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A recent article by Mathur attempts a precise formulation for the paradox of black hole information loss [S. D. Mathur, arXiv:1108.0302v2 (hep-th)]. We point out that a key component of the above work, which refers to entangled pairs inside and outside of the horizon and their associated entropy gain or information loss during black hole evaporation, is a presumptuous false outcome not backed by the very foundation of physics. The very foundation of Mathurs above work is thus incorrect. We further show that within the framework of Hawking radiation as tunneling the so-called small corrections are sufficient to resolve the information loss problem.
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We specify the semiclassical no-boundary wave function of the universe without relying on a functional integral of any kind. The wave function is given as a sum of specific saddle points of the dynamical theory that satisfy conditions of regularity on geometry and field and which together yield a time neutral state that is normalizable in an appropriate inner product. This specifies a predictive framework of semiclassical quantum cosmology that is adequate to make probabilistic predictions, which are in agreement with observations in simple models. The use of holography to go beyond the semiclassical approximation is briefly discussed.
In quantum information theory, Fisher Information is a natural metric on the space of perturbations to a density matrix, defined by calculating the relative entropy with the unperturbed state at quadratic order in perturbations. In gravitational physics, Canonical Energy defines a natural metric on the space of perturbations to spacetimes with a Killing horizon. In this paper, we show that the Fisher information metric for perturbations to the vacuum density matrix of a ball-shaped region B in a holographic CFT is dual to the canonical energy metric for perturbations to a corresponding Rindler wedge R_B of Anti-de-Sitter space. Positivity of relative entropy at second order implies that the Fisher information metric is positive definite. Thus, for physical perturbations to anti-de-Sitter spacetime, the canonical energy associated to any Rindler wedge must be positive. This second-order constraint on the metric extends the first order result from relative entropy positivity that physical perturbations must satisfy the linearized Einsteins equations.
The information loss paradox is usually stated as an incompatibility between general relativity and quantum mechanics. However, the assumptions leading to the problem are often overlooked and, in fact, a careful inspection of the main hypothesises suggests a radical reformulation of the problem. Indeed, we present a thought experiment involving a black hole that emits radiation and, independently of the nature of the radiation, we show the existence of an incompatibility between (i) the validity of the laws of general relativity to describe infalling matter far from the Planckian regime, and (ii) the so-called central dogma which states that as seen from an outside observer a black hole behaves like a quantum system whose number of degrees of freedom is proportional to the horizon area. We critically revise the standard arguments in support of the central dogma, and argue that they cannot hold true unless some new physics is invoked even before reaching Planck scales. This suggests that the information loss problem, in its current formulation, is not necessarily related to any loss of information or lack of unitarity. Therefore, in principle, semiclassical general relativity and quantum mechanics can be perfectly compatible before reaching the final stage of the black hole evaporation where, instead, a consistent theory of quantum gravity is needed to make any prediction.
It is known that time-dependent perturbations can enhance superconductivity and increase the critical temperature. If this phenomenon happens to high-T_c superconductors, one could obtain room-temperature superconductors, but this is still an open issue experimentally. Meanwhile, we would like to understand this phenomenon from gravity dual and see if the enhancement is possible for holographic superconductors. Previous work (arXiv:1104.4098 [hep-th]) has studied this issue by adding a time-dependent chemical potential, but their analysis is questionable as a true dynamic equilibrium. In particular, the AdS boundary does not supply energy to the bulk spacetime in their setup. A more appropriate way to discuss the enhancement is to add a time-dependent vector potential, i.e., a time-dependent electric field. However, the enhancement does not occur for holographic superconductors.
This paper answers Bells question: What does quantum information refer to? It is about quantum properties represented by subspaces of the quantum Hilbert space, or their projectors, to which standard (Kolmogorov) probabilities can be assigned by using a projective decomposition of the identity (PDI or framework) as a quantum sample space. The single framework rule of consistent histories prevents paradoxes or contradictions. When only one framework is employed, classical (Shannon) information theory can be imported unchanged into the quantum domain. A particular case is the macroscopic world of classical physics whose quantum description needs only a single quasiclassical framework. Nontrivial issues unique to quantum information, those with no classical analog, arise when aspects of two or more incompatible frameworks are compared.
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