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Free keywords:
Condensed Matter, Statistical Mechanics, cond-mat.stat-mech
Abstract:
Randomized measurements (RMs) provide a practical scheme to probe complex
many-body quantum systems. While they are a very powerful tool to extract local
information, global properties such as entropy or bipartite entanglement remain
hard to probe, requiring a number of measurements or classical post-processing
resources growing exponentially in the system size. In this work, we address
the problem of estimating global entropies and mixed-state entanglement via
partial-transposed (PT) moments, and show that efficient estimation strategies
exist under the assumption that all the spatial correlation lengths are finite.
Focusing on one-dimensional systems, we identify a set of approximate
factorization conditions (AFCs) on the system density matrix which allow us to
reconstruct entropies and PT moments from information on local subsystems.
Combined with the RM toolbox, this yields a simple strategy for entropy and
entanglement estimation which is provably accurate assuming that the state to
be measured satisfies the AFCs, and which only requires polynomially-many
measurements and post-processing operations. We prove that the AFCs hold for
finite-depth quantum-circuit states and translation-invariant matrix-product
density operators, and provide numerical evidence that they are satisfied in
more general, physically-interesting cases, including thermal states of local
Hamiltonians. We argue that our method could be practically useful to detect
bipartite mixed-state entanglement for large numbers of qubits available in
today's quantum platforms.
