Probing mixed-state, symmetry-resolved, entanglement, with randomized measurements

Benoît Vermersch

Antoine Neven, José A. Carrasco, Vittorio Vitale +8 more

Abstract We propose an ordered set of experimentally accessible conditions for detecting entanglement in mixed states. The k -th condition involves comparing moments of the partially transposed density operator up to order k . Remarkably, the union of all moment inequalities reproduces the Peres-Horodecki criterion for detecting entanglement. Our empirical studies highlight that the first four conditions already detect mixed state entanglement reliably in a variety of quantum architectures. Exploiting symmetries can help to further improve their detection capabilities. We also show how to estimate moment inequalities based on local random measurements of single state copies (classical shadows) and derive statistically sound confidence intervals as a function of the number of performed measurements. Our analysis includes the experimentally relevant situation of drifting sources, i.e. non-identical, but independent, state copies.

Mostafa Mansour, Mohammed Daoud A, Zakaria Dahbi

Gabriele Bellomia, Carlos Mejuto-Zaera, Massimo Capone +1 more

In order to identify intrinsic quantum resources in strongly interacting fermionic systems, we introduce a symmetry resolution of the parity-superselected two-site entanglement, as measured by both the fermionic negativity and the relative entropy of entanglement. We discuss how the symmetry resolution can be extended also to the full entanglement in pure and mixed two-site states. We apply our recipe to the Hubbard model, first for a dimer, and then for a plaquette cluster dynamical mean-field theory, an established method tailored to accurately capture short-range correlations. Following the evolution of the model through the interaction- and density-driven Mott transitions at zero temperature, we highlight how the three symmetry-resolved components of the two-site entanglement probe different key aspects of Mott and pseudogap physics.

Sophia Ohnemus, Heinz‐Peter Breuer, Andreas Ketterer

Randomized measurements constitute a simple measurement primitive that exploits the information encoded in the outcome statistics of samples of local quantum measurements defined through randomly selected bases. In this work we exploit the potential of randomized measurements in order to probe the amount of entanglement contained in multiparticle quantum systems as quantified by the multiparticle concurrence. We further present a detailed statistical analysis of the underlying measurement resources required for a confident estimation of the introduced quantifiers using analytical tools from the theory of random matrices. The introduced framework is demonstrated by a series of numerical experiments analyzing the concurrence of typical multiparticle entangled states as well as of ensembles of output states produced by random quantum circuits. Finally, we examine the multiparticle entanglement of mixed states produced by noisy quantum circuits consisting of single- and two-qubit gates with nonvanishing depolarization errors, thus showing that our framework is directly applicable in the noisy intermediate-scale regime.

Fan Wu, Liang Bao Tang