We study the disorder-perturbed transport of two noninteracting entangled particles in the absence of backscattering. This situation is, for instance, realized along edges of topological insulators. We find profoundly different responses to disorder-induced dephasing for the center-of-mass and relative coordinates: While a mirror symmetry protects even highly delocalized relative states when resonant with the symmetry condition, delocalizations in the center of mass [e.g., two-particle (N=2) N00N states] remain fully sensitive to disorder. We demonstrate the relevance of these differences to the example of interferometric entanglement detection. Our platform-independent analysis is based on the treatment of disorder-averaged quantum systems with quantum master equations.
We study the disorder-perturbed transport of two noninteracting entangled particles in the absence of backscattering. This situation is, for instance, realized along edges of topological insulators. We find profoundly different responses to disorder-induced dephasing for the center-of-mass and relative coordinates: While a mirror symmetry protects even highly delocalized relative states when resonant with the symmetry condition, delocalizations in the center of mass [e.g., two-particle (N=2) N00N states] remain fully sensitive to disorder. We demonstrate the relevance of these differences to the example of interferometric entanglement detection. Our platform-independent analysis is based on the treatment of disorder-averaged quantum systems with quantum master equations.
We analyze the disorder-perturbed transport of quantum states in the absence of backscattering. This comprises, for instance, the propagation of edge-mode wave packets in topological insulators, or the propagation of photons in inhomogeneous media. We quantify the disorder-induced dephasing, which we show to be bound. Moreover, we identify a gap condition to remain in the backscattering-free regime despite disorder-induced momentum broadening. Our analysis comprises the full disorder-averaged quantum state, on the level of both populations and coherences, appreciating states as potential carriers of quantum information. The well-definedness of states is guaranteed by our treatment of the nonequilibrium dynamics with Lindblad master equations.
We analyze the propagation of quantum states in the presence of weak disorder. In particular, we investigate the reliable transmittance of quantum states, as potential carriers of quantum information, through disorder-perturbed waveguides. We quantify wave-packet distortion, backscattering, and disorder-induced dephasing, which all act detrimentally on transport, and identify conditions for reliable transmission. Our analysis relies on the treatment of the nonequilibrium dynamics of ensemble-averaged quantum states in terms of quantum master equations.
Spin chains with symmetry-protected edge zero modes can be seen as prototypical systems for exploring topological signatures in quantum systems. These are useful for robustly encoding quantum information. However in an experimental realization of such a system, spurious interactions may cause the edge zero modes to delocalize. To stabilize against this influence beyond simply increasing the bulk gap, it has been proposed to harness suitable notions of disorder. Equipped with numerical tools for constructing locally conserved operators that we introduce, we comprehensively explore the interplay of local interactions and disorder on localized edge modes in the XZX cluster Hamiltonian. This puts us in a position to challenge the narrative that disorder necessarily stabilizes topological order. Contrary to heuristic reasoning, we find that disorder has no effect on the edge modes in the Anderson localized regime. Moreover, disorder helps localize only a subset of edge modes in the many-body interacting regime. We identify one edge mode operator that behaves as if subjected to a non-interacting perturbation, i.e., shows no disorder dependence. This implies that in finite systems, edge mode operators effectively delocalize at distinct interaction strengths. In essence, our findings suggest that the ability to identify and control the best localized edge mode trumps any gains from introducing disorder.
Spin chains with a symmetry-protected edge zero modes can be seen as prototypical systems for exploring topological signatures in quantum systems. However in an experimental realization of such a system, spurious interactions may cause the edge zero modes to delocalize. To combat this influence beyond simply increasing the bulk gap, it has been proposed to harness disorder which does not drive the system out of a topological phase. Equipped with numerical tools for constructing locally conserved operators that we introduce, we comprehensively explore the interplay of local interactions and disorder on localized edge modes in such systems. Contrary to established heuristic reasoning, we find that disorder has no effect on the edge mode localization length in the non-interacting regime. Moreover, disorder helps localize only a subset of edge modes in the truly interacting regime. We identify one edge mode operator that behaves as if subjected to a non-interacting perturbation, i.e., shows no disorder dependence. This implies that in finite systems, edge mode operators effectively delocalize at distinct interaction strengths despite the presence of disorder. In essence, our findings suggest that the ability to identify and control the best localized edge mode trumps any gains from introducing disorder.
The active harnessing of quantum resources in engineered quantum devices poses unprecedented requirements on device control. Besides the residual interaction with the environment, causing environment-induced decoherence, uncontrolled parameters in the system itself---disorder---remain as a substantial factor limiting the precision and thus the performance of devices. These perturbations may arise, for instance, due to imperfect sample production, stray fields, or finite accuracy of control electronics. Disorder-dressed quantum evolution means a unifying framework, based on quantum master equations, to analyze how these detrimental influences cause deviations from the desired system dynamics. This description may thus contribute to unveiling and mitigating disorder effects towards robust schemes. To demonstrate the broad scope of this framework, we evaluate two distinct scenarios: a central spin immersed in an isotropic spin bath and a random mass Dirac particle. In the former scenario, we demonstrate how the disorder average reflects purity oscillations, indicating the time- and state-dependent severity of the disorder impact. In the latter scenario, we discuss disorder-induced backscattering and disorder-induced Zitterbewegung as consequences of the breakup of spin-momentum locking.
We study quantum transport in disordered systems with particle-hole symmetric Hamiltonians. The particle-hole symmetry is spontaneously broken after averaging with respect to disorder, and the resulting massless mode is treated in a random-phase representation of the invariant measure of the symmetry group. We compute the resulting fermionic functional integral of the average two-particle Green's function in a perturbation theory around the diffusive limit. The results up to two-loop order show that the corrections vanish, indicating that the diffusive quantum transport is robust. On the other hand, the diffusion coefficient depends strongly on the particle-hole symmetric Hamiltonian we choose to study. This reveals a connection between the underlying microscopic theory and the classical long-scale metallic behaviour of these systems.