We extend to finite temperature the fidelity approach to quantum phase transitions (QPTs). This is done by resorting to the notion of mixed-state fidelity that allows one to compare two density matrices corresponding to two different thermal states. By exploiting the same concept we also propose a finite-temperature generalization of the Loschmidt echo. Explicit analytical expressions of these quantities are given for a class of quasi-free fermionic Hamiltonians. A numerical analysis is performed as well showing that the associated QPTs show their signatures in a finite range of temperatures.
The notion of fidelity susceptibility, introduced within the context of quantum metric tensor, has been an important quantity to characterize the criticality near quantum phase transitions. We demonstrate that for topological phase transitions in Dirac models, provided the momentum space is treated as the manifold of the quantum metric, the fidelity susceptibility coincides with the curvature function whose integration gives the topological invariant. Thus the quantum criticality of the curvature function near a topological phase transition also describes the criticality of the fidelity suscep…
Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学引力物理与量子信息研究中心、汤川理论物理研究所）；Department of Physics, Princeton University（普林斯顿大学物理系）；Graduate School of Science, The University of Tokyo（东京大学理学研究科）
General semiclassical expression for quantum fidelity (Loschmidt echo) of arbitrary pure and mixed states is derived. It expresses fidelity as an interference sum of dephasing trajectories weighed by the Wigner function of the initial state, and does not require that the initial state be localized in position or momentum. This general dephasing representation is special in that, counterintuitively, all of fidelity decay is due to dephasing and none due to the decay of classical overlaps. Surprising accuracy of the approximation is justified by invoking the shadowing theorem: twice--both for ph…
A Necessary And Sufficient Condition of Distillability with unite fidelity from Finite Copies of a Mixed State: The Most Efficient Purification Protocol
Using the adiabatic perturbation theory of driven dynamics [Phys. Rev. A 78, 052508 (2008)] we design a hierarchy of quantum state preparation protocols that systematically increase the fidelity at very long driving times. We test these and other protocols, including those based on the geometric analysis of the parameter space, in a single-qubit system and in a fully connected multi-qubit system showing in its infinite-size limit several quantum phase transitions. The new protocols excel in the asymptotic driving regime, above a crossover time from the Landau-Zener regime which increases with …
We implement a two-qubit logic gate between a $^{43}\mathrm{Ca}^+\,$ hyperfine qubit and a $^{88}\mathrm{Sr}^+\,$ Zeeman qubit. For this pair of ion species, the S--P optical transitions are close enough that a single laser of wavelength $402\,\mathrm{nm}$ can be used to drive the gate, but sufficiently well separated to give good spectral isolation and low photon scattering errors. We characterize the gate by full randomized benchmarking, gate set tomography and Bell state analysis. The latter method gives a fidelity of $99.8(1)\%$, comparable to that of the best same-species gates and consis…
Quantum information-based approaches, in particular the fidelity, have been flexible probes for phase boundaries of quantum matter. A major hurdle to a more widespread application of fidelity and other quantum information measures to strongly correlated quantum materials is the inaccessibility of the fidelity susceptibility to most state-of-the-art numerical methods. This is particularly apparent away from equilibrium where, at present, no general critical theory is available and many standard techniques fail. Motivated by the usefulness of quantum information based measures we show that a wid…
Polynomial-time certification of fidelity for many-body mixed states and mixed-state universality classes
Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）
In this paper, we analyze the quantum criticality of the Rabi-Stark model at finite ratios of the qubit and cavity frequencies in terms of the energy gap, the order parameter, as well as the fidelity, if the Stark coupling strength is the same as the cavity frequency. The critical exponents are derived analytically. The energy gap and the length critical exponents are different from those in the quantum Rabi model and the Dicke model. The finite size scaling analysis for the order parameter and the fidelity susceptibility is also performed. The universal scaling behaviors are demonstrated and …
Decoherence-induced self-dual criticality in topological states of matter
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；University of Geneva（日内瓦大学）；University of Cologne（科隆大学）；University of California, Santa Barbara（加州大学圣塔芭芭拉分校）
We study quantum phase transitions in Heisenberg antiferromagnetic chains with a staggered power-law decaying long-range interactions. Employing the density-matrix renormalization group (DMRG) algorithm and the fidelity susceptibility as the criticality measure, we establish more accurate values of quantum critical points than the results obtained from the spin-wave approximation, quantum Monte Carlo and DMRG in literatures. The deviation is especially evident for strong long-range interactions. We extend isotropic long-range interactions to the anisotropic cases and find that kaleidoscope of …
