The quantum information and the Bures metric are equivalent to each other, except at points where the rank of the density matrix changes. Here we show that by slightly modifying the definition of the Bures metric, the quantum information will be fully equivalent to the Bures metric without exception.
Variational quantum algorithms (VQAs) that estimate values of widely used physical quantities such as the rank, quantum entropies, the Bures fidelity and the quantum Fisher information of mixed quantum states are developed. In addition, variations of these VQAs are also adapted to perform other useful functions such as quantum state learning and approximate fractional inverses. The common theme shared by the proposed algorithms is that their cost functions are all based on minimizing the quantum purity of a quantum state. Strategies to mitigate or avoid the problem of exponentially vanishing c…
We generalize the Fubini-Study method for pure-state complexity to generic quantum states by taking Bures metric or quantum Fisher information metric on the space of density matrices as the complexity measure. Due to Uhlmann's theorem, we show that the mixed-state complexity exactly equals the purification complexity measured by the Fubini-Study metric for purified states but without explicitly applying any purification. We also find the purification complexity is non-increasing under any trace-preserving quantum operations. We also study the mixed Gaussian states as an example to explicitly i…
Giant bubbles of Fisher zeros in the quantum XY chain
Key Laboratory of Polar Materials and Devices (MOE), School of Physics, East China Normal University（华东师范大学极化材料与器件教育部重点实验室物理系）；Department of Physics and Astronomy, University of California, Riverside（加州大学河滨分校物理与天文学系）；Department of Physics and Astronomy, George Mason University（乔治梅森大学物理与天文学系）；State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University（清华大学物理系低维量子物理国家重点实验室）；Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室中心）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
We focus on two types of coherent states, the coherent states of multi graviton states and the coherent states of giant graviton states, in the context of gauge/gravity correspondence. We conveniently use a phase shift operator and its actions on the superpositions of these coherent states. We find $N$-state Schrodinger cat states which approach the one-row Young tableau states, with fidelity between them asymptotically reaches 1 at large $N$. The quantum Fisher information of these states is proportional to the variance of the excitation energy of the underlying states, and characterizes the …
We present an information geometric analysis of both entropic speeds and entropy production rates arising from geodesic evolution on manifolds parametrized by pure quantum states. In particular, we employ pure states that emerge as outputs of suitably chosen su(2; C) time-dependent Hamiltonian operators that characterize analog quantum search algorithms of specific types. The su(2; C) Hamiltonian models under consideration are specified by external time-dependent magnetic fields within which spin-1/2 test particles are immersed. The positive definite Riemannian metrization of the parameter man…
In this paper we address a special case of "sloppy" quantum estimation procedures which happens in the presence of intertwined parameters. A collection of parameters are said to be intertwined when their imprinting on the quantum probe that mediates the estimation procedure, is performed by a set of linearly dependent generators. Under this circumstance the individual values of the parameters can not be recovered unless one tampers with the encoding process itself. An example is presented by studying the estimation of the relative time-delays that accumulate along two parallel optical transmis…
The proposed in J. Math. Phys. v.57,071903 (2016) analytical expansion of monotone (contractive) Riemannian metrics (called also quantum Fisher information(s)) in terms of moments of the dynamical structure factor (DSF) relative to an original intensive observable is reconsidered and extended. The new approach through the DSF which characterizes fully the set of monotone Riemannian metrics on the space of Gibbs thermal states is utilized to obtain an extension of the spectral presentation obtained for the Bogoliubov-Kubo-Mori metric (the generalized isothermal susceptibility) on the entire cla…
Quantum circuit complexity and unsupervised machine learning of topological order
Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA（密歇根大学物理系，安娜堡，密歇根州，48109-1040，美国）；Center for Quantum Computing, RIKEN, Wako-shi, Saitama 351-0198, Japan（日本理化学研究所量子计算中心，武藏野市，埼玉县，351-0198，日本）；Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China（浙江科技学院物理系，杭州310018，中国）
Comment on "Quantum teleportation, entanglement, LQU and LQFI in $e^{+} e^{-} \rightarrow \mathrm{Y} \overline{\mathrm{Y}}$ processes at BESIII through noisy channels''
School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM)（粒子与加速器学院，基础科学研究院）
Quantum Information Geometry of Multicomponent Superconducting Fluctuation Transport
RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所凝聚态科学研究中心）；Fundamental Quantum Science Program (FQSP), TRIP Headquarters, RIKEN（理化学研究所基础量子科学项目（FQSP）、TRIP总部）
