A quantum circuit interpretation of evaporating black hole geometry
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Springer
Received: March 25, Revised: June 7, Accepted: June 15, Published: July 21,
2020 2020 2020 2020
Ying Zhao Institute for Advanced Study, Princeton, NJ 08540, U.S.A.
E-mail: [email protected] Abstract: We give a quantum circuit interpretation of evaporating black hole geometry. We make an analogy between the appearance of island for evaporating black hole and the transition from two-sided to one-sided black hole in the familiar example of perturbed thermofield double. If Alice perturbs thermofield double and waits for scrambling time, she will have a one-sided black hole with interior of her own. We argue that by similar mechanism the radiation gets access to the interior (island forms) after Page time. The growth of the island happens as a result of the constant transitions from two-sided to one-sided black holes. Keywords: Black Holes, Models of Quantum Gravity ArXiv ePrint: 1912.00909v2
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)139
JHEP07(2020)139
A quantum circuit interpretation of evaporating black hole geometry
Contents 1
2 Review of quantum circuit 2.1 Bulk tensor network and quantum circuit 2.2 Quantum circuit belonging to different subsystems 2.3 Transition from two-sided to one-sided black hole 2.3.1 Two-sided black hole 2.3.2 Compare two-sided and one-sided black holes 2.3.3 Perturbed thermofield double
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3 Evaporating black hole 3.1 Before Page time: Bob’s one-sided black hole 3.2 Around Page time: two-sided black hole 3.3 After Page time 3.3.1 Comments on one-sided black hole 3.4 Growth of the island: transition from two-sided to one-sided black holes constantly happening
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A Charged black hole geometry
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1
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Introduction
In the recent work of [1] and [2], the authors studied the geometry of an evaporating black hole. They found that there is a jump of the location of RT surface around Page time. In this paper we give an interpretation of this geometry from the point of view of quantum circuit. Consider an evaporating black hole formed from a pure state as discussed in [1, 2]. Before Page time, the RT surface is empty set and the interior is inside the entanglement wedge of the black hole. After Page time, the interior is mostly inside the entanglement wedge of the radiation due to the appearance of an island [3]. This may seem puzzling from the point of view of radiation since just after the transition we have a large jump in the size of the region contained in its entanglement wedge. Why is it that adding a few more qubits to the radiation gives rise to such large change? Why does the bulk region belonging to the radiation (island in [3]) keep growing after Page time while the radiation itself doesn’t do any computations? In this paper we will answer these questions from the point of view of quantum circuit.
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JHEP07(2020)139
1 Introduction
2
Review of quantum circuit
2.1
Bulk tensor network and quantum circuit
In [4], Swingle argued that AdS bulk geometry reflects a MERA-like tensor network p
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