Communications in Mathematical Physics

, Volume 265, Issue 1, pp 95–117 | Cite as

Aspects of Generic Entanglement

  • Patrick HaydenEmail author
  • Debbie W. Leung
  • Andreas Winter


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.


Entropy Quantum State Mutual Information Entangle State Mixed State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Patrick Hayden
    • 1
    • 2
    Email author
  • Debbie W. Leung
    • 1
  • Andreas Winter
    • 3
  1. 1.Institute for Quantum InformationPasadenaUSA
  2. 2.Department of Computer ScienceMcGill UniversityMontrealCanada
  3. 3.Department of MathematicsUniversity of BristolBristolUnited Kingdom

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