In quantum mechanics, subsystems of a composite system can exhibit correlations (► correlations in quantum mechanics) that are stronger than any classical correlations. Quantum correlations are also called entanglement [1]. A mixed quantum state ? consisting of two subsystems (i.e. a bipartite state) can be either separable or entangled. It is separable [2] if ϱ = Σi p i | a i⟩ ⟨a i | ⊗ | b i⟩⟨b i |, with p i being probabilities, and entangled otherwise. Entanglement can be quantified via entanglement measures. Maximally entangled states are pure, and mixing generally decreases entanglement. For further reading on entanglement, see [18–20] and general textbooks on quantum information, e.g. [21–23].
In quantum information entanglement is viewed as a resource, see protocols such as quantum teleportation [3], superdense coding [4] or entanglement-based quantum cryptography (► quantum communication) [5]. Therefore, one is interested in maximally entangled (pure) quantum states. In a realistic scenario, noise due to interaction with the environment (► decoherence) or imperfect gate operations generally reduces both purity and entanglement of a given state. However, if one has several copies of some less than maximally entangled state available, it is possible that the two parties Alice (A) and Bob (B) concentrate or distill the entanglement, by acting locally on their parts of the states (in their corresponding laboratories) and exchanging classical information via a telephone. Thus, by using so-called local operations and classical communication (LOCC) they can create fewer pairs with higher entanglement and higher degree of purity. This process is called entanglement purification or entanglement distillation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Primary Literature
E. Schrödinger: Naturwissenschaften 23, 807 (1935).
R. Werner: Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277 (1989).
C. Bennett et al: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett. 70, 1895 (1993).
C. Bennett, S. Wiesner: Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states, Phys. Rev. Lett. 69, 2881 (1992).
A. Ekert: Quantum cryptography based on Bell's theorem. Phys. Rev. Lett. 67, 661 (1991).
N. Gisin: Hidden quantum nonlocality revealed by local filters. Phys. Lett. A 210, 151 (1996).
C. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. Smolin, W. Wootters: Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels. Phys. Rev. Lett. 76, 722 (1996).
D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, A. Sanpera: Quantum Privacy Amplification and the Security of Quantum Cryptography over Noisy Channels. Phys. Rev. Lett. 77, 2818 (1996).
M. Horodecki, P. Horodecki, R. Horodecki: Inseparable Two Spin-1/2 Density Matrices Can Be Distilled to a Singlet Form. Phys. Rev. Lett. 78, 574 (1997).
A. Peres: Separability Criterion for Density Matrices. Phys. Rev. Lett. 77, 1413 (1996).
M. Horodecki, P. Horodecki, R. Horodecki: Separability of Mixed States: Necessary and Sufficient Conditions. Phys. Lett. A 223, 1 (1996).
P. Horodecki: Separability criterion and inseparable mixed states with positive partial transposition. Phys. Lett. A 232, 333 (1997).
M. Horodecki, P. Horodecki, R. Horodecki: Mixed-State Entanglement and Distillation: Is there a Bound Entanglement in Nature? Phys. Rev. Lett. 80, 5239 (1998).
W. Dür, J.I. Cirac, M. Lewenstein, D. Bruß: Distillability and partial transposition in bipartite systems. Phys. Rev. A 61, 062313 (2000).
D. DiVincenzo, P. Shor, J. Smolin, B. Terhal, A. Thapliyal: Evidence for bound entangled states with negative partial transpose. Phys. Rev. A 61, 062312 (2000).
J. Watrous: Many Copies May Be Required for Entanglement Distillation. Phys. Rev. Lett. 93, 010502 (2004).
Z.-W. Wang et al: Experimental Entanglement Distillation of Two-Qubit Mixed States under Local Operations, Phys. Rev. Lett. 96, 220505 (2006).
Secondary Literature
M. Lewenstein, D. Bruß, J. I. Cirac, B. Kraus, M. Kuś, J. Samsonowicz, A. Sanpera, R. Tarrach: Separability and distillability in composite quantum systems — a primer. Journ. Mod. Opt. 47, 2841 (2000).
D. Bruß: Characterizing entanglement. J. Math. Phys. 43, 4237 (2002).
R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki: Quantum entanglement. arXiv: quant-ph/0702225, subm. to Rev. Mod. Phys.
M. Nielsen, I. Chuang: Quantum Computation and Information. Cambridge University Press (2000).
Quantum Information: An Introduction to Basic Theoretical Concepts and Experiments (Springer Tracts in Modern Physics, 173). Eds. G. Alber, T. Beth, M. Horodecki, P. Horodecki, R. Horodecki, M. Rötteler, H. Weinfurter, R. Werner, A. Zeilinger, Springer-Verlag (April 2001).
Lectures on Quantum Information. Eds. D. Bruß G. Leuchs: WILEY-VCH Weinheim (2007).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Bruß, D. (2009). Entanglement Purification and Distillation. In: Greenberger, D., Hentschel, K., Weinert, F. (eds) Compendium of Quantum Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70626-7_65
Download citation
DOI: https://doi.org/10.1007/978-3-540-70626-7_65
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70622-9
Online ISBN: 978-3-540-70626-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)