Aspects of Generic Entanglement |
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Authors: | Patrick Hayden Debbie W Leung Andreas Winter |
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Institution: | (1) Institute for Quantum Information, Caltech 107–81, Pasadena, CA 91125, USA;(2) Department of Computer Science, McGill University, Montreal, Quebec, H3A 2A7, Canada;(3) Department of Mathematics, University of Bristol, Bristol, BS8 1TW, United Kingdom |
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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 the 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. |
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