Emergent classicality in general multipartite states and channels

Abstract

In a quantum measurement process, classical information about the measured system spreads throughout the environment. Meanwhile, quantum information about the system becomes inaccessible to local observers. Here we prove a result about quantum channels indicating that an aspect of this phenomenon is completely general. We show that for any evolution of the system and environment, for everywhere in the environment excluding an $O(1)$-sized region we call the "quantum Markov blanket," any locally accessible information about the system must be approximately classical, i.e. obtainable from some fixed measurement. The result strengthens the earlier result of arXiv:1310.8640 in which the excluded region was allowed to grow with total environment size. It may also be seen as a new consequence of the principles of no-cloning or monogamy of entanglement. Our proof offers a constructive optimization procedure for determining the "quantum Markov blanket" region, as well as the effective measurement induced by the evolution. Alternatively, under channel-state duality, our result characterizes the marginals of multipartite states.

24 pages, 3 figures; main theorems from v2 rephrased using equivalent statements

References in corpus (9)

• Quantum Decoherence
• Strong and weak thermalization of infinite non-integrable quantum systems
• Quantum Darwinism, Classical Reality, and the Randomness of Quantum Jumps
• Generic emergence of objectivity of observables in infinite dimensions
• Quantum de Finetti theorem under fully-one-way adaptive measurements
• Universal gaps for XOR games from estimates on tensor norm ratios
• Approximate quantum Markov chains
• Whenever a quantum environment emerges as a classical system, it behaves like a measuring apparatus
• Refined diamond norm bounds on the emergence of objectivity of observables

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• Quantum Theory of the Classical: Einselection, Envariance, Quantum Darwinism and Extantons
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• One dimensional gapped quantum phases and enriched fusion categories
• Jordan products of quantum channels and their compatibility
• Redundantly amplified information suppresses quantum correlations in many-body systems
• Bootstrap Embedding on a Quantum Computer
• Branching States as The Emergent Structure of a Quantum Universe
• Maximal gap between local and global distinguishability of bipartite quantum states
• Emergence of Objectivity for Quantum Many-Body Systems
• Observing Schrödinger's Cat with Artificial Intelligence: Emergent Classicality from Information Bottleneck
• On the relation between quantum Darwinism and approximate quantum Markovianity
• Quantitative bounds to propagation of quantum correlations in many-body systems