage modern quantum information to incarnate this idea in a realistic model of quantised radiation.…”

A random unitary circuit model for black hole evaporation

“…It is also worth to stress that over the years many qudit models have been introduced to capture aspects of the black hole evaporation process [66][67][68][69][70][71][72][73][74][75][76][77][78][79][80][81][82]. In particular, a Page-like behavior in time for the entanglement entropy has already been observed in some of these [67,68,79,81].…”