Title: Symmetry: a fundamental resource for quantum coherence and metrology Show Chinese title

Title: 对称性：量子相干性和计量学的基本资源

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. Show Chinese abstract

Abstract: 我们引入了一种新的制备深度纠缠态的范式，这对于量子计量学是有用的。 我们表明，当量子态是算符$A$的本征态时，相对于$A$完全非对角的可观测量$G$具有纯粹的量子涨落，如量子费舍尔信息所量化，即$F_Q(G)=4\langle G^2 \rangle$。 这一性质与量子态的纯度无关，并意味着非对角涨落代表了相位估计的计量资源。 特别是对于多体系统，如量子自旋集合或玻色气体，非对角长程序的存在（对于自旋可观测量或玻色算符）直接转化为计量资源，前提是系统保持在明确的对称性子空间中。 后者例如由集体自旋的一个分量或自旋系统中的奇偶性定义；对于玻色子，则由粒子数子空间定义。 我们的结果确立了在各种多体系统中任意非高斯量子关联在计量学中的最优使用。