We discuss the behavior of quantum and classical pairwise correlations in critical systems, with quantumness measured by discord. analytically derive these for general real density matrices displaying ${Z}_{2}$ symmetry. As an illustration, we analyze both $XXZ$ transverse field Ising models. Finite size as well infinite chains are investigated criticality is discussed. Moreover, identify spin functions that govern correlations. a further example, also consider Hartree-Fock ground state...

We develop a general theory of the relation between quantum phase transitions (QPTs) characterized by nonanalyticities in energy and bipartite entanglement. derive functional matrix elements two-particle reduced density matrices eigenvalues two-body Hamiltonians d-level systems. The ground state eigenvalue its derivatives, whose nonanalyticity characterizes QPT, are directly tied to entanglement measures. show that first-order QPTs signaled themselves second-order first derivative elements....

We propose a global measure for quantum correlations in multipartite systems, which is obtained by suitably recasting the discord terms of relative entropy and local von Neumann measurements. The symmetric with respect to subsystem exchange shown be non-negative an arbitrary state. As illustration, we consider tripartite Werner-GHZ state at criticality. In particular, contrast pairwise discord, show that able characterize infinite-order phase transition Ashkin-Teller spin chain.

It has recently been pointed out that the geometric quantum discord, as defined by Hilbert-Schmidt norm (2-norm), is not a good measure of correlations, since it may increase under local reversible operations on unmeasured subsystem. Here, we revisit discord considering general Schatten $p$-norms, explicitly showing 1-norm only $p$-norm able to define consistent correlation measure. In addition, restricting optimization tetrahedron two-qubit Bell-diagonal states, provide an analytical...

We investigate pairwise quantum correlation as measured by the discord well its classical counterpart in thermodynamic limit of anisotropic $\mathit{XY}$ spin-$1/2$ chains a transverse magnetic field for both zero and finite temperatures. Analytical expressions correlations are obtained spin pairs at any distance. In case temperature, it is shown that farther than second neighbors able to characterize phase transition, even though entanglement absent such distances. For temperatures, we show...

We analyze the performance of adiabatic quantum computation (AQC) subject to decoherence. To this end, we introduce an inherently open-systems approach, based on a recent generalization approximation. In contrast closed systems, show that system may initially be in regime, but then undergo transition regime where adiabaticity breaks down. As consequence, success AQC depends sensitively competition between various pertinent rates, giving rise optimality criteria.

We generalize the standard quantum adiabatic approximation to case of open systems. define limit an system as regime in which its dynamical superoperator can be decomposed terms independently evolving Jordan blocks. then establish validity and invalidity conditions for this discuss their applicability superoperators changing slowly time. As example, evolution a two-level is analyzed.

Geometric quantum discord is a well-defined measure of correlation if Schatten 1-norm (trace norm) adopted as distance measure. Here, we analytically investigate the dynamical behavior geometric under effect decoherence. By starting from arbitrary Bell-diagonal mixed states Markovian local noise, provide decays function decoherence parameters. In particular, show that exhibits possibility double sudden changes and freezing during its evolution. For non-trivial simple channels, these are new...

A fully operational loss-free quantum battery requires an inherent control over the energy transfer process, with ability of keeping retained no leakage. Moreover, it also a stable discharge mechanism, which entails that revivals occur as device starts its distribution. Here we provide scalable solution for both requirements. To this aim, propose general design based on current (EC) observable quantifying rate to consumption hub. More specifically, introduce instantaneous EC operator...

We introduce a shortcut to the adiabatic gate teleportation model of quantum computation. More specifically, we determine fast local counterdiabatic Hamiltonians able implement as universal computational primitive. In this scenario, provide driving for arbitrary n-qubit gates, which allows achieve universality through variety sets. Remarkably, our approach maps superadiabatic Hamiltonian an into implementation rotated dynamics state teleportation. This result is rather general, with speed...

Correlations in quantum systems exhibit a rich phenomenology under the effect of various sources noise. We investigate theoretically and experimentally dynamics correlations their classical counterparts two nuclear magnetic resonance setups, as measured by geometric quantifiers based on trace norm. consider two-qubit prepared Bell diagonal states, perform experiments real decohering environments resulting from Markovian local noise which preserves form states. then report first observation...

Abstract Adiabatic state engineering is a powerful technique in quantum information and control. However, its performance limited by the adiabatic theorem of mechanics. In this scenario, shortcuts to adiabaticity, such as provided superadiabatic theory, constitute valuable tool speed up behavior. Here, we propose route implement universal computation. Our method based on realization piecewise controlled evolutions. Remarkably, they can be obtained simple time-independent counter-diabatic...

Density functional theory (DFT) is shown to provide a novel conceptual and computational framework for entanglement in interacting many-body quantum systems. DFT can, particular, shed light on the intriguing relationship between phase transitions entanglement. We use concepts express measures terms of first or second derivative ground state energy. illustrate versatility approach via variety analytically solvable models. As further application we discuss case mean field approximations...

We show that quantum correlations as quantified by discord can characterize phase transitions exhibiting nontrivial long-range decay a function of distance in spin systems. This is rather different from the behavior pairwise entanglement, which typically short-ranged even critical In particular, we find clear change rate system crosses point. illustrate this phenomenon for first-order, second-order, and infinite-order transitions, indicating an appealing correlation condensed matter

One of the current major challenges surrounding use quantum annealers for solving practical optimization problems is their inability to encode even moderately sized problems, main reason this being rigid layout bits as well sparse connectivity. In particular, implementation constraints has become a bottleneck in embedding because latter typically achieved by adding harmful penalty terms problem Hamiltonian, technique that often requires an all-to-all connectivity between qubits. Recently,...

We investigate the effect of localization on local charging quantum batteries (QBs) modeled by disordered spin systems. Two distinct schemes based transverse-field random Ising model are considered, with couplings defined a Chimera graph and linear chain up to next-to-nearest-neighbor interactions. By adopting low-energy demanding process driven fields only, we obtain that maximum extractable energy unitary processes (ergotropy) is highly enhanced in ergodic phase comparison many-body (MBL)...

We investigate a dynamical mass generation mechanism for the off-diagonal gluons and ghosts in $\mathrm{S}\mathrm{U}(N)$ Yang-Mills theories, quantized maximal Abelian gauge. Such can be seen as evidence dominance that It originates from condensation of mixed gluon-ghost operator dimension two, which lowers vacuum energy. construct an effective potential this by combined use local composite operators technique with algebraic renormalization we discuss gauge parameter independence results....

We introduce a self-consistent framework for the analysis of both Abelian and non-Abelian geometric phases associated with open quantum systems, undergoing cyclic adiabatic evolution. derive general expression phases, based on an approximation developed within inherently open-systems approach. This provides natural generalization analogous one closed we prove that it satisfies all properties might expect good definition phase, including gauge invariance. A striking consequence is emergence...

We discuss the detection of entanglement in interacting quantum spin systems. First, thermodynamic Hamiltonian-based witnesses are computed for a general class one-dimensional spin-1/2 models. Second, we introduce optimal bipartite observables. show that measure can generally be associated to set independent two-body observables whose expectation values used witness entanglement. The number necessary is ruled by symmetries model. Illustrative examples presented.

We introduce a monogamy inequality for quantum correlations, which implies that the sum of pairwise correlations is upper limited by amount multipartite as measured global discord. This bound holds either pure or mixed states provided bipartite discord does not increase under discard subsystems. illustrate behavior with Schmidt decomposition well $W$-GHZ states. As by-product, we apply to investigate residual correlations.

We propose a scheme for inverse engineering control in open quantum systems. Starting from an undetermined time evolution operator, time-dependent Hamiltonian is derived order to guide the system attain arbitrary target state at predefined time. calculate fidelity of our protocol presence noise with respect stochastic fluctuation linear parameters during evolution. For special family Hamiltonians two-level systems, we show that under can be categorized into two standard decohering processes:...

The ground state of a quantum spin chain is natural playground for investigating correlations. Nevertheless, not all correlations are genuinely nature. Here we review the recent progress to quantify 'quantumness' throughout phase diagram systems. Focusing one spatial dimension, discuss behavior discord close transitions. In contrast two-spin entanglement, pairwise effectively long-ranged in critical regimes. Besides features transitions, especially feasible explore factorization phenomenon,...

It is known that high intensity fields are usually required to implement shortcuts adiabaticity via Transitionless Quantum Driving (TQD). Here, we show this requirement can be relaxed by exploiting the gauge freedom of generalized TQD, which expressed in terms an arbitrary phase when mimicking adiabatic evolution. We experimentally investigate performance TQD comparison with both traditional and dynamics. By using a $^{171}$Yb$^+$ trapped ion hyperfine qubit, Landau-Zener Hamiltonian its...

We discuss the energetic cost of superadiabatic models quantum computation. Specifically, we investigate energy-time complementarity in general transitionless controlled evolutions and shortcuts to adiabatic search over an unstructured list. show that additional energy resources required by superadiabaticity for arbitrary can be minimized using probabilistic dynamics, so optimal success probability is fixed choice evolution time. In case analog search, approach induces a non-oracular...