We consider a class of entangled states of a quantum system (S) and a second system (A) where pure states of the former are correlated with mixed states of the latter, and work out the entanglement measure with reference to the nearest separable state. Such `pure-mixed' entanglement is expected when the system S interacts with a macroscopic measuring apparatus in a quantum measurement, where the quantum correlation is destroyed in the process of environment-induced decoherence whereafter only the classical correlation between S and A remains, the latter being large compared to the former. We present numerical evidence that the entangled S-A state drifts towards the nearest separable state through decoherence, with an additional tendency of equimixing among relevant groups of apparatus states.
We illustrate through numerical results a number of features of environment-induced decoherence under a broad class of apparatus-environment interactions in quantum measurements wherein the reduced system-apparatus density matrix evolves towards the nearest separable state and, in addition, there occurs a mixing in relevant groups of apparatus microstates (see below). The resulting final state is unique and correctly embodies the measurement statistics even in the absence of environment-induced superselection because of energy differences between these groups of states. The partial transpose r…
This paper describes the dynamics of a quantum two-level system (qubit) under the influence of an environment modeled by an ensemble of random matrices. In distinction to earlier work, we consider here separable couplings and focus on a regime where the decoherence time is of the same order of magnitude than the environmental Heisenberg time. We derive an analytical expression in the linear response approximation, and study its accuracy by comparison with numerical simulations. We discuss a series of unusual properties, such as purity oscillations, strong signatures of spectral correlations (i…
Every entangled state can be perturbed, for instance by decoherence, and stay entangled. For a large class of pure entangled states, we show how large the perturbation can be. Our class includes all pure bipartite and all maximally entangled states. For an entangled state, E, the constucted neighborhood of entangled states is the region outside two parallel hyperplanes, which sandwich the set of all separable states. The states for which these neighborhoods are largest are the maximally entangled ones. As the number of particles, or the dimensions of the Hilbert spaces for two of the particles…
Distillability sudden death and sudden birth in a two-qutrit system under decoherence of finite temperature is studied in detail. By using of the negativity and realignment criterion, it is shown that certain initial prepared free entangled states may become bound entangled or separable states in a finite time. Moreover, initial prepared bound entangled or separable states also may become distillabile entangled states in a finite time.
We investigate system-environment correlations based on the exact dynamics of a qubit and its environment in the framework of pure decoherence (phase damping). We focus on the relation of decoherence and the build-up of system-reservoir entanglement for an arbitrary (possibly mixed) initial qubit state. In the commonly employed regime where the qubit dynamics can be described by a Markov master equation of Lindblad type, we find that for almost all qubit initial states inside the Bloch sphere, decoherence is complete while the total state is still separable - no entanglement is involved. In ge…
We address the question of whether or not global entanglement of a quantum state can be inferred from local properties. Specifically, we are interested in genuinely multiparticle entangled states whose two-body marginals are all separable, but where the entanglement can be proven using knowledge of a subset of the marginals only. Using an iteration of semidefinite programs we prove that for any possible marginal configuration up to six particles multiqubit states with the desired properties can be found. We then present a method to construct states with the same properties for more particles i…
The evolution of two qubits coupled by a general nonlocal interaction is studied in two distinct regimes. In the first regime the purity of the individual qubits is interchanged through the entanglement shared by the two. We illustrate how this can be a mechanism for decoherence. In the second regime, the interaction entangles two initially pure qubits. The dynamical maps for the reduced unitary evolution of both initially simply separable and not-simply-separable states are found. We outline a protocol for optimizing the entanglement generation subject to constraints.
The basic ingredients of the consistent histories approach to quantum mechanics are the space of histories and the space of decoherence functionals. In this work we extend the classification theorem for decoherence functionals proven by Isham, Linden and Schreckenberg to the case where the space of histories is the lattice of projection operators on an arbitrary separable or non-separable complex Hilbert space of dimension strictly greater than two.
The possibility of consistency between the basic quantum principles of quantum mechanics and wave function collapse is reexamined. A specific interpretation of environment is proposed for this aim and applied to decoherence. When the organization of a measuring apparatus is taken into account, this approach leads also to an interpretation of wave function collapse, which would result in principle from the same interactions with environment as decoherence. This proposal is shown consistent with the non-separable character of quantum mechanics.
Quantum properties of the probes used to estimate a classical parameter can be used to attain accuracies that beat the standard quantum limit. When qubits are used to construct a quantum probe, it is known that initializing $n$ qubits in an entangled "cat state," rather than in a separable state, can improve the measurement uncertainty by a factor of $1/\sqrt{n}$. We investigate how the measurement uncertainty is affected when the individual qubits in a probe are subjected to decoherence. In the face of such decoherence, we regard the rate $R$ at which qubits can be generated and the total dur…
By considering an exactly solvable model of a two interacting spin-1/2 qubits described by the Heisenberg anisotropic interaction in the presence of intrinsic decoherence, we study the dynamics of entanglement quantified by the concurrence and measurement-induced nonlocality (MIN) based on Hilbert-Schmidt norm and trace distance with different initial conditions. We highlight the relationship between the entanglement and MIN for the pure initial state. For an initial separable state, it is found that the robustness and the generation of the quantum correlations depend on the physical parameter…
In this paper, we study mixing and large decoherence in continuous-time quantum walks on one dimensional regular networks, which are constructed by connecting each node to its $2l$ nearest neighbors($l$ on either side). In our investigation, the nodes of network are represented by a set of identical tunnel-coupled quantum dots in which decoherence is induced by continuous monitoring of each quantum dot with nearby point contact detector. To formulate the decoherent CTQWs, we use Gurvitz model and then calculate probability distribution and the bounds of instantaneous and average mixing times. …
In this article, we study the dynamics of quantum correlation measures such as entanglement and measurement-induced nonlocality (MIN). Starting from an arbitrary Bell diagonal mixed states under Markovian local noise such as bit-phase flip, depolarizing and generalized amplitude damping channel, we provide the decays of the entanglement measured by concurrence and quantum correlation captured by different forms of MIN (trace distance, Hilbert-Schmidt norm and relative entropy) as a function of the decoherence parameters. The effect of local noises on the dynamical behaviors of quantum correlat…
We propose a quantum-information processor that consists of decoherence-free logical qubits encoded into arrays of dipole-coupled qubits. High-fidelity single-qubit operations are performed deterministically within a decoherence-free subsystem without leakage via global addressing of bichromatic laser fields. Two-qubit operations are realized locally with four physical qubits, and between separated logical qubits using linear optics. We show how to prepare cluster states using this method. We include all non-nearest-neighbor effects in our calculations, and we assume the qubits are not located…
We employ the concepts of local quantum uncertainty and geometric quantum discord based on the trace norm to investigate the environmental effects on quantum correlations of two bipartite quantum systems. The first one concerns a two-qubit system coupled with two independent bosonic reservoirs. We show that the trace discord exhibits frozen phenomenon contrarily to local quantum uncertainty. The second scenario deals with a two-level system, initially prepared in a separable state, interacting with a quantized electromagnetic radiation. Our results show that there exists an exchange of quantum…
The entanglement of two qubits, each defined as an effective two-level, spin 1/2 system, is investigated for the case that the qubits interact via a Heisenberg XY interaction and are subject to decoherence due to population relaxation and thermal effects. For zero temperature, the time dependent concurrence is studied analytically and numerically for some typical initial states, including a separable (unentangled) initial state. An analytical formula for non-zero steady state concurrence is found for any initial state, and optimal parameter values for maximizing steady state concurrence are gi…
We study the spontaneous decoherence of the coupled harmonic oscillators confined in a ring container, where the nearest-neighbor harmonic potentials are taken into consideration. Without any external symmetry breaking field or surrounding environment, the quantum superposition state prepared in the relative degrees of freedom gradually loses its quantum coherence spontaneously. This spontaneous decoherence is interpreted by the hidden couplings between the center-of-mass and relative degrees of freedoms, which actually originates from the symmetries of the ring geometry and corresponding nont…
We propose an experimental setup, feasible with present day technology, involving two highquality- factor cavities, one Ramsey zone and a two-level atom which interacts with them. The dynamics in the cavities is modeled by a dissipative dispersive Jaynes-Cummings model. Analytical expresions for the evolution superoperator in each part of the proposed setup and for the concurrence between the atom and the first cavity are given, and the pairwise entanglement of the subsystems is calculated numerically. We consider initial separable states given by the tensor product of a superposition of the t…
Combining two entanglement-breaking channels into a correlated-noise environment restores the distribution of entanglement. Surprisingly, this reactivation can be induced by the injection of separable correlations from the composite environment. In any dimension (finite or infinite), we can construct classically-correlated "twirling" environments which are entanglement-breaking in the transmission of single systems but entanglement-preserving when two systems are transmitted. Here entanglement is simply preserved by the existence of decoherence-free subspaces. Remarkably, even when such subspa…
The evolution of entanglement in a 3-spin chain with nearest-neighbor Heisenberg-XY interactions for different initial states is investigated here. In an NMR experimental implementation, we generate multipartite entangled states starting from initial separable pseudo-pure states by simulating nearest-neighbor XY interactions in a 3-spin linear chain of nuclear spin qubits. For simulating XY interactions, we follow algebraic method of Zhang et al. [Phys. Rev. A 72, 012331 (2005)]. Bell state between end qubits has been generated by using only the unitary evolution of the XY Hamiltonian. For gen…
We analyze decoherence-free (DF) quantum information in the presence of an arbitrary non-nearest-neighbor bath-induced system Hamiltonian using a Markovian master equation. We show that the most appropriate encoding for N qubits is probably contained within the ~(2/9) N excitation subspace. We give a timescale over which one would expect to apply other methods to correct for the system Hamiltonian. In order to remain applicable to experiment, we then focus on small systems, and present examples of DF quantum information for three and four qubits. We give an encoding for four qubits that, while…
The geometric measure of entanglement of a pure state, defined by its distance to the set of pure separable states, is extended to multipartite mixed states. We characterize the nearest disentangled mixed state to a given mixed state with respect to this measure by a system of equations. The entanglement eigenvalue for a mixed state is introduced. For a given mixed state, we show that its nearest disentangled mixed state is associated with its entanglement eigenvalue.
The possibility of masking an accelerated two-qubit system by using a minimum number of qubits is discussed. It is shown that, the information may be masked in either entangled local states or product non-local separable states. We examine that each partition of these states satisfies the masking conditions. Due to the presence of non-local separable partition, one may consider that it is a type of quantum data hiding scheme. The local /non-local information encoded in the masked entangled state is robust against the decoherence of the acceleration process. The possibility of estimating the ac…
A scalable superconducting architecture for adiabatic quantum computers is proposed. The architecture is based on time-independent, nearest-neighbor interqubit couplings: it can handle any problem in the class NP even in the presence of measurement errors, noise, and decoherence. The implementation of this architecture with superconducting persistent-current qubits and the natural robustness of such an implementation to manufacturing imprecision and decoherence are discussed.
The maximal overlap with the fully separable state for the multipartite entangled pure state with translational invariance is studied explicitly by some exact and numerical evaluations, focusing on the one-dimensional qubit system and some representative types of translational invariance. The results show that the translational invariance of the multipartite state could have an intrinsic effect on the determinations of the maximal overlap and the nearest fully separable state for multipartite entangled states. Furthermore a hierarchy of the basic entangled states with translational invariance …
Multiple quantum (MQ) NMR methods \cite{Baum} are applied to the analysis of various problems of quantum information processing. It is shown that the two-spin/two-quantum Hamiltonian \cite{Baum} describing MQ NMR dynamics is related to the flip-flop Hamiltonian of a one-dimensional spin system in the approximation of the nearest neighbor interactions. As a result, it is possible to organize quantum state transfer along a linear chain. MQ NMR experiments are performed on quasi-one-dimensional chains of \BPChem{\^{19}F} nuclei in calcium fluorapatite \BPChem{Ca\_5(PO\_4)\_3F}. Relaxation of the …
Entangled systems with large quantum Fisher information (QFI) can be used to outperform the standard quantum limit of the separable systems in quantum metrology. However, the interaction between the system and the environments inevitably leads to decoherence and decrease of the QFI, and it is not clear whether the entanglement systems can be better resource than separable systems in the realistic physical condition. In this work, we study the steady QFI of two driven and collectively damped qubits with homodyne-mediated feedback. We show that the steady QFI can be significantly enhanced both i…
We show that the decoherence, which in the long run destroys quantum features of a system, can be used to reveal the entanglement in a two-qubit system. To this end, we consider a criterion that formally resembles the Clauser-Horne-Shimony-Holt (CHSH) inequality. In our case the local observables are set by the coupling of each qubit to the environmental noise, controlled with the dynamical decoupling method. We demonstrate that the constructed inequality is an entanglement criterion---it can only be violated by non-separable initial two-qubit states, provided that the local noises are correla…
We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite programming relaxations of the set of quantum state marginals admitting a fully separable extension. We connect the completeness of each hierarchy to the resolution of an analog classical marginal problem and thus identify relevant experimental situations where the hierarchies are complete. For finitely many parties on a star configuration or a chain, we find …
Quantum metrology is the use of genuinely quantum properties such as entanglement as a resource to outperform classical sensing strategies. Typically, entanglement is created by implementing gate operations or inducing many-body interactions. However, existing sensing schemes with these approaches require accurate control of the probe system such as switching on and off the interaction among qubits, which can be challenging for practical applications. Here, we propose an entanglement-enhanced sensing scheme with an always-on nearest-neighbor interaction between qubits. We adopt the transverse …
We investigate entanglement properties of multipartite states under the influence of decoherence. We show that the lifetime of (distillable) entanglement for GHZ-type superposition states decreases with the size of the system, while for a class of other states -namely all graph states with constant degree- the lifetime is independent of the system size. We show that these results are largely independent of the specific decoherence model and are in particular valid for all models which deal with individual couplings of particles to independent environments, described by some quantum optical mas…
We study two anisotropically interacting spins coupled to optical phonons; we restrict our analysis to the regime of strong coupling to the environment, to the antiadiabatic region, and to the subspace with zero value for $S^z_T$ (the z-component of the total spin). In the case where each spin is coupled to a different phonon bath, we assume that the system and the environment are initially uncorrelated (and form a simply separable state) in the polaronic frame of reference. By analyzing the {polaron} dynamics through non-Markovian quantum master equation, we find that the system manifests a s…
In quantum-optics experiments with both natural and artificial atoms, the atoms are usually small enough that they can be approximated as point-like compared to the wavelength of the electromagnetic radiation they interact with. However, superconducting qubits coupled to a meandering transmission line, or to surface acoustic waves, can realize "giant artificial atoms" that couple to a bosonic field at several points which are wavelengths apart. Here, we study setups with multiple giant atoms coupled at multiple points to a one-dimensional (1D) waveguide. We show that the giant atoms can be pro…
We develop a new entanglement measure by extending Jaeger's Minkowskian norm entanglement measure. This measure can be applied to a much wider class of multipartite mixed states, although still "quasi" in the sense that it is still incapable of dividing precisely the sets of all separable and entangled states. As a quadratic scalar function of the system density matrix, the quasi measure can be easily expressed in terms of the so-called coherence vector of the system density matrix, by which we show the basic properties of the quasi measure including (1) zero-entanglement for all separable sta…
The evolution of entanglement in a one-dimensional Ising chain is numerically studied under various initial conditions. We analyze two problems concerning the dynamics of the entanglement: (i) generation of the entanglement from the pseudopure separable state and (ii) transportation of the entanglement from one end of the chain to the other. The investigated model is a one-dimensional Ising spin-1/2 chain with nearest-neighbor interactions placed in an external magnetic field and irradiated by a weak resonant transverse field. The possibility of selective initialization of partially entangled …
A new method is developed to derive an algebraic equations for the geometric measure of entanglement of three qubit pure states. The equations are derived explicitly and solved in cases of most interest. These equations allow oneself to derive the analytic expressions of the geometric entanglement measure in the wide range of the three qubit systems, including the general class of W-states and states which are symmetric under permutation of two qubits. The nearest separable states are not necessarily unique and highly entangled states are surrounded by the one-parametric set of equally distant…
The unitary evolution of a quantum system preserves its coherence, but interactions between the system and its environment result in decoherence, a process in which the quantum information stored in the system becomes degraded. A spin-polarized positively-charged muon implanted in a fluoride crystal realises such a coherent quantum system, and the entanglement of muon and nearest-neighbour fluorine nuclear spins gives rise to an oscillatory time-dependence of the muon polarization which can be detected and measured. Here we show that the decohering effect of more distant nuclear spins can be p…
A thermal field, which frequently appears in problems of decoherence, provides us with minimal information about the field. We study the interaction of the thermal field and a quantum system composed of two qubits and find that such a chaotic field with minimal information can nevertheless entangle the qubits which are prepared initially in a separable state. This simple model of a quantum register interacting with a noisy environment allows us to understand how memory of the environment affects the state of a quantum register.
We study the connection between the Hilbert-Schmidt measure of entanglement (that is the minimal distance of an entangled state to the set of separable states) and entanglement witness in terms of a generalized Bell inequality which distinguishes between entangled and separable states. A method for checking the nearest separable state to a given entangled one is presented. We illustrate the general results by considering isotropic states, in particular 2-qubit and 2-qutrit states -- and their generalizations to arbitrary dimensions -- where we calculate the optimal entanglement witnesses expli…
There is growing belief that the next decade will see the emergence of sensing devices based on the laws of quantum physics that outperform some of our current sensing devices. For example, in frequency estimation, using a probe prepared in an entangled state can, in principle, lead to a precision gain compared to a probe prepared in a separable state. Even in the presence of some forms of decoherence, it has been shown that the precision gain can increase with the number of probe particles $N$. Usually, however, the entangled and separable state preparation and readout times are assumed to be…
We use a fiber based double slit Young interferometer for studying the far-field spatial distribution of the two-photon coincidence rate (coincidence pattern) for various quantum states with different degree of spatial entanglement. The realized experimental approach allows to characterize coincidence patterns for different states without any modifications of the setup. Measurements were carried out with path-entangled and separable states. The dependence of the coincidence pattern on the phase of the interferometer for superposition and separable states was studied. The results have implicati…
It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurement-based quantum computation on decohered weighted graph states. To show intractability of classical simulation above the boundary, we…
We derive a general criterion to detect entangled states in multi-partite systems based on the symmetric logarithmic derivative quantum Fisher information. This criterion is a direct consequence of the fact that separable states do not improve the accuracy upon estimating one-parameter family of quantum channels. Our result is a generalization of the previously known criterion for one-parameter unitary channel to any one-parameter quantum channel. We discuss several examples to illustrate our criterion. The proposed criterion is extended to the case of open quantum systems and we briefly discu…
We investigate decoherence in quantum systems coupled via dephasing-type interactions to an arbitrary environment with chaotic underlying classical dynamics. The coherences of the reduced state of the central system written in the preferential energy eigenbasis are quantum Loschmidt echoes, which in the strong coupling regime are characterized at long times scales by fluctuations around a constant mean value. We show that due to the chaotic dynamics of the environment, the mean value and the width of the Loschmidt echo fluctuations are inversely proportional to the quantity we define as the ef…
We outline an exact approach to decoherence and entanglement problems for continuous variable systems. The method is based on a construction of quantum distribution functions introduced by Ford and Lewis \cite{ford86} in which a system in thermal equilibrium is placed in an initial state by a measurement and then sampled by subsequent measurements. With the Langevin equation describing quantum Brownian motion, this method has proved to be a powerful tool for discussing such problems. After reviewing our previous work on decoherence and our recent work on disentanglement, we apply the method to…
A general $n$-partite state $| Ψ>$ of a composite quantum system can be regarded as an element in a Hilbert tensor product space $\HH = \otimes_{k=1}^n \HH_k$, where the dimension of $\HH_k$ is $d_k$ for $k = 1,..., n$. Without loss of generality we may assume that $d_1 \le...\le d_n$. A separable (Hartree) $n$-partite state $| ϕ>$ can be described by $| ϕ> = \otimes_{k=1}^n | ϕ^{(k)}>$ with $| ϕ^{(k)}> \in \HH_k$. We show that $σ:= \min \{< Ψ| ϕ_Ψ> : | Ψ> \in \HH,.$ $. < Ψ| Ψ> = 1\}$ is a positive number, where $| ϕ_Ψ>$ is the nearest separable state to $| Ψ>$. We call $σ$ the minimum Hartree…
For parameter estimation from an $N$-component composite quantum system, it is known that a separable preparation leads to a mean-squared estimation error scaling as $1/N$ while an entangled preparation can in some conditions afford a smaller error with $1/N^2$ scaling. This quantum superefficiency is however very fragile to noise or decoherence, and typically disappears with any small amount of random noise asymptotically at large $N$. To complement this asymptotic characterization, we characterize how the estimation efficiency evolves as a function of the size $N$ of the entangled system and…
We study generic open quantum systems with Markovian dissipation, focusing on a class of stochastic Liouvillian operators of Lindblad form with independent random dissipation channels (jump operators) and a random Hamiltonian. We perform a thorough numerical study, focusing on global spectral features, the spectral gap, and the steady-state purity and statistics. We establish that all properties follow three different regimes as a function of the dissipation strength, whose boundaries depend on the particular observable. Within each regime, we determine the scaling exponents with the dissipati…
The concurrence between first and the last sites of a fermionic spin chain containing a single boson is rigorously investigated at finite low temperature in the vicinity of a weak homogeneous magnetic field. We consider the boson as a mobile spin-1 particle through the chain and study concurrence without/under decoherence and express some interesting phase flip and bit flip reactions of the pairwise entanglement between first and the last half-spins in the chain. Our investigations show that the concurrence between two considered half-spins has different behavior for various positions of the s…
