2008/05/20 by Peter Reimann · 31 citations
Computer Science · Physics and Astronomy · #Gaussian #Hilbert space #Measure (data warehouse) #Microcanonical ensemble #Observable #Operator (biology) #POVM #Probability measure #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum many-body systems #Statistical ensemble #Subspace topology #cond-mat.stat-mech
paper · pdf · doi:10.1007/s10955-008-9576-1
published in Journal of Statistical Physics 132(5), 921-935 (Springer Science+Business Media) · accepted for publication in J. Stat. Phys
arxiv created 2008/05/20 · openalex publication_date 2008/06/24 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Consider a mixed quantum mechanical state, describing a statistical ensemble in terms of an arbitrary density operator ρ of low purity, \trρ2≪ 1, and yielding the ensemble averaged expectation value \tr(ρA) for any observable A. Assuming that the given statistical ensemble ρ is generated by randomly sampling pure states |ψ> according to the corresponding so-called Gaussian adjusted projected measure [Goldstein et al., J. Stat. Phys. 125, 1197 (2006)], the expectation value <ψ|A|ψ> is shown to be extremely close to the ensemble average \tr(ρA) for the overwhelming majority of pure states |ψ> and any experimentally realistic observable A. In particular, such a `typicality' property holds whenever the Hilbert space \hr of the system contains a high dimensional subspace \hr+⊂\hr with the property that all |ψ>∈\hr+ are realized with equal probability and all other |ψ> ∈\hr are excluded.