日本物理学会誌及びJournal of the Physical Society of Japanの月刊について

Annual review of condensed matter physics

We study information retrieval from evaporating black holes, assuming that the internal dynamics of a black hole is unitary and rapidly mixing, and assuming that the retriever has unlimited control over the emitted Hawking radiation. If the evaporation of the black hole has already proceeded past the ``half-way'' point, where half of the initial entropy has been radiated away, then additional quantum information deposited in the black hole is revealed in the Hawking radiation very rapidly. Information deposited prior to the half-way point remains concealed until the half-way point, and then emerges quickly. These conclusions hold because typical local quantum circuits are efficient encoders for quantum error-correcting codes that nearly achieve the capacity of the quantum erasure channel. Our estimate of a black hole's information retention time, based on speculative dynamical assumptions, is just barely compatible with the black hole complementarity hypothesis.

http://absimage.aps.org/image/MAR08/MWS_MAR08-2007-003180.pdf

Black holes as mirrors: quantum information in random subsystems

A new class of quantum entanglement transitions separating phases with different entanglement entropy scaling has been observed in recent numerical studies. Despite the numerical efforts, an analytical understanding of such transitions has remained elusive. Here, the authors propose a theory for the area-law to volume-law entanglement transition in many-body systems that undergo both random unitary evolutions and projective measurements. Using the replica method, the authors map analytically this entanglement transition to an ordering transition in a classical statistical mechanics model. They derive the general entanglement scaling properties at the transition and show a solvable limit where this transition can be mapped onto two-dimensional percolation.

Measurement-induced criticality in random quantum circuits

We analyze the dynamics of entanglement entropy in a generic quantum many-body open system from the perspective of quantum information and error corrections. We introduce a random unitary circuit model with intermittent projective measurements, in which the degree of information scrambling by the unitary and the rate of projective measurements are independently controlled. This model displays two stable phases, characterized by the volume-law and area-law scaling entanglement entropy in steady states. The transition between the two phases is understood from the point of view of quantum error correction: the chaotic unitary evolution protects quantum information from projective measurements that act as errors. A phase transition occurs when the rate of errors exceeds a threshold that depends on the degree of information scrambling. We confirm these results using numerical simulations and obtain the phase diagram of our model. Our work shows that information scrambling plays a crucial role in understanding the dynamics of entanglement in an open quantum system and relates the entanglement phase transition to changes in quantum channel capacity.

Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition

The interplay of entanglement, measurement, and noise in near-term quantum devices may lead to novel emergent phenomena. This work presents a theoretical framework to understand collective effects in the dynamics of quantum entanglement and information, using the tools of statistical mechanics. The new effective description of generic quantum circuits lends insight into a measurement-induced phase transition in the information content of the system and points toward novel schemes to identify this transition in experiments.

Theory of the phase transition in random unitary circuits with measurements

Symmetry enriched phases of quantum circuits

Generic many-body systems coupled to an environment lose their quantum entanglement due to decoherence and evolve to a mixed state with only classical correlations. Here, we show that measurements can stabilize quantum entanglement within open quantum systems. Specifically, in random unitary circuits with dephasing at the boundary, we find both numerically and analytically that projective measurements performed at a small nonvanishing rate result in a steady state with an L^{1/3} power-law scaling entanglement negativity within the system. Using an analytical mapping to a statistical mechanics model of directed polymers in a random environment, we show that the power-law negativity scaling can be understood as Kardar-Parisi-Zhang fluctuations due to the random measurement locations. Further increasing the measurement rate leads to a phase transition into an area-law negativity phase, which is of the same universality as the entanglement transition in monitored random circuits without decoherence.

Measurement-Induced Power-Law Negativity in an Open Monitored Quantum Circuit.

We analyze the dynamics of entanglement entropy in a generic quantum many-body open system from the perspective of quantum information and error corrections. We introduce a random unitary circuit model with intermittent projective measurements, in which the degree of information scrambling by the unitary and the rate of projective measurements are independently controlled. This model displays two stable phases, characterized by volume law and area law of the steady state entanglement entropy, respectively. The transition between the two phases is understood from the point of view of quantum error correction: the chaotic unitary time evolution protects quantum information from projective measurements that act as errors. A phase transition occurs when the rate of errors exceeds a threshold that depends on the degree of information scrambling, which is estimated by the quantum decoupling theorem in a strong scrambling limit. We confirm these results using numerical simulations and obtain the phase diagram of our model.

Yimu Bao

Papers

Theory of the phase transition in random unitary circuits with measurements

Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition

Symmetry enriched phases of quantum circuits

Measurement-Induced Power-Law Negativity in an Open Monitored Quantum Circuit.

Quantum error correction and entanglement phase transition in random unitary circuits with projective measurements