Aspects of generic entanglement

Abstract

We study entanglement and other correlation properties of random states in high-dimensional bipartite systems. These correlations are quantified by parameters that are subject to the "concentration of measure" phenomenon, meaning that on a large-probability set these parameters are close to their expectation. For the entropy of entanglement, this has the counterintuitive consequence that there exist large subspaces in which all pure states are close to maximally entangled. This, in turn, implies the existence of mixed states with entanglement of formation near that of a maximally entangled state, but with negligible quantum mutual information and, therefore, negligible distillable entanglement, secret key, and common randomness. It also implies a very strong locking effect for the entanglement of formation: its value can jump from maximal to near zero by tracing over a number of qubits negligible compared to the size of total system. Furthermore, such properties are generic. Similar phenomena are observed for random multiparty states, leading us to speculate on the possibility that the theory of entanglement is much simplified when restricted to asymptotically generic states. Further consequences of our results include a complete derandomization of the protocol for universal superdense coding of quantum states.

22 pages, 1 figure, 1 table

References in corpus (30)

• Mixed State Entanglement and Quantum Error Correction
• Separability Criterion for Density Matrices
• Quantifying Entanglement
• Persistent entanglement in arrays of interacting particles
• Average Entropy of a Subsystem
• On the volume of the set of mixed entangled states
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Distillation of secret key and entanglement from quantum states
• Monogamy of entanglement and other correlations
• "Squashed Entanglement" - An Additive Entanglement Measure
• Induced measures in the space of mixed quantum states
• On the Entangling Power of Quantum Evolutions
• Randomizing quantum states: Constructions and applications
• The asymptotic entanglement cost of preparing a quantum state
• On the volume of the set of mixed entangled states II
• Random Quantum Circuits and Pseudo-Random Operators: Theory and Applications
• Average Entropy of a Subsystem
• The Uniqueness Theorem for Entanglement Measures
• Superdense coding of quantum states
• Entanglement cost of mixed states
• Statistical properties of random density matrices
• Random quantum correlations and density operator distributions
• Distilling common randomness from bipartite quantum states
• Relating quantum privacy and quantum coherence: an operational approach
• Irreversibility in asymptotic manipulations of entanglement
• Separable balls around the maximally mixed multipartite quantum states
• The volume of separable states is super-doubly-exponentially small
• Multiparty data hiding of quantum information
• Bounds on entanglement in qudit subsystems
• A new type of complementarity between quantum and classical information

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