相关论文: Remarks on Black Hole Complexity Puzzle
Quantifying quantum states' complexity is a key problem in various subfields of science, from quantum computing to black-hole physics. We prove a prominent conjecture by Brown and Susskind about how random quantum circuits' complexity…
We present a new effective description of macroscopic Kruskal black holes that incorporates corrections due to quantum geometry effects of loop quantum gravity. It encompasses both the `interior' region that contains classical singularities…
In general, black-hole perturbations are governed by a discrete spectrum of complex eigen-frequencies (quasi-normal modes). This signals the breakdown of unitarity. In asymptotically AdS spaces, this is puzzling because the corresponding…
The black hole information paradox has caused enormous confusion over four decades. But in recent years, the theorem of quantum strong-subaddditivity has sorted out the possible resolutions into three sharp categories: (A) No new physics at…
The information paradox in the quantum evolution of black holes is studied within the framework of the AdS/CFT correspondence. The unitarity of the CFT strongly suggests that all information about an initial state that forms a black hole is…
Understanding the fate of semi-classical black hole solutions at very late times is one of the most important open questions in quantum gravity. In this paper, we provide a path integral definition of the volume of the black hole interior…
This work is originally a Cambridge Part III essay paper. Quantum complexity arises as an alternative measure to the Fubini metric between two quantum states. Given two states and a set of allowed gates, it is defined as the least complex…
In this paper we discuss quantum computational restrictions on the types of thought experiments recently used by Almheiri, Marolf, Polchinski, and Sully to argue against the smoothness of black hole horizons. We argue that the quantum…
Bringing gravity into a quantum-mechanical framework is likely the most profound remaining problem in fundamental physics. The "unitarity crisis" for black hole evolution appears to be a key facet of this problem, whose resolution will…
Circuit complexity, defined as the minimum circuit size required for implementing a particular Boolean computation, is a foundational concept in computer science. Determining circuit complexity is believed to be a hard computational problem…
Despite its successes, the large-$N$ holographic dictionary remains incomplete. Key features of gravitational path integrals--most notably Euclidean wormholes and the associated failure of factorization--lack a clear interpretation in the…
Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently, this concept has found applications beyond quantum computing -- in studying the…
The loop quantization of the Schwarzschild interior region, as described by a homogeneous anisotropic Kantowski-Sachs model, is re-examined. As several studies of different -inequivalent- loop quantizations have shown, to date there exists…
The holographic complexity of a static spherically symmetric black hole, defined as the volume of an extremal surface, grows linearly with time at late times in general relativity. The growth comes from a region at a constant transverse…
Black hole complementarity, as originally formulated in the 1990's by Preskill, 't Hooft, and myself is now being challenged by the Almheiri-Marolf-Polchinski-Sully firewall argument. The AMPS argument relies on an implicit assumption---the…
In this paper, we discuss the black hole complementarity and the firewall proposal at length. Black hole complementarity is inevitable if we assume the following five things: unitarity, entropy-area formula, existence of an information…
It is not known what the limitations are on using quantum computation to speed up classical computation. An example would be the power to speed up PSPACE-complete computations. It is also not known what the limitations are on the duration…
The interior volume of black holes as defined by Christodoulou and Rovelli exhibits many surprising features. For example, it increases with time, even under Hawking evaporation. For some black holes, the interior volume is not even a…
From a conceptual point of view, this chapter may be viewed as an exercise in combining quantum field theory and general relativity in a controlled setting. Despite its apparent simplicity, this exercise is deeply rooted in highly…
Based on the AdS/CFT correspondence, we study how to reconstruct bulk spacetime metrics by various quantum information measures on the boundary field theories, which include entanglement entropy, mutual information, entanglement of…