Detecting entanglement with a thermometer

We present a general argument showing that the temperature as well as other thermodynamical state variables can qualify as entanglement witnesses (EWs) for spatial entanglement. This holds for a variety of systems and we exemplify our ideas using a simple free non-interacting bosonic gas. We find that entanglement can exist at arbitrarily high temperatures, provided that we can probe smaller and smaller regions of space. We then discuss the relationship between the occurrence of Bose–Einstein condensation and our conditions for the presence of entanglement and compare the respective critical temperatures. We close with a short discussion of the idea of seeing entanglement as a macroscopic property in thermodynamical systems and its possible relation to phase transitions in general.

[1]  Č. Brukner,et al.  Entanglement between collective operators in a linear harmonic chain (7 pages) , 2005, quant-ph/0506236.

[2]  V. Vedral,et al.  Macroscopic thermal entanglement due to radiation pressure. , 2005, Physical review letters.

[3]  J. Zaanen.  Technology meets quantum criticality , 2005 .

[4]  H. Weinfurter,et al.  Experimental one-way quantum computing , 2005, Nature.

[5]  G. Tóth,et al.  Multipartite entanglement in spin chains , 2005, quant-ph/0502160.

[6]  Daniel A. Lidar,et al.  Entanglement observables and witnesses for interacting quantum spin systems , 2004, quant-ph/0412099.

[7]  Č. Brukner,et al.  Equation of state for entanglement in a Fermi gas , 2004, quant-ph/0410166.

[8]  T. Martin,et al.  Spin-current noise and Bell inequalities in a realistic superconductor-quantum dot entangler , 2004, cond-mat/0410325.

[9]  Jaewan Kim,et al.  Entanglement of electron spins in superconductors , 2004, quant-ph/0406013.

[10]  C. Emary,et al.  Entanglement and the phase transition in single-mode superradiance. , 2003, Physical review letters.

[11]  G. Aeppli,et al.  Entangled quantum state of magnetic dipoles , 2003, Nature.

[12]  V. Vedral.  Quantum physics: Entanglement hits the big time , 2003, Nature.

[13]  W. Ketterle.  Nobel lecture: When atoms behave as waves: Bose-Einstein condensation and the atom laser* , 2002 .

[14]  K. Audenaert,et al.  Entanglement properties of the harmonic chain , 2002, quant-ph/0205025.

[15]  A. L. Ivanov,et al.  Towards Bose–Einstein condensation of excitons in potential traps , 2002, Nature.

[16]  A. Osterloh,et al.  Scaling of entanglement close to a quantum phase transition , 2002, Nature.

[17]  C. Simon.  Natural Entanglement in Bose-Einstein Condensates , 2001, quant-ph/0110114.

[18]  Hans J. Briegel,et al.  The one-way quantum computer--a non-network model of quantum computation , 2001, quant-ph/0108118.

[19]  B. Terhal.  Detecting quantum entanglement , 2001, Theor. Comput. Sci..

[20]  Jian-Wei Pan,et al.  Entanglement purification for quantum communication , 2000, Nature.

[21]  J. Cirac,et al.  Many-particle entanglement with Bose–Einstein condensates , 2000, Nature.

[22]  D. Strekalov,et al.  Direct observation of growth and collapse of a Bose–Einstein condensate with attractive interactions , 1998, Nature.

[23]  M. Lewenstein,et al.  Volume of the set of separable states , 1998, quant-ph/9804024.

[24]  H. Weinfurter,et al.  Experimental quantum teleportation , 1997, Nature.

[25]  W. Ketterle,et al.  Bose-Einstein condensation of a finite number of particles trapped in one or three dimensions. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[26]  Charles H. Bennett,et al.  Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. , 1993, Physical review letters.

[27]  Ekert,et al.  Quantum cryptography based on Bell's theorem. , 1991, Physical review letters.

[28]  Physics Letters , 1962, Nature.