We study the evolution of conditional mutual information in generic open quantum systems, focusing on one-dimensional random circuits with interspersed local noise. Unlike in noiseless circuits, where conditional mutual information spreads linearly while being bounded by the lightcone, we find that noisy random circuits with an error rate $p$ exhibit superlinear propagation of conditional mutual information, which diverges far beyond the lightcone at a critical circuit depth $t_c \propto p^{-1}$. We demonstrate that the underlying mechanism for such rapid spreading is the combined effect of local noise and a scrambling unitary, which selectively removes short-range correlations while preserving long-range correlations. To analytically capture the dynamics of conditional mutual information in noisy random circuits, we introduce a coarse-graining method, and we validate our theoretical results through numerical simulations. Furthermore, we identify a universal scaling law governing the spreading of conditional mutual information.
We study noise-averaged observables for a system of exchange-coupled quantum spins (qubits), each subject to a stochastic drive, by establishing mappings onto stochastic models in the strong-noise limit. Averaging over noise yields Lindbladian equations of motion; when these are subjected to a strong-noise perturbative treatment, classical master equations are found to emerge. The dynamics of noise averages of operators displays diffusive behaviour or exponential relaxation, depending on whether the drive conserves one of the spin components or not. In the latter case, the second moment of ope…
We provide the optimal measurement strategy for a class of noisy channels that reduce to the identity channel for a specific value of a parameter (spreading channels). We provide an example that is physically relevant: the estimation of the absolute value of the displacement in the presence of phase randomizing noise. Surprisingly, this noise does not affect the effectiveness of the optimal measurement. We show that, for small displacement, a squeezed vacuum probe field is optimal among strategies with same average energy. A squeezer followed by photodetection is the optimal detection strategy…
Understanding the spreading of quantum correlations in out-of-equilibrium many-body systems is one of the major challenges in physics. For {\it isolated} systems, a hydrodynamic theory explains the origin and spreading of entanglement via the propagation of quasi-particle pairs. However, when systems interact with their surrounding much less has been established. Here we show that the quasi-particle picture remains valid for open quantum systems: while information is still spread by quasiparticles, the environment modifies their correlation and introduces incoherent and mixing effects. For fre…
We study the spreading of quantum correlations and information in a one-dimensional quantum spin chain with critical disorder as encoded in an infinite randomness fixed point. Specifically, we focus on the dynamics after a quantum quench of the Rényi entropies, of the mutual information and of the entanglement negativity in the prototypical XXZ spin chain with random bonds and anisotropy parameters. We provide analytic predictions in the scaling regime based on real-space renormalization group methods. We support these findings through numerical simulations in the non-interacting limit, where …
We use a noisy signal with finite correlation time to drive a spin (dissipative impurity) in the quantum XY spin chain and calculate the dynamics of entanglement entropy of a bipartition of spins, for a stochastic quantum trajectory. We compute the noise averaged entanglement entropy of a bipartition of spins and observe that its speed of spreading decreases at strong dissipation, as a result of the Zeno effect. We recover the Zeno crossover and show that noise averaged entanglement entropy can be used as a proxy for the heating and Zeno regimes. Upon increasing the correlation time of the noi…
Quantum information spreading and scrambling in many-body systems attract interests these days. Tripartite mutual information (TMI) based on operator-based entanglement entropy (EE) is an efficient tool for measuring them. In this paper, we study random spin chains that exhibit phase transitions accompanying nontrivial change in topological properties. In their phase diagrams, there are two types of many-body localized (MBL) states and one thermalized regime intervening these two MBL states. Quench dynamics of the EE and TMI display interesting behaviors providing essential perspective concern…
Institute for Quantum Information and Matter, California Institute of Technology（加州理工学院量子信息与物质研究所）；Leinweber Institute for Theoretical Physics, Stanford University（斯坦福大学莱因韦伯理论物理研究所）
Tripartite mutual information (TMI) is an efficient observable to quantify the ability of scrambler for unitary time-evolution operator with quenched many-body Hamiltonian. In this paper, we give numerical demonstrations of the TMI in disorder-free (translational invariant) spin models with 3-body and 4-body multiple-spin interactions. The dynamical behavior of the TMI of these models does {\it not} exhibit linear light-cone for sufficiently strong interactions. In early-time evolution, the TMI displays distinct negative increase behavior fitted by a logarithmic-like function. This is in contr…
Starting from several copies of bipartite noisy entangled states, we design a global and optimal local measurement-based protocol in one- and two-dimensional lattices by which any two or more prefix sites can be connected via entanglement. Production of bipartite as well as multipartite entangled states in a network is verified in a device independent way through the violation of Bell inequalities with two settings per site and with continuous range of settings. We also note that if the parties refuse to perform local measurements, the entanglement distribution scheme fails. We obtain critical…
Partial projected ensembles reveal slow tilt-constrained information spreading
Institute for Quantum Science and Technology, Shanghai University（上海大学量子科学与技术研究院）；School of Physics and Optoelectronics, Xiangtan University（湘潭大学物理与光电工程学院）；Department of Physics, National University of Singapore（新加坡国立大学物理系）
We consider the problem of estimating the spatial separation between two mutually incoherent point light sources using the super-resolution imaging technique based on spatial mode demultiplexing with noisy detectors. We show that in the presence of noise the resolution of the measurement is limited by the signal-to-noise ratio (SNR) and the minimum resolvable spatial separation has a characteristic dependence of $\sim$SNR$^{-1/2}$. Several detection techniques, including direct photon counting, as well as homodyne and heterodyne detection are considered.
The process by which open quantum systems thermalize with an environment is both of fundamental interest and relevant to noisy quantum devices. As a minimal model of this process, we consider a qudit chain evolving under local random unitaries and local depolarization channels. After mapping to a statistical mechanics model, the depolarization (noise) acts like a symmetry-breaking field, and we argue that it causes the system to thermalize within a timescale independent of system size. We show that various bipartite entanglement measures -- mutual information, operator entanglement, and entang…
We present a scheme for joint remote state preparation (JRSP) of three-particle state via three tripartite Greenberger-Horne-Zeilinger (GHZ) entangled states as the quantum channel linking the parties. We use eight-qubit mutually orthogonal basis vector as measurement point of departure. The likelihood of success for this scheme has been found to be $1/8$. However, by putting some special cases into consideration, the chances can be ameliorated to $1/4$ and $1$. The effects of amplitude-damping noise, phase-damping noise and depolarizing noise on this scheme have been scrutinized and the analy…
Local pure states represent a fundamental resource in quantum information theory. In this work we obtain one-shot achievable bounds on the rates for local purity distillation, in the single-party and in the two-party cases. In both situations, local noisy operations are freely available, while in the two-party case also one-way classical communication can be used. In addition, in both situations local pure ancillas can be borrowed, as long as they are discounted from the final net rate of distillation. The one-shot rates that we obtain, written in terms of mutual information-like quantities, a…
The central philosophy of statistical mechanics (stat-mech) and random-matrix theory of complex systems is that while individual instances are essentially intractable to simulate, the statistical properties of random ensembles obey simple universal "laws". This same philosophy promises powerful methods for studying the dynamics of quantum information in ideal and noisy quantum circuits -- for which classical description of individual circuits is expected to be generically intractable. Here, we review recent progress in understanding the dynamics of quantum information in ensembles of random qu…
Spacetime picture for entanglement generation in noisy fermion chains
Rudolf Peierls Centre for Theoretical Physics（鲁道夫·皮尔斯理论物理中心）；Laboratoire de Physique de l’École Normale Supérieure, CNRS, ENS & Université PSL, Sorbonne Université, Université Paris Cité（巴黎高等师范学院物理实验室，法国国家科学研究中心，巴黎高等师范学院及巴黎文理研究大学，索邦大学，巴黎西岱大学）
