Inferring physical properties of symmetric states from fewest copies

• URL: http://arxiv.org/abs/2301.10982v1
• Date: Thu, 26 Jan 2023 08:18:10 GMT
• Title: Inferring physical properties of symmetric states from fewest copies
• Authors: Da-Jian Zhang and D. M. Tong
• Abstract summary: We find that the expectation value $langle Xrangle_rho$ of an observable $X$ in a state $rho$ can be obtained more precisely through measuring another observable $Y$ without consuming more copies of $rho when $rho$ respects some symmetries. We show that such a precision improvement is available in all circumstances involving the symmetries described by finite or compact Lie groups, and moreover, it can reach the ultimate limit of precision imposed by quantum mechanics if nothing but the symmetries of $rho$ is known.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We find that the expectation value $\langle X\rangle_\rho$ of an observable $X$ in a state $\rho$, which is typically obtained in experiments by measuring $X$ itself, can be generally obtained more precisely through measuring another observable $Y$ without consuming more copies of $\rho$ when $\rho$ respects some symmetries. We show that such a precision improvement is available in all circumstances involving the symmetries described by finite or compact Lie groups, and moreover, it can reach the ultimate limit of precision imposed by quantum mechanics if nothing but the symmetries of $\rho$ is known. We illustrate the general result by applying it to an experiment which implements witness operators to detect the entanglement of an unknown Werner state of two polarized photons https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.170402

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