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      Symmetry-resolved entanglement detection using partial transpose moments

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          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.

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          Quantum Computing in the NISQ era and beyond

          Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future. Quantum computers with 50-100 qubits may be able to perform tasks which surpass the capabilities of today's classical digital computers, but noise in quantum gates will limit the size of quantum circuits that can be executed reliably. NISQ devices will be useful tools for exploring many-body quantum physics, and may have other useful applications, but the 100-qubit quantum computer will not change the world right away - we should regard it as a significant step toward the more powerful quantum technologies of the future. Quantum technologists should continue to strive for more accurate quantum gates and, eventually, fully fault-tolerant quantum computing.
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            Computable measure of entanglement

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              Separability Criterion for Density Matrices

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                Author and article information

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                Journal
                npj Quantum Information
                npj Quantum Inf
                Springer Science and Business Media LLC
                2056-6387
                December 2021
                October 20 2021
                December 2021
                : 7
                : 1
                Article
                10.1038/s41534-021-00487-y
                a20147f7-f025-4f95-af6e-ba1eb1dd30e7
                © 2021

                https://creativecommons.org/licenses/by/4.0

                https://creativecommons.org/licenses/by/4.0

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