Symmetry: a fundamental resource for quantum coherence and metrology

• URL: http://arxiv.org/abs/2407.01025v1
• Date: Mon, 1 Jul 2024 07:19:37 GMT
• Title: Symmetry: a fundamental resource for quantum coherence and metrology
• Authors: Irénée Frérot, Tommaso Roscilde,
• Abstract summary: We show that when the quantum state is an eigenstate of an operator $A$, observables $G$ which are completely off-diagonal have purely quantum fluctuations. This property holds regardless of the purity of the quantum state, and it implies that off-diagonal fluctuations represent a metrological resource for phase estimation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a new paradigm for the preparation of deeply entangled states useful for quantum metrology. We show that when the quantum state is an eigenstate of an operator $A$, observables $G$ which are completely off-diagonal with respect to $A$ have purely quantum fluctuations, as quantified by the quantum Fisher information, namely $F_Q(G)=4\langle G^2 \rangle$. This property holds regardless of the purity of the quantum state, and it implies that off-diagonal fluctuations represent a metrological resource for phase estimation. In particular, for many-body systems such as quantum spin ensembles or bosonic gases, the presence of off-diagonal long-range order (for a spin observable, or for bosonic operators) directly translates into a metrological resource, provided that the system remains in a well-defined symmetry sector. The latter is defined e.g. by one component of the collective spin or by its parity in spin systems; and by a particle-number sector for bosons. Our results establish the optimal use for metrology of arbitrarily non-Gaussian quantum correlations in a large variety of many-body systems.

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