Efficiently computing the Uhlmann fidelity for density matrices

2022/11/04 by Andrew J. Baldwin, Jonathan A. Jones · 1 voice · 3 citations
Computer Science · Mathematics · #Matrix Theory and Algorithms #Tensor decomposition and applications #Blind Source Separation Techniques

paper · pdf · doi:10.1103/physreva.107.012427

Abstract

We consider the problem of efficiently computing the Uhlmann fidelity in the case when explicit density matrix descriptions are available. We derive an alternative formula which is simpler to evaluate numerically, saving a factor of 10 in time for large matrices.

Citations

• Pseudo-Inverses in Associative Rings and Semigroups

Cited by

• Efficient algorithm for fidelity estimation of two quantum states
• Subsystem fidelity in two-dimensional conformal field theories
• Efficient computation of average subsystem Bures distance in transverse field Ising chain

Discussions

• The fidelity F(ρ,σ) = tr[√(√(ρ)σ√(ρ))] = ||√(ρ)√(σ)||_1 of two quantum states ρ and σ can also be expressed as F(ρ,σ) = tr(√(ρσ)). Not sure how well-known this is! It is proved in arxiv.org/abs [bsky, 47 points, 6 comments]

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