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Recent studies have pointed out the intrinsic dependence of figures of merit of thermodynamic relevance -- such as work, heat and entropy production -- on the amount of quantum coherences that is made available to a system. However, whether coherences hinder or enhance the value taken by such quantifiers of thermodynamic performance is yet to be ascertained. We show that, when considering entropy production generated in a process taking a finite-size bipartite quantum system out of equilibrium through local non-unitary channels, no general monotonicity relationship exists between the entropy production and degree of quantum coherence in the state of the system. A direct correspondence between such quantities can be retrieved when considering specific forms of open-system dynamics applied to suitably chosen initial states. Our results call for a systematic study of the role of genuine quantum features in the non-equilibrium thermodynamics of quantum processes., Comment: 10 pages, 5 figures, RevTeX4-1. Close to published version in New J. Phys

The phenomenon of localization usually happens due to the existence of disorder in a medium. Nevertheless, certain quantum systems allow dynamical localization solely due to the nature of internal interactions. We study a discrete time quantum walker which exhibits disorder free localization. The quantum walker moves on a one-dimensional lattice and interacts with on-site spins by coherently rotating them around a given axis at each step. Since the spins do not have dynamics of their own, the system poses the local spin components along the rotation axis as an extensive number of conserved moments. When the interaction is weak, the spread of the walker shows subdiffusive behaviour having downscaled ballistic tails in the evolving probability distribution at intermediate time scales. However, as the interaction gets stronger the walker gets exponentially localized in the complete absence of disorder in both lattice and initial state. Using a matrix-product-state ansatz, we investigate the relaxation and entanglement dynamics of the on-site spins due to their coupling with the quantum walker. Surprisingly, we find that even in the delocalized regime, entanglement growth and relaxation occur slowly unlike marjority of the other models displaying a localization transition., Comment: 13 pages, 8 figures

We explore the environment-induced synchronization phenomenon in two-level systems in contact with a thermal dissipative environment. We first discuss the conditions under which synchronization emerges between a pair of two-level particles. That is, we analyze the impact of various model parameters on the emergence of (anti-)synchronization such as the environment temperature, the direct interaction between the particles, and the distance between them controlling the collectivity of the dissipation. We then enlarge the system to be composed of three two-level atoms to study the mutual synchronization between different particle pairs. Remarkably, we observe in this case a rich synchronization dynamics which stems from different possible spatial configurations of the atoms. Particularly, in sharp contrast with the two-atom case, we show that when the three atoms are in close proximity, appearance of anti-synchronization can be obstructed across all particle pairs due to frustration., Comment: 10 pages, 6 figures. Published version

We reveal the emergence of environment-induced spontaneous synchronization between two spin-1/2 quantum objects in a collision model setting. In particular, we determine the conditions for the dynamical establishment of synchronous evolution between local spin observables of a pair of spins undergoing open-system dynamics in the absence of an external drive. Exploiting the versatility of the collision model framework, we show that the formation of quantum or classical correlations between the principal spin pair are of no significant relevance to the manifestation of spontaneous quantum synchronization between them. Furthermore, we discuss the consequences of thermal effects on the environmental spins for the emergence of quantum synchronization., Comment: 12 pages, 8 figures. Close to published version. Appendices added and Acknowledgements updated

Protecting quantum states from the decohering effects of the environment is of great importance for the development of quantum computation devices and quantum simulators. Here, we introduce a continuous dynamical decoupling protocol that enables us to protect the entangling gate operation between two qubits from the environmental noise. We present a simple model that involves two qubits which interact with each other with a strength that depends on their mutual distance and generates the entanglement among them, as well as in contact with an environment. The nature of the environment, that is, whether it acts as an individual or common bath to the qubits, is also controlled by the effective distance of qubits. Our results indicate that the introduced continuous dynamical decoupling scheme works well in protecting the entangling operation. Furthermore, under certain circumstances, the dynamics of the qubits naturally led them into a decoherence-free subspace which can be used complimentary to the continuous dynamical decoupling., Comment: 9 pages, 3 figures, close to published version

We consider finite sized atomic systems with varying number of particles which have dipolar interactions among them and also under the collective driving and dissipative effect of thermal photon environment. Focusing on the simple case of two atoms, we investigate the impact of different parameters of the model on the coherence contained in the system. We observe that even though the system is initialized in a completely incoherent state, it evolves to a state with a finite amount of coherence and preserve that coherence in the long-time limit in the presence of thermal photons. We propose a novel scheme to utilize the created coherence in order to change the thermal state of a single two-level atom by repeatedly interacting it with a coherent atomic beam. Finally, we discuss the scaling of coherence as a function of the number of particles in our system up to $N=7$., Comment: 9 pages, 4 figures. Close to published version

We consider the dynamics of a collisional model in which both the system and environment are embodied by spin-$1/2$ particles. In order to include non-Markovian features in our model we introduce interactions among the environmental qubits and investigate the effect that different models of such interaction have on the degree of non-Markovianity of the system's dynamics. By extending that interaction beyond the nearest-neighbour, we enhance the degree of non-Markovianity in the system's dynamics. A further significant increase can be observed if a collective interaction with the forthcoming environmental qubits is considered. However, the observed degree of non-Markovianity in this case is non-monotonic with the increasing number of qubits included in the interaction. Moreover, one can establish a connection between the degree of non-Markovianity in the evolution of the system and the fading behaviour of quantum coherence in its state as the number of collisions grow. We complement our study with an investigation on system-environment correlations and present an example of their importance on a physical upper bound on the trace distance derivative., Comment: 9 pages, 7 figures. Close to published version

We explore quantum and classical correlations along with coherence in the ground states of spin-1 Heisenberg chains, namely the one-dimensional XXZ model and the one-dimensional bilinear biquadratic model, with the techniques of density matrix renormalization group theory. Exploiting the tools of quantum information theory, that is, by studying quantum discord, quantum mutual information and three recently introduced coherence measures in the reduced density matrix of two nearest neighbor spins in the bulk, we investigate the quantum phase transitions and special symmetry points in these models. We point out the relative strengths and weaknesses of correlation and coherence measures as figures of merit to witness the quantum phase transitions and symmetry points in the considered spin-1 Heisenberg chains. In particular, we demonstrate that as none of the studied measures can detect the infinite order Kosterlitz-Thouless transition in the XXZ model, they appear to be able to signal the existence of the same type of transition in the biliear biquadratic model. However, we argue that what is actually detected by the measures here is the SU(3) symmetry point of the model rather than the infinite order quantum phase transition. Moreover, we show in the XXZ model that examining even single site coherence can be sufficient to spotlight the second-order phase transition and the SU(2) symmetry point., Comment: 8 pages. 5 figures

We study the occurrence of errors in a continuously decoupled two-qubit state during a $\sqrt{SWAP}$ quantum operation under decoherence. We consider a realization of this quantum gate based on the Heisenberg exchange interaction, which alone suffices for achieving universal quantum computation. Furthermore, we introduce a continuous-dynamical-decoupling scheme that commutes with the Heisenberg Hamiltonian to protect it from the amplitude damping and dephasing errors caused by the system-environment interaction. We consider two error-protection settings. One protects the qubits from both amplitude damping and dephasing errors. The other features the amplitude damping as a residual error and protects the qubits from dephasing errors only. In both settings, we investigate the interaction of qubits with common and independent environments separately. We study how errors affect the entanglement and fidelity for different environmental spectral densities., Comment: Extended version of arXiv:1005.1666. To appear in PRA

In this review, we discuss the zero and finite temperature behavior of various bipartite quantum and total correlation measures, the skew information-based quantum coherence, and the local quantum uncertainty in the thermal ground state of the one-dimensional anisotropic XY model in transverse magnetic field. We compare the ability of considered measures to correctly detect or estimate the quantum critical point and the non-trivial factorization point possessed by the spin chain., Comment: 29 pages, 8 figures. A review paper accepted for publication in the special issue Entanglement Entropy in the journal Entropy

Exchange of information between a quantum system and its surrounding environment plays a fundamental role in the study of the dynamics of open quantum systems. Here we discuss the role of the information exchange in the non-Markovian behavior of dynamical quantum processes following the decoherence approach, where we consider a quantum system that is initially correlated with its measurement apparatus, which in turn interacts with the environment. We introduce a new way of looking at the information exchange between the system and environment using the quantum loss, which is shown to be closely related to the measure of non-Markovianity based on the quantum mutual information. We also extend the results of [Phys. Rev. Lett. 112, 210402 (2014)] by Fanchini et al. in several directions, providing a more detailed investigation of the use of the accessible information for quantifying the backflow of information from the environment to the system. Moreover, we reveal a clear conceptual relation between the entanglement and mutual information based measures of non-Markovianity in terms of the quantum loss and accessible information. We compare different ways of studying the information flow in two theoretical examples. We also present experimental results on the investigation of the quantum loss and accessible information for a two-level system undergoing a zero temperature amplitude damping process. We use an optical approach that allows full access to the state of the environment., Comment: 11 pages, 7 figures

Quantum algorithms are known for presenting more efficient solutions to certain computational tasks than any corresponding classical algorithm. It has been thought that the origin of the power of quantum computation has its roots in non-classical correlations such as entanglement or quantum discord. However, it has been recently shown that even a single pure qudit is sufficient to design an oracle-based algorithm which solves a black-box problem faster than any classical approach to the same problem. In particular, the algorithm that we consider determines whether eight permutation functions defined on a set of four elements is positive or negative cyclic. While any classical solution to this problem requires two evaluations of the function, quantum mechanics allows us to perform the same task with only a single evaluation. Here, we present the first experimental demonstration of the considered quantum algorithm with a quadrupolar nuclear magnetic resonance setup using a single four-level quantum system, i.e., a ququart., Comment: Improved version with new title. 5 pages, 3 figures

We explore the local quantum coherence and the local quantum uncertainty, based on Wigner-Yanase skew information, in the ground state of the anisotropic spin-1/2 XY chain in transverse magnetic field. We show that the skew information, as a figure of merit, supplies the necessary information to reveal the occurrence of the second order phase transition and the completely factorized ground state in the XY model. Additionally, in the same context, we also discuss the usefulness of a simple experimentally friendly lower bound of local quantum coherence. Furthermore, we demonstrate how the connection between the appearance of non-analyticities in the local quantum uncertainty of the ground state and the quantum phase transitions does not hold in general, by providing explicit examples of the situation. Lastly, we discuss the ability of the local quantum coherence to accurately estimate the critical point of the phase transition, and investigate the robustness of the factorization phenomenon at low temperatures., Comment: 7 pages, 6 figures. Title changed. Close to published version

Quantum algorithms are known for providing more efficient solutions to certain computational tasks than any corresponding classical algorithm. Here we show that a single qudit is sufficient to implement an oracle based quantum algorithm, which can solve a black-box problem faster than any classical algorithm. For $2d$ permutation functions defined on a set of $d$ elements, deciding whether a given permutation is even or odd, requires evaluation of the function for at least two elements. We demonstrate that a quantum circuit with a single qudit can determine the parity of the permutation with only one evaluation of the function. Our algorithm provides an example for quantum computation without entanglement since it makes use of the pure state of a qudit. We also present an experimental realization of the proposed quantum algorithm with a quadrupolar nuclear magnetic resonance using a single four-level quantum system, i.e., a ququart., Comment: Combined version of arXiv:1403.5861 [quant-ph] and arXiv:1406.3579 [quant-ph]

The degree of non-Markovianity of quantum processes has been characterized in several different ways in the recent literature. However, the relationship between the non-Markovian behavior and the flow of information between the system and the environment through an entropic measure has not been yet established. We propose an entanglement-based measure of non-Markovianity by employing the concept of assisted knowledge, where the environment E, acquires information about a system S, by means of its measurement apparatus A. The assisted knowledge, based on the accessible information in terms of von-Neumann entropy, monotonically increases in time for all Markovian quantum processes. We demonstrate that the signatures of non-Markovianity can be captured by the nonmonotonic behaviour of the assisted knowledge. We explore this scenario for a two-level system undergoing a relaxation process, through an experimental implementation using an optical approach that allows full access to the state of the environment., Comment: Final Version

We have analytically calculated the quantum discord for a system composed of spin-$j$ and spin-1/2 subsystems possessing SU(2) symmetry. We have compared our results with the quantum discord of states having similar symmetries and seen that in our case amount of quantum discord is much higher. Moreover, using the well known entanglement properties of these states, we have also compared their quantum discord with entanglement. Although the system under consideration is separable nearly all throughout of its parameter space as $j$ increases, we have seen that discord content remains significantly large. Investigation of quantum discord in SU(2) invariant states may find application in quantum computation protocols that utilize quantum discord as a resource since they arise in many real physical systems., Comment: 9 pages, 2 figures

We study the thermal quantum correlations and entanglement in spin-1 Bose-Hubbard model with two and three particles. While we use negativity to calculate entanglement, more general non-classical correlations are quantified using a new measure based on a necessary and sufficient condition for zero-discord state. We demonstrate that the energy level crossings in the ground state of the system are signalled by both the behavior of thermal quantum correlations and entanglement., Comment: To be published in the Proceedings of CEWQO-2012

We investigate the thermal quantum and total correlations in the anisotropic XY spin chain in transverse field. While we adopt concurrence and geometric quantum discord to measure quantum correlations, we use measurement-induced nonlocality and an alternative quantity defined in terms of Wigner-Yanase information to quantify total correlations. We show that the ability of these measures to estimate the critical point at finite temperature strongly depend on the anisotropy parameter of the Hamiltonian. We also identify a correlation measure which detects the factorized ground state in this model. Furthermore, we study the effect of temperature on long-range correlations., Comment: 7 pages, 6 figures

Special relativity forbids superluminal influences. Using only the no-signaling principle and an assumption about the form of the Schmidt decomposition, we show that for "any" allowed fidelity there is a "unique" approximate qubit cloner which can be written explicitly. We introduce the prime cloners whose fidelities have multiplicative property and show that the fidelity of the prime cloners for the infinite copy limit is 1/2., Comment: 8 pages, no figures