Mixed Entangled States Research Articles

Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities

We present an entanglement purification protocol and an entanglement concentration protocol for electron-spin entangled states, resorting to quantum-dot spin and optical-microcavity-coupled systems. The parity-check gates (PCGs) constructed by the cavity-spin-coupling system provide a different method for the entanglement purification of electron-spin entangled states. This protocol can efficiently purify an electron ensemble in a mixed entangled state. The PCGs can also concentrate electron-spin pairs in less-entangled pure states efficiently. The proposed methods are more flexible as only single-photon detection and single-electron detection are needed.

All Nonclassical Correlations Can Be Activated into Distillable Entanglement

We devise a protocol in which general nonclassical multipartite correlations produce a physically relevant effect, leading to the creation of bipartite entanglement. In particular, we show that the relative entropy of quantumness, which measures all nonclassical correlations among subsystems of a quantum system, is equivalent to and can be operationally interpreted as the minimum distillable entanglement generated between the system and local ancillae in our protocol. We emphasize the key role of state mixedness in maximizing nonclassicality: Mixed entangled states can be arbitrarily more nonclassical than separable and pure entangled states.

Positive finite rank elementary operators and characterizing entanglement of states

In this paper, some indecomposable positive finite rank elementary operators of order (n, n) are constructed. This allows us to give a simple necessary and sufficient criterion for the separability of pure states in bipartite systems of any dimension in terms of positive elementary operators of order (2, 2) and obtain some new mixed entangled states that cannot be detected by the positive partial transpose criterion and the realignment criterion.

Quantum entanglement between a nonlinear nanomechanical resonator and a microwave field

We consider a theoretical model for a nonlinear nanomechanical resonator coupled to a superconducting microwave resonator. The nanomechanical resonator is driven parametrically at twice its resonance frequency, while the superconducting microwave resonator is driven with two tones that differ in frequency by an amount equal to the parametric driving frequency. We show that the semiclassical approximation of this system has an interesting fixed-point bifurcation structure. In the semiclassical dynamics a transition from stable fixed points to limit cycles is observed as one moves from positive to negative detuning. We show that signatures of this bifurcation structure are also present in the full dissipative quantum system and further show that the bifurcation structure leads to mixed-state entanglement between the nanomechanical resonator and the microwave cavity in the dissipative quantum system that is a maximum close to the semiclassical bifurcation. Quantum signatures of the semiclassical limit cycles are presented.

Bell inequality, separability and entanglement distillation

In this review, we introduce well-known Bell inequalities, the relations between the Bell inequality and quantum separability, and the entanglement distillation of quantum states. It is shown that any pure entangled quantum state violates one of Bell-like inequalities. Moreover, quantum states that violate any one of these Bell-like inequalities are shown to be distillable. New Bell inequalities that detect more entangled mixed states are also introduced.

Bipartite Bell Inequality and Maximal Violation

We present new bell inequalities for arbitrary dimensional bipartite quantum systems. The maximal violation of the inequalities is computed. The Bell inequality is capable of detecting quantum entanglement of both pure and mixed quantum states more effectively.

D-Concurrence Bounds for Pair Coherent States

Pair coherent state can be regarded as a state of a two-mode radiation field such that the wave function is non-Gaussian and infinite dimensional, too. Since the entanglement for high dimensional mixed states is difficult to calculate, it is necessary to find bound for entanglement measures. In this paper, some features of quantum entanglement for the pair coherent state are studied and also the upper and lower bounds for D-concurrence (a new entanglement measure) over this state are obtained.

Distillation of mixed-state continuous-variable entanglement by photon subtraction

We present a detailed theoretical analysis for the distillation of one copy of a mixed two-mode continuous-variable entangled state using beamsplitters and coherent photon-detection techniques, including conventional on-off detectors and photon number resolving detectors. The initial Gaussian mixed-entangled states are generated by transmitting a two-mode squeezed state through a lossy bosonic channel, corresponding to the primary source of errors in current approaches to optical quantum communication. We provide explicit formulas to calculate the entanglement in terms of logarithmic negativity before and after distillation, including losses in the channel and the photon detection, and show that one-copy distillation is still possible even for losses near the typical fiber channel attenuation length. A lower bound for the transmission coefficient of the photon-subtraction beamsplitter is derived, representing the minimal value that still allows to enhance the entanglement.

Linking a distance measure of entanglement to its convex roof

An important problem in quantum information theory is the quantification of entanglement in multipartite mixed quantum states. In this work, a connection between the geometric measure of entanglement and a distance measure of entanglement is established. We present a new expression for the geometric measure of entanglement in terms of the maximal fidelity with a separable state. A direct application of this result provides a closed expression for the Bures measure of entanglementof two qubits. We also prove that the number of elements in an optimal decomposition w.r.t. the geometric measure of entanglement is bounded from above by the Caratheodory bound, and we find necessary conditions for the structure of an optimal decomposition.

Experimental EPR-steering using Bell-local states

The concept of ‘steering’ was introduced in 1935 by Schrödinger1 as a generalization of the EPR (Einstein–Podolsky–Rosen) paradox. It has recently been formalized as a quantum-information task with arbitrary bipartite states and measurements2, for which the existence of entanglement is necessary but not sufficient. Previous experiments in this area3,4,5,6 have been restricted to an approach7 that followed the original EPR argument in considering only two different measurement settings per side. Here we demonstrate experimentally that EPR-steering occurs for mixed entangled states that are Bell local (that is, that cannot possibly demonstrate Bell non-locality). Unlike the case of Bell inequalities8,9,10,11, increasing the number of measurement settings beyond two—we use up to six—significantly increases the robustness of the EPR-steering phenomenon to noise.

Entanglement between internal and external degrees of freedom of a driven trapped atom

We study the dynamics of a Λ-shaped trapped atom that is driven by two lasers to conditions approaching electromagnetically induced transparency. Solving numerically the full quantum master equation describing the coupled system of electronic and vibrational degrees of freedom, we investigate the dynamics of the entanglement and the quantum mutual information during the cooling process. Far from the Lamb–Dicke limit, an intricate behaviour of these quantities is found, as well as the emergence of a mixed entangled non-equilibrium stationary state.

ENTANGLEMENT PROPERTY AND MONOGAMY RELATION OF GENERALIZED MIXED W STATES

We introduce a new class of multipartite entangled mixed states with pure state decompositions of generalized W states, similar to Schmidt-correlated states having generalized GHZ states in the pure state decomposition. The entanglement and separability properties are studied according to PPT operations. Monogamy relations linked to these states are also investigated.

Dynamics of quantum entanglement in Gaussian open systems

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the dynamics of entanglement for a system consisting of two uncoupled harmonic oscillators interacting with a thermal environment. Using the Peres–Simon necessary and sufficient criterion for separability of two-mode Gaussian states, we describe the evolution of entanglement in terms of the covariance matrix for a Gaussian input state. For some values of the temperature of the environment, the state keeps for all times its initial type: separable or entangled. In other cases, entanglement generation, entanglement sudden death or a repeated collapse and revival of entanglement takes place. We determine the asymptotic Gaussian maximally entangled mixed states (GMEMS) and their corresponding asymptotic maximal logarithmic negativity.

Uncertainty relations and entanglement in fermion systems

The violation of uncertainty relations is used as a signature of entanglement for both pure and mixed states of two identical fermions. In the case of fermions with a four-dimensional single-particle Hilbert space we obtain several different types of uncertainty-related entanglement criteria based on local uncertainty relations, on the sum of variances of projectors, and on various entropic measures. Within the latter approach we consider either entropic uncertainty relations involving a single observable or relations based upon the sum of entropies associated with more than one observable. We extend the projector-based entanglement criterion to the case of two-fermion and three-fermion systems with a six-dimensional single-particle Hilbert space.

Sudden birth versus sudden death of entanglement for the extended Werner-like state in a dissipative environment

In this paper, we investigate the dynamical behaviour of entanglement in terms of concurrence in a bipartite system subjected to an external magnetic field under the action of dissipative environments in the extended Werner-like initial state. The interesting phenomenon of entanglement sudden death as well as sudden birth appears during the evolution process. We analyse in detail the effect of the purity of the initial entangled state of two qubits via Heisenberg XY interaction on the apparition time of entanglement sudden death and entanglement sudden birth. Furthermore, the conditions on the conversion of entanglement sudden death and entanglement sudden birth can be generalized when the initial entangled state is not pure. In particular, a critical purity of the initial mixed entangled state exists, above which entanglement sudden birth vanishes while entanglement sudden death appears. It is also noticed that stable entanglement, which is independent of different initial states of the qubits (pure or mixed state), occurs even in the presence of decoherence. These results arising from the combination of the extended Werner-like initial state and dissipative environments suggest an approach to control and enhance the entanglement even after purity induced sudden birth, death and revival.

Teleportation via maximally and non-maximally entangled mixed states

We study the efficiency of two-qubit mixed entangled states as resources for quantumteleportation. We first consider two maximally entangled mixed states, viz., the Wernerstate[1], and a class of states introduced by Munro et al. [2]. We show that the Wernerstate when used as teleportation channel, gives rise to better average teleportation fidelitycompared to the latter class of states for any finite value of mixedness. We then introducea non-maximally entangled mixed state obtained as a convex combination of a two-qubitentangled mixed state and a two-qubit separable mixed state. It is shown that such ateleportation channel can outperform another non-maximally entangled channel, viz.,the Werner derivative for a certain range of mixedness. Further, there exists a rangeof parameter values where the former state satisfies a Bell-CHSH type inequality andstill performs better as a teleportation channel compared to the Werner derivative eventhough the latter violates the inequality.

Teleportation via maximally and non-maximally entangled mixed states

We study the efficiency of two-qubit mixed entangled states as resources for quantum teleportation. We first consider two maximally entangled mixed states, viz., the Werner state\cite{werner}, and a class of states introduced by Munro {\it et al.} \cite{munro}. We show that the Werner state when used as teleportation channel, gives rise to better average teleportation fidelity compared to the latter class of states for any finite value of mixedness. We then introduce a non-maximally entangled mixed state obtained as a convex combination of a two-qubit entangled mixed state and a two-qubit separable mixed state. It is shown that such a teleportation channel can outperform another non-maximally entangled channel, viz., the Werner derivative for a certain range of mixedness. Further, there exists a range of parameter values where the former state satisfies a Bell-CHSH type inequality and still performs better as a teleportation channel compared to the Werner derivative even though the latter violates the inequality.

Decoherence-immune generation of highly entangled states for two atoms

This paper proposes a decoherence-immune scheme for generating highly entangled states for two atoms trapped in a cavity. The scheme is based on two resonant atom-cavity interactions. Conditional upon the detection of no photon, the two atoms may exchange an excitation via the first resonant interaction, which leads to entanglement. Due to the loss of the excitation, the two atoms are in a mixed entangled state. With the help of an auxiliary ground state not coupled to the cavity mode, the state related to the excitation loss is eliminated by the detection of a photon resulting from the second resonant interaction. Thus, the fidelity of entanglement is almost not affected by the decoherence.

Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement

Entanglement purification is a very important element for long-distance quantum communication. Different from all the existing entanglement purification protocols (EPPs) in which two parties can only obtain some quantum systems in a mixed entangled state with a higher fidelity probabilistically by consuming quantum resources exponentially, here we present a deterministic EPP with hyperentanglement. Using this protocol, the two parties can, in principle, obtain deterministically maximally entangled pure states in polarization without destroying any less-entangled photon pair, which will improve the efficiency of long-distance quantum communication exponentially. Meanwhile, it will be shown that this EPP can be used to complete nonlocal Bell-state analysis perfectly. We also discuss this EPP in a practical transmission.

Entanglement Purification for Mixed Entangled Quantum Dot States via Superconducing Transmission Line Resonators

An entanglement purification protocol for mixed entangled states is presented via double quantum dot molecules inside a superconducing transmission line resonator (TLR). In the current scenario, coupling for arbitrary double quantum dot molecules can be tuned via the TLR in the large detuning region by controlling the qubit level splitting. The TLR is always empty and only virtually excited, so the interaction is insensitive to both the TLR decay and thermal field. Discussion about the feasibility of our scheme shows that the entanglement purification can be implemented with high fidelity and successful probability.