arXiv subjects

Lorenza Viola

Publications and source records attributed to Lorenza Viola.

At least 109 records · Page 6Linked to original sources

arXiv2008

Quantum Markovian Subsystems: Invariance, Attractivity, and Control

We characterize the dynamical behavior of continuous-time, Markovian quantum systems with respect to a subsystem of interest. Markovian dynamics describes a wide class of open quantum systems of relevance to quantum information processing, subsystem encodings offering a general pathway to faithfully represent quantum information. We provide explicit linear-algebraic characterizations of the notion of invariant and noiseless subsystem for Markovian master equations, under different robustness assumptions for model-parameter and initial-state variations. The stronger concept of an attractive quantum subsystem is introduced, and sufficient existence conditions are identified based on Lyapunov's stability techniques. As a main control application, we address the potential of output-feedback Markovian control strategies for quantum pure state-stabilization and noiseless-subspace generation. In particular, explicit results for the synthesis of stabilizing semigroups and noiseless subspaces in finite-dimensional Markovian systems are obtained.

quant-ph↗

arXiv2008

Quantum Chaos, Delocalization, and Entanglement in Disordered Heisenberg Models

We investigate disordered one- and two-dimensional Heisenberg spin lattices across a transition from integrability to quantum chaos from both a statistical many-body and a quantum-information perspective. Special emphasis is devoted to quantitatively exploring the interplay between eigenvector statistics, delocalization, and entanglement in the presence of nontrivial symmetries. The implications of basis dependence of state delocalization indicators (such as the number of principal components) is addressed, and a measure of {\em relative delocalization} is proposed in order to robustly characterize the onset of chaos in the presence of disorder. Both standard multipartite and {\em generalized entanglement} are investigated in a wide parameter regime by using a family of spin- and fermion- purity measures, their dependence on delocalization and on energy spectrum statistics being examined. A distinctive {\em correlation between entanglement, delocalization, and integrability} is uncovered, which may be generic to systems described by the two-body random ensemble and may point to a new diagnostic tool for quantum chaos. Analytical estimates for typical entanglement of random pure states restricted to a proper subspace of the full Hilbert space are also established and compared with random matrix theory predictions.

quant-ph↗

arXiv2008

Generalized entanglement in static and dynamic quantum phase transitions

We investigate a class of one-dimensional, exactly solvable anisotropic XY spin-1/2 models in an alternating transverse magnetic field from an entanglement perspective. We find that a physically motivated Lie-algebraic generalized entanglement measure faithfully portraits the static phase diagram -- including second- and fourth-order quantum phase transitions belonging to distinct universality classes. In the simplest time-dependent scenario of a slow quench across a quantum critical point, we identify parameter regimes where entanglement exhibits universal dynamical scaling relative to the static limit.

cond-mat.stat-mech↗

arXiv2008

Long-time electron spin storage via dynamical suppression of hyperfine-induced decoherence in a quantum dot

The coherence time of an electron spin decohered by the nuclear spin environment in a quantum dot can be substantially increased by subjecting the electron to suitable dynamical decoupling sequences. We analyze the performance of high-level decoupling protocols by using a combination of analytical and exact numerical methods, and by paying special attention to the regimes of large inter-pulse delays and long-time dynamics, which are outside the reach of standard average Hamiltonian theory descriptions. We demonstrate that dynamical decoupling can remain efficient far beyond its formal domain of applicability, and find that a protocol exploiting concatenated design provides best performance for this system in the relevant parameter range. In situations where the initial electron state is known, protocols able to completely freeze decoherence at long times are constructed and characterized. The impact of system and control non-idealities is also assessed, including the effect of intra-bath dipolar interaction, magnetic field bias and bath polarization, as well as systematic pulse imperfections. While small bias field and small bath polarization degrade the decoupling fidelity, enhanced performance and temporal modulation result from strong applied fields and high polarizations. Overall, we find that if the relative errors of the control parameters do not exceed 5%, decoupling protocols can still prolong the coherence time by up to two orders of magnitude.

cond-mat.mes-hall↗

arXiv2008

Suppression of electron spin decoherence in a quantum dot

The dominant source of decoherence for an electron spin in a quantum dot is the hyperfine interaction with the surrounding bath of nuclear spins. The decoherence process may be slowed down by subjecting the electron spin to suitable sequences of external control pulses. We investigate the performance of a variety of dynamical decoupling protocols using exact numerical simulation. Emphasis is given to realistic pulse delays and the long-time limit, beyond the domain where available analytical approaches are guaranteed to work. Our results show that both deterministic and randomized protocols are capable to significantly prolong the electron coherence time, even when using control pulse separations substantially larger than what expected from the {\em upper cutoff} frequency of the coupling spectrum between the electron and the nuclear spins. In a realistic parameter range, the {\em total width} of such a coupling spectrum appears to be the physically relevant frequency scale affecting the overall quality of the decoupling.

cond-mat.mes-hall↗

arXiv2007

The structure of preserved information in quantum processes

We introduce a general operational characterization of information-preserving structures (IPS) -- encompassing noiseless subsystems, decoherence-free subspaces, pointer bases, and error-correcting codes -- by demonstrating that they are isometric to fixed points of unital quantum processes. Using this, we show that every IPS is a matrix algebra. We further establish a structure theorem for the fixed states and observables of an arbitrary process, which unifies the Schrodinger and Heisenberg pictures, places restrictions on physically allowed kinds of information, and provides an efficient algorithm for finding all noiseless and unitarily noiseless subsystems of the process.

quant-ph↗

arXiv2007

Generalized Coherent States as Preferred States of Open Quantum Systems

We investigate the connection between quasi-classical (pointer) states and generalized coherent states (GCSs) within an algebraic approach to Markovian quantum systems (including bosons, spins, and fermions). We establish conditions for the GCS set to become most robust by relating the rate of purity loss to an invariant measure of uncertainty derived from quantum Fisher information. We find that, for damped bosonic modes, the stability of canonical coherent states is confirmed in a variety of scenarios, while for systems described by (compact) Lie algebras stringent symmetry constraints must be obeyed for the GCS set to be preferred. The relationship between GCSs, minimum-uncertainty states, and decoherence-free subspaces is also elucidated.

quant-ph↗

arXiv2007

Generalized entanglement as a framework for complex quantum systems: Purity vs delocalization measures

We establish contact between the delocalization properties of pure quantum states, as quantified by their number of principal components, and the average generalized entanglement properties, as quantified by purity measures relative to different observable sets. We find that correlations between products of state vector components with respect to Hamming distance play an important role in the structure of subsystem-based purity measures. In particular, we derive general conditions under which the amount of global multipartite entanglement relates to the inverse participation ratio averaged over a maximal set of mutually unbiased product bases. Furthermore, we provide a method for computing the expected amount of generalized entanglement with respect to an arbitrary observable set for random pure states. Specific examples and an explicit application to a disordered quantum spin chain are discussed.

quant-ph↗

arXiv2007

Dynamical control of electron spin coherence in a quantum dot

We investigate the performance of dynamical decoupling methods at suppressing electron spin decoherence from a low-temperature nuclear spin reservoir in a quantum dot. The controlled dynamics is studied through exact numerical simulation, with emphasis on realistic pulse delays and long-time limit. Our results show that optimal performance for this system is attained by a periodic protocol exploiting concatenated design, with control rates substantially slower than expected from the upper spectral cutoff of the bath. For a known initial electron spin state, coherence can saturate at long times, signaling the creation of a stable ``spin-locked'' decoherence-free subspace. Analytical insight on saturation is obtained for a simple echo protocol, in good agreement with numerical results.

cond-mat.mes-hall↗

arXiv2007

Entanglement and Subsystems, Entanglement beyond Subsystems, and All That

Entanglement plays a pervasive role nowadays throughout quantum information science, and at the same time provides a bridging notion between quantum information science and fields as diverse as condensed-matter theory, quantum gravity, and quantum foundations. In recent years, a notion of ''Generalized Entanglement'' (GE) has emerged, based on the idea that entanglement may be directly defined through expectation values of preferred observables -- without reference to a preferred subsystem decomposition. Preferred observables capture the physically relevant point of view, as defined by dynamical, operational, or fundamental constraints. While reducing to the standard entanglement notion when preferred observables are restricted to arbitrary local observables acting on individual subsystems, GE substantially expands subsystem-based entanglement theories, in terms of both conceptual foundations and range of applicability. Remarkably, the GE framework allows for non-trivial entanglement to exist within a single, indecomposable quantum system, demands in general a distinction between quantum separability and absence of entanglement, and naturally extends to situations where existing approaches may not be directly useful -- such as entanglement in arbitrary convex-cones settings and entanglement for indistinguishable quantum particles. In this paper, we revisit the main motivations leading to GE, and summarize the accomplishments and prospects of the GE program to date, with an eye toward conceptual developments and implications. In particular, we explain how the GE approach both shares strong points of contact with abstract operational quantum theories and, ultimately, calls for an observer-dependent redefinition of concepts like locality, completeness, and reality in quantum theory.

quant-ph↗

arXiv2006

Randomized Dynamical Decoupling Techniques for Coherent Quantum Control

The need for strategies able to accurately manipulate quantum dynamics is ubiquitous in quantum control and quantum information processing. We investigate two scenarios where randomized dynamical decoupling techniques become more advantageous with respect to standard deterministic methods in switching off unwanted dynamical evolution in a closed quantum system: when dealing with decoupling cycles which involve a large number of control actions and/or when seeking long-time quantum information storage. Highly effective hybrid decoupling schemes, which combine deterministic and stochastic features are discussed, as well as the benefits of sequentially implementing a concatenated method, applied at short times, followed by a hybrid protocol, employed at longer times. A quantum register consisting of a chain of spin-1/2 particles interacting via the Heisenberg interaction is used as a model for the analysis throughout.

quant-ph↗

arXiv2006

Enhanced Convergence and Robust Performance of Randomized Dynamical Decoupling

We demonstrate the advantages of randomization in coherent quantum dynamical control. For systems which are either time-varying or require decoupling cycles involving a large number of operations, we find that simple randomized protocols offer superior convergence and stability as compared to deterministic counterparts. In addition, we show how randomization always allows to outperform purely deterministic schemes at long times, including combinatorial and concatenated methods. General criteria for optimally interpolating between deterministic and stochastic design are proposed and illustrated in explicit decoupling scenarios relevant to quantum information storage.

quant-ph↗

arXiv2006

Generalized Entanglement as a Natural Framework for Exploring Quantum Chaos

We demonstrate that generalized entanglement [Barnum {\em et al.}, Phys. Rev. A {\bf 68}, 032308 (2003)] provides a natural and reliable indicator of quantum chaotic behavior. Since generalized entanglement depends directly on a choice of preferred observables, exploring how generalized entanglement increases under dynamical evolution is possible without invoking an auxiliary coupled system or decomposing the system into arbitrary subsystems. We find that, in the chaotic regime, the long-time saturation value of generalized entanglement agrees with random matrix theory predictions. For our system, we provide physical intuition into generalized entanglement within a single system by invoking the notion of extent of a state. The latter, in turn, is related to other signatures of quantum chaos.

quant-ph↗

arXiv2006

Single-bit Feedback and Quantum Dynamical Decoupling

Synthesizing an effective identity evolution in a target system subjected to unwanted unitary or non-unitary dynamics is a fundamental task for both quantum control and quantum information processing applications. Here, we investigate how single-bit, discrete-time feedback capabilities may be exploited to enact or to enhance quantum procedures for effectively suppressing unwanted dynamics in a finite-dimensional open quantum system. An explicit characterization of the joint unitary propagators correctable by a single-bit feedback strategy for arbitrary evolution time is obtained. For a two-dimensional target system, we show how by appropriately combining quantum feedback with dynamical decoupling methods, concatenated feedback-decoupling schemes may be built, which can operate under relaxed control assumptions and can outperform purely closed-loop and open-loop protocols.

quant-ph↗

arXiv2006

Multipartite entanglement generation and fidelity decay in disordered qubit systems

We investigate multipartite entanglement dynamics in disordered spin-1/2 lattice models exhibiting a transition from integrability to quantum chaos. Borrowing from the recently introduced generalized entanglement framework, we construct measures for correlations relative to arbitrary local and bi-local spin observables, and show how they naturally signal the crossover between distinct dynamical regimes. In particular, we find that the generation of global entanglement is directly ruled by the local density of states in the short time limit, whereas the asymptotic amount of entanglement is proportional to the degree of delocalization of the chaotic many-body state. Our results are relevant to the stability of quantum information in disordered quantum computing hardware.

quant-ph↗

arXiv2006

Randomized control of open quantum systems

The problem of open-loop dynamical control of generic open quantum systems is addressed. In particular, I focus on the task of effectively switching off environmental couplings responsible for unwanted decoherence and dissipation effects. After revisiting the standard framework for dynamical decoupling via deterministic controls, I describe a different approach whereby the controller intentionally acquires a random component. An explicit error bound on worst-case performance of stochastic decoupling is presented.

quant-ph↗

arXiv2005

Dynamical control of qubit coherence: Random versus deterministic schemes

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 protocols based on purely deterministic, purely random, as well as hybrid design, and identify their relative merits and weaknesses at improving system performance. We find that for time-independent systems, hybrid protocols tend to perform better than pure random and may improve over standard asymmetric schemes, whereas random protocols can be considerably more stable against fluctuations in the system parameters. Beside shedding light on the physical requirements underlying randomized control, our analysis further demonstrates the potential for explicit control settings where the latter may significantly improve over conventional schemes.

quant-ph↗

arXiv2005

Random decoupling schemes for quantum dynamical control and error suppression

We present a general control-theoretic framework for constructing and analyzing random decoupling schemes, applicable to quantum dynamical control of arbitrary finite-dimensional composite systems. The basic idea is to design the control propagator according to a random rather than deterministic path on a group. We characterize the performance of random decoupling protocols, and identify control scenarios where they can significantly weaken time scale requirements as compared to cyclic counterparts. Implications for reliable quantum computation are discussed.

quant-ph↗