The law of large numbers for discrete generalized quantum channels

2025/04/14 by Dzhenzher, S. V., Sakbaev, V. Zh. · 2 citations
#FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · doi:10.48550/arxiv.2504.10033

Abstract

We consider random linear operators Ω→ L(T_p, T_p) acting in a p-th Schatten class T_p in a separable Hilbert space H for some 1 \leqslant p < ∞. Such a superoperator is called a pre-channel since it is an extension of a quantum channel to a wider class of operators without requirements of trace-preserving and positivity. Instead of the sum of i.i.d. variables there may be considered the composition of random semigroups e^{A_i t/n} in the Banach space T_p. The law of large numbers is known in the case p=2 in the form of the usual law of large numbers for random operators in a Hilbert space. We obtain the law of large numbers for the case 1\leqslant p \leqslant 2.

Cited by

• The Central Limit Theorem for random exponents on a Hilbert space in the Weak Operator Topology
• The Strong Law of Large Numbers for random semigroups on uniformly smooth Banach spaces

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