2007/01/10 by A. Serafini, Alessio Serafini, O. C. O. Dahlsten +5 · 1 citation
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1088/1751-8113/40/31/027
published as J. Phys. A: Math. Theor. 40, 9551 (2007) · 24 pages, 5 figures, IOP style; conclusions extended, minor layout adjustment
arxiv created 2007/01/10 · openalex publication_date 2007/07/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We present a framework, compliant with the general canonical principle of statistical mechanics, to define measures on the set of pure Gaussian states of continuous variable systems. Within such a framework, we define two specific measures, referred to as 'micro-canonical' and 'canonical', and apply them to study systematically the statistical properties of the bipartite entanglement of n -mode pure Gaussian states at, respectively, given maximal energy and given temperature. We prove the 'concentration of measure' around a finite average, occurring for the entanglement in the thermodynamical limit in both the canonical and the micro-canonical approach. For finite n , we determine analytically the average and standard deviation of the entanglement (as quantified by the reduced purity) between one mode and all the other modes. Furthermore, we numerically investigate more general situations, clearly showing that the onset of the concentration of measure already occurs at relatively small n .