Universality of black hole quantum computing

By analyzing the key properties of black holes from the point of view of quantum information, we derive a model‐independent picture of black hole quantum computing. It has been noticed that this picture exhibits striking similarities with quantum critical condensates, allowing the use of a common language to describe quantum computing in both systems. We analyze such quantum computing by allowing coupling to external modes, under the condition that the external influence must be soft‐enough in order not to offset the basic properties of the system. We derive model‐independent bounds on some crucial time‐scales, such as the times of gate operation, decoherence, maximal entanglement and total scrambling. We show that for black hole type quantum computers all these time‐scales are of the order of the black hole half‐life time. Furthermore, we construct explicitly a set of Hamiltonians that generates a universal set of quantum gates for the black hole type computer. We find that the gates work at maximal energy efficiency. Furthermore, we establish a fundamental bound on the complexity of quantum circuits encoded on these systems, and characterize the unitary operations that are implementable. It becomes apparent that the computational power is very limited due to the fact that the black hole life‐time is of the same order of the gate operation time. As a consequence, it is impossible to retrieve its information, within the life‐time of a black hole, by externally coupling to the black hole qubits. However, we show that, in principle, coupling to some of the internal degrees of freedom allows acquiring knowledge about the micro‐state. Still, due to the trivial complexity of operations that can be performed, there is no time advantage over the collection of Hawking radiation and subsequent decoding.     

A black hole with quantum core

A model black hole, holding a ‘quantum core’ characterized by the Planck order matter density, is revisited here. Based on the quantum improved Newton’s potential drawn out of the loop quantum cosmology we propose a Schwarzschild class, quantum improved black hole line-element that upholds the existence of Planck-dense quantum matter core. Causality is kept preserved in this proposal. Quite in a natural way the quantum core emerges closely homogeneous in its interior matter distribution. The radius of the quantum core turns out to be necessarily proportional to one-third power of the black hole mass. Hawking process of black hole evaporation leads to a shrinking quantum core, and as the mass of black hole approaches near about the Planck mass, the rate of evaporation diminishes rapidly and eventually leaves a cold remnant having a Planck order mass. Proposed model supports the standard quantum geometrical logarithmic correction to black hole entropy-area law.     

Black hole quantum tunnelling and black hole entropy correction

The Parikh–Wilczek tunnelling framework, which treats Hawking radiation as a tunnelling process, is investigated once more in this work. The first order correction, the log-corrected entropy-area relation, emerges naturally in the tunnelling picture if we consider the emission of a spherical shell. The second order correction to the emission rate for the Schwarzschild black hole is also calculated. At this level, the entropy of the black hole will contain three parts: the usual Bekenstein–Hawking entropy, a logarithmic term and an inverse area term. We find that the coefficient of the logarithmic term is −1. Thus, apart from a coefficient, our correction to the black hole entropy is consistent with that calculated in loop quantum gravity.     

Interacting quantum fields around a black hole

If one studies interacting fields on a black hole background using ordinary Feynman diagrams, one is faced with a problem of what to do with lines that cross the horizon. To avoid this difficulty a formulation is developed which can be expressed graphically in terms of a new class of diagram with external lines only at infinity. This formalism is applied to study the question of whether spontaneously broken symmetry would be restored near the black hole. It is also used to show that a black hole can emit more particles than antiparticles even in theories where the particle number is locally conserved by a globalU(1) symmetry.     

A primer for black hole quantum physics

The mechanisms which give rise to Hawking radiation are revealed by analyzing in detail pair production in the presence of horizons. In preparation for the black hole problem, three preparatory problems are dwelt with at length: pair production in an external electric field, thermalization of a uniformly accelerated detector and accelerated mirrors. In the light of these examples, the black hole evaporation problem is then presented.

The leitmotif is the singular behavior of modes on the horizon which gives rise to a steady rate of production. Special emphasis is put on how each produced particle contributes to the mean albeit arising from a particular vacuum fluctuation. It is the mean which drives the semiclassical back reaction. This aspect is analyzed in more detail than heretofore and in particular its drawbacks are emphasized. It is the semiclassical theory which gives rise to Hawking's famous equation for the loss of mass of the black hole due to evaporation dM/dt − −1/M². Black hole thermodynamics is derived from the evaporation process whereupon the reservoir character of the black hole is manifest. The relation to the thermodynamics of the eternal black hole through the Hartle-Hawking vacuum and the Killing identity are displayed.

It is through the analysis of the fluctuations of the field configurations which give rise to a particular Hawking photon that the dubious character of the semiclassical theory is manifest. The present frontier of research revolves around this problem and is principally concerned with the fact that one calls upon energy scales that are greater than Planckian and the possibility of a non unitary evolution as well. These last subjects are presented in qualitative fashion only, so that this review stops at the threshold of quantum gravity.     

黑洞量子隧穿过程的时间

讨论了弯曲时空中黑洞量子隧穿的时间.在假定了黑洞量子隧穿是一个瞬时过程的情况下,通过利用WKB法得出了有静止质量粒子的量子隧穿辐射谱.该辐射谱表明对于在黑洞视界处有静止质量粒子的出射也满足量子力学中的幺正性原理,支持Parikh-Wilczek的结论.结果的合理性表明,在黑洞视界处的量子隧穿过程可以看成是一个瞬时过程.     

Loop quantum gravity and black hole entropy quantization

Using the spin networks and the asymptotic quasinormal mode frequencies of black holes given by loop quantum gravity, the minimum horizon area gap is obtained. Then the quantum area spectrum of black holes is derived and the black hole entropy is a realized quantization. The results show that the black hole entropy given by loop quantum gravity is in full accord with the Bekenstein-Hawking entropy with a suitable Immirzi. Supported by the National Natural Science Foundation of China (Grant No. 10773002)     

Physics with nonperturbative quantum gravity: Radiation from a quantum black hole

We study quantum gravitational effects on black hole radiation, using loop quantum gravity. Bekenstein and Mukhanov have recently considered the modifications caused by quantum gravity on Hawking's thermal black-hole radiation. Using a simple ansatz for the eigenstates of the area, they have obtained the intriguing result that the quantum properties of geometry affect the radiation considerably, yielding a discrete spectrum, definitely non-thermal. Here, we replace the simple ansatz employed by Bekenstein and Mukhanov with the actual eigenstates of the area computed using loop quantum gravity. We derive the emission spectra, using a classic result in number theory by Hardy and Ramanujan. Disappointingly, we do not recover the Bekenstein-Mukhanov discrete spectrum, but — effectively — a continuum spectrum, consistent with Hawking's result. The Bekenstein-Mukhanov argument for the discreteness of the specrum is therefore likely to be an artifact of the ansatz, rather than a robust result (at least in its present kinematical version). The result is an example of concrete (although somewhat disappointing) application of nonperturbative quantum gravity.This essay received the second award from the Gravity Research Foundation, 1996—Ed.     

Hawking radiation from Kerr--Newman--Kasuya black hole via quantum anomalies

We have studied the Hawking radiation of the Kerr-Newman-Kasuya black hole via gauge and gravitational anomaly in the dragging coordinates. The fluxes of the electromagnetic current and the energy momentum tensor for each partial wave in two-dimensional field are obtained.     

A predictive framework for quantum gravity and black hole to white hole transition

The apparent incompatibility between quantum theory and general relativity has long hampered efforts to find a quantum theory of gravity. The recently proposed positive formalism for quantum theory purports to remove this incompatibility. We showcase the power of the positive formalism by applying it to the black hole to white hole transition scenario that has been proposed as a possible effect of quantum gravity. We show how the characteristic observable of this scenario, the bounce time, can be predicted within the positive formalism, while a traditional S-matrix approach fails at this task. Our result also involves a conceptually novel use of positive operator valued measures.     

The ringing of quantum corrected Schwarzschild black hole with GUP

Schwarzschild black holes with quantum corrections are studied under scalar field perturbations and electromagnetic field perturbations to analyze the effect of the correction term on the potential function and quasinormal mode (QNM). In classical general relativity, spacetime is continuous and there is no existence of the so-called minimal length. The introduction of the correction items of the generalized uncertainty principle, the parameter β, can change the singularity structure of the black hole gauge and may lead to discretization in time and space. We apply the sixth-order WKB method to approximate the QNM of Schwarzschild black holes with quantum corrections and perform numerical analysis to derive the results of the method. Also, we find that the effective potential and QNM in scalar fields are larger than those in electromagnetic fields.     

Reissner-Nordstroem de Sitter黑洞的量子隧穿效应

运用Parikh的量子隧穿模型，研究了Reissner—Nordstrom de Sitter黑洞的量子隧穿效应。结果表明，在能量守恒的条件下，黑洞外视界和宇宙视界处的粒子出射率与Bekenstein—Hawking熵有关，辐射谱不再是严格的纯热谱。     

Entropy function approach to charged BTZ black hole

We find solution to the metric function f(r) = 0 of charged BTZ black hole making use of the Lambert function. The condition of extremal charged BTZ black hole is determined by a non-linear relation of M _e (Q) = Q ²(1 − ln Q ²). Then, we study the entropy of extremal charged BTZ black hole using the entropy function approach. It is shown that this formalism works with a proper normalization of charge Q for charged BTZ black hole because AdS₂ × S¹ represents near-horizon geometry of the extremal charged BTZ black hole. Finally, we introduce the Wald’s Noether formalism to reproduce the entropy of the extremal charged BTZ black hole without normalization when using the dilaton gravity approach.