Quantum information is scrambled via chaotic time evolution in many-body systems. The recovery of initial information embedded locally in the system from the scrambled quantum state is a fundamental concern in many contexts. From a dynamical perspective, information recovery can measure dynamical instability in quantum chaos, fault-tolerant quantum computing, and the black hole information paradox. This article considers general aspects of quantum information recovery when the scrambling dynamics have conservation laws due to Lie group symmetries. Here, we establish fundamental limitations on the information recovery from scrambling dynamics with arbitrary Lie group symmetries. We show universal relations between information recovery, symmetry, and quantum coherence, which apply to many physical situations. The relations predict that the behavior of the Hayden-Preskill black hole model changes qualitatively under the assumption of the energy conservation law. Consequently, we can rigorously prove that under the energy conservation law, the error of the information recovery from a small black hole remains unignorably large until it completely evaporates. Moreover, even when the black hole is very large, the recovery of information thrown into the black hole is not completed until most of the black hole evaporates. The relations also provide a unified view of the symmetry restrictions on quantum information processing, such as the approximate Eastin-Knill theorem and the Wigner-Araki-Yanase theorem for unitary gates.
We consider the quantum discord in a two-particle spin-1/2 system (dimer) governed by the standard multiple quantum (MQ) Hamiltonian and reveal the relation between the discord and the intensity of the second-order MQ coherence. Since the coherence intensities may be measured in experiment, we obtain a method of detecting the quantum discord in experiment. Comparison of discord and concurrence is represented.
We show that measurement can recover the quantum coherence of a qubit in a non-Markovian environment. The experimental demonstration in an optical system is provided by comparing the visibilities (and fidelities) of the final states with and without measurement. This method can be extended to other two-level quantum systems and entangled states in a non-Markovian evolution environment. It may also be used to implement other quantum information processing.
In this study, we model a harmonic oscillator that enters an interferometer partially coupled to a thermal bath of oscillatory fields by employing a Brownian-type Lindblad master equation. More specifically, we investigate the dynamics and the variations of the thermodynamic quantities of the system at different temperatures. We recognize that although the system can remain coherent during its interaction with the thermal bath in the low-temperature limit, the system's entropy production violates the Clausius inequality. Furthermore, we argue that the system's coherence is the source of this v…
We study the dynamics of quantum coherence and quantum correlations in two semiconductor double-dot molecules separated by a distance and indirectly coupled via a transmission line resonator. Dominant dissipation processes are considered. The numerical results show the sudden death of entanglement and the robustness of quantum discord to sudden death. Furthermore, the results indicate the dephasing processes in our model can lead in the revival and decay of coherence and discord with the absence of entanglement for certain initial states. By observing the dynamics of coherence versus discord f…
Coherence evolution and echo effect of an electron spin, which is coupled inhomogeneously to an interacting one-dimensional finite spin bath via hyperfine-type interaction, is studied using the adaptive time dependent density matrix renormalization group (t-DMRG) method. It is found that the interplay of the coupling inhomogeneity and the transverse intra-bath interactions results in two qualitatively different coherence evolutions, namely, a coherence preserving evolution characterized by periodic oscillation and a complete decoherence evolution. Correspondingly, the echo effects induced by a…
Complete complementarity relations, as e.g. $P(ρ_{A})^{2} + C(ρ_{A})^{2} + E(|Ψ\rangle_{AB})^{2}=1$, constrain the local predictability, $P$, and local coherence, $C$, and the entanglement, $E$, of bipartite pure states. For pairs of qubits prepared initially in a particular class of partially entangled pure states with null local coherence, these relations were used in Ref. [Phys. Lett. A, 451, 128414 (2022)] to provide an operational connection between local predictability of the pre-measurement states with the probability of the maximally entangled components of the states after the Bell-ba…
Coherence arises from the superposition principle, where it plays a central role in quantum mechanics. In [Phys.Rev.Lett.114,210401(2015)], it has been shown that the freezing phenomenon of quantum correlations beyond entanglement, is intimately related to the freezing of quantum coherence (QC). In this paper, we compare the behaviour of entanglement and quantum discord with quantum coherence in two di erent subsystems (optical and mechanical). We use respectively the en-tanglement of formation (EoF) and the Gaussian quantum discord (GQD) to quantify entanglement and quantum discord. Under the…
Dicke superradiance, i.e., the enhanced spontaneous emission of coherent radiation, is often attributed to radiation emitted by synchronized dipoles coherently oscillating in phase. At the same time, Dicke derived superradiance assuming atoms in entangled Dicke states which do not display any dipole moment. To shed light on this apparent paradox, we study the intensity distribution arising from two identical two-level atoms prepared either in an entangled Dicke state or in a separable atomic state with non-vanishing dipole moment. We find that the two configurations produce similar far field i…
The double-slit interferometer and the Mach-Zehnder interferometer (MZI) with balanced beam splitters are prototypical setups for investigating the quantum wave-particle duality. These setups induced a quantitative association of interferometric visibility (IVI) with the wave aspect of a single quantum system (WAQ). Recently, it was realized that quantum coherence (QC) can be better suited than IVI for quantifying the WAQ in complementarity relations. In this article, we investigate a MZI with biased beam splitters both in the input and the output, and we show that in some cases the IVI is not…
The dynamics of entanglement between three - level atoms coupled to the common vacuum is investigated. We show that the collective effects such as collective damping, dipole - dipole interaction and the cross coupling between orthogonal dipoles, play a crucial role in the process of creation of entanglement. In particular, the additional cross coupling enhances the production of entanglement. For the specific initial states we find that the effect of delayed sudden birth of entanglement, recently invented by Ficek and Tanas [Phys. Rev. A 77, o54301(2008)] in the case of two - level atoms, can …
The coherence and correlation properties of effective bosonic modes of a nano-mechanical cavity composed of an oscillating mirror and containing an optical lattice of regularly trapped atoms are studied. The system is modeled as a three-mode system, two orthogonal polariton modes representing the coupled optical lattice and the cavity mode, and one mechanical mode representing the oscillating mirror. We examine separately the cases of two-mode and three-mode interactions which are distinguished by a suitable tuning of the mechanical mode to the polariton mode frequencies. In the two-mode case,…
The reconstruction of the state of a multipartite quantum mechanical system represents a fundamental task in quantum information science. At its most basic, it concerns a state of a bipartite quantum system whose subsystems are subjected to local operations. We compare two different methods for obtaining the original state from the state resulting from the action of these operations. The first method involves quantum operations called Petz recovery maps, acting locally on the two subsystems. The second method is called matrix (or state) reconstruction and involves local, linear maps which are …
We revisit the problem of switching off unwanted phase evolution and decoherence in a single two-state quantum system in the light of recent results on random dynamical decoupling methods [L. Viola and E. Knill, Phys. Rev. Lett. {\bf 94}, 060502 (2005)]. A systematic comparison with standard cyclic decoupling is effected for a variety of dynamical regimes, including the case of both semiclassical and fully quantum decoherence models. In particular, exact analytical expressions are derived for randomized control of decoherence from a bosonic environment. We investigate quantitatively control pr…
In this work we study the nature of correlations among mixed states in the setup of two symmetric strips. We use various tools to determine how the bulk geometry could be reconstructed from the boundary mixed information. These tools would be the modular Hamiltonian and modular flow, OPE blocks, quantum recovery channels such as Petz map, Uhlmann holonomy and Wilson lines. We comment on the similarities and connections between these approaches in our symmetric setup of a mixed system. Specially, we use parameters such as dissipation which is being modeled by the mass of graviton, and also the …
Condensed matter physics at room temperature usually assumes that electrons in conductors can be described as spatially narrow wave packets - in contrast to what the Schrödinger equation would predict. How a finite-temperature environment can localize wave functions is still being debated. Here, we represent the environment by a fluctuating potential and investigate different unravellings of the Lindblad equation that describes the one-dimensional tight-binding model in the presence of such a potential. While all unravellings show a fast loss of phase coherence, only part of them lead to narro…
We consider the problem of energy transport in a chain of coupled quantum systems with the goal of shedding light on how nonclassical resources can affect transport. We study the cases for which either coherent or incoherent energy hopping takes place in the chain. Here, incoherent energy hopping is referred to as the "classical" scenario in allusion to its fully diagonal dynamics in the basis formed by the eigenstates of the decoupled sites. We focus on the case of a linear chain of two-level sites and find a hopping rate threshold above which the coherent quantum case is more efficient than …
Typical studies of quantum error correction assume probabilistic Pauli noise, largely because it is relatively easy to analyze and simulate. Consequently, the effective logical noise due to physically realistic coherent errors is relatively unknown. Here, we prove that encoding a system in a stabilizer code and measuring error syndromes decoheres errors, that is, causes coherent errors to converge toward probabilistic Pauli errors, even when no recovery operations are applied. Two practical consequences are that the error rate in a logical circuit is well quantified by the average gate fidelit…
We investigate the relationship between non-Markovianity and the effectiveness of a dynamical decoupling protocol for qubits undergoing pure dephasing. We consider an exact model in which dephasing arises due to a bosonic environment with a spectral density of the Ohmic class. This is parametrised by an Ohmicity parameter by changing which we can model both Markovian and non-Markovian environments. Interestingly, we find that engineering a non-Markovian environment is detrimental to the efficiency of the dynamical decoupling scheme, leading to a worse coherence preservation. We show that each …
Pulse-Level Compilation of Measurement-Free Recovery in Transmon Circuits
Beijing National Laboratory for Condensed Matter Physics, 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）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Hefei National Laboratory（合肥国家实验室）
We analyze non-Markovian evolution of open quantum systems. It is shown that any dynamical map representing evolution of such a system may be described either by non-local master equation with memory kernel or equivalently by equation which is local in time. These two descriptions are complementary: if one is simple the other is quite involved, or even singular, and vice versa. The price one pays for the local approach is that the corresponding generator keeps the memory about the starting point `t_0'. This is the very essence of non-Markovianity. Interestingly, this generator might be highly …
We analyze interrelation of quantum and classical entanglement. The latter notion is widely used in classical optic simulation of some quantum-like features of light. We criticize the common interpretation that "quantum nonlocality" is the basic factor differing quantum and classical realizations of entanglement. Instead, we point to the breakthrough Grangier et al. experiment on coincidence detection which was done in 1986 and played the crucial role in rejection of (semi-)classical field models in favor of quantum mechanics. Classical entanglement sources produce light beams with the coeffic…
We analyze the light scattered by a single InAs quantum dot interacting with a resonant continuous-wave laser. High resolution spectra reveal clear distinctions between coherent and incoherent scattering, with the laser intensity spanning over four orders of magnitude. We find that the fraction of coherently scattered photons can approach unity under sufficiently weak or detuned excitation, ruling out pure dephasing as a relevant decoherence mechanism. We show how spectral diffusion shapes spectra, correlation functions, and phase-coherence, concealing the ideal radiatively-broadened two-level…
The interplay between dissipation and internal interactions in quantum many-body systems gives rise to a wealth of novel phenomena. Here we investigate spin-1/2 chains with uniform local couplings to a Markovian environment using the time-dependent density matrix renormalization group (tDMRG). For the open XXZ model, we discover that the decoherence time diverges in the thermodynamic limit. The coherence decay is then algebraic instead of exponential. This is due to a vanishing gap in the spectrum of the corresponding Liouville superoperator and can be explained on the basis of a perturbative …
The random magnetic field produced by nuclear spins has long been viewed as the dominating source of decoherence in the quantum-dot based spins. Here we obtain in both exact and analytical manner the dynamics of spin qubits coupled to nuclear spin environments via the hyperfine interaction, going beyond the weak system-bath interaction and Markovian approximation. We predict that the detailed-balance breaking produced by chemical potential gradient in nuclear baths leads to the rapid oscillations of populations, quantum coherence and entanglement, which are absent in the conventional case (i.e…
We demonstrate that the coupling of excitonic and vibrational motion in biological complexes can provide mechanisms to explain the long-lived oscillations that have been obtained in non linear spectroscopic signals of different photosynthetic pigment protein complexes and we discuss the contributions of excitonic versus purely vibrational components to these oscillatory features. Considering a dimer model coupled to a structured spectral density we exemplify the fundamental aspects of the electron-phonon dynamics, and by analyzing separately the different contributions to the non linear signal…
