Mixed Entangled States Research Articles

Fine-Grained Lower Limit of Entropic Uncertainty in the Presence of Quantum Memory

The limitation on obtaining precise outcomes of measurements performed on two noncommuting observables of a particle as set by the uncertainty principle in its entropic form can be reduced in the presence of quantum memory. We derive a new entropic uncertainty relation based on fine graining, which leads to an ultimate limit on the precision achievable in measurements performed on two incompatible observables in the presence of quantum memory. We show that our derived uncertainty relation tightens the lower bound set by entropic uncertainty for members of the class of two-qubit states with maximally mixed marginals, while accounting for the recent experimental results using maximally entangled pure states and mixed Bell-diagonal states. An implication of our uncertainty relation on the security of quantum key generation protocols is pointed out.

Experimentally testing the Bell inequality violation by optimizing the measurement settings

Many experiments have been made to test the Clauser–Horne–Shimony–Holt (CHSH)–Bell inequality (CBI). However, the Cirel’son’s limit has not been reached yet, due to various practically existing imperfections. In this paper, we experimentally investigate how to select the measurement settings for obtaining the optimal violation of CBI for a mixed entangled state. With the commercialized entangled source, we first determine the entanglement degree of the generated photon pairs by using the tomographic technique, and then numerically optimize the measurement settings. Finally, we experimentally obtain the optimal violation of the CBI with the present commercialized entangled source without the maximal entanglement.

Minimax optimization of entanglement witness operator for the quantification of three-qubit mixed-state entanglement

We develop a numerical approach for quantifying entanglement in mixed quantum states by convex-roof entanglement measures, based on the optimal entanglement witness operator and the minimax optimization method. Our approach is applicable to general entanglement measures and states and is an efficient alternative to the conventional approach based on the optimal pure-state decomposition. Compared with the conventional one, it has two important merits: (i) that the global optimality of the solution is quantitatively verifiable, and (ii) that the optimization is considerably simplified by exploiting the common symmetry of the target state and measure. To demonstrate the merits, we quantify Greenberger-Horne-Zeilinger (GHZ) entanglement in a class of three-qubit full-rank mixed states composed of the GHZ state, the W state, and the white noise, the simplest mixtures of states with different genuine multipartite entanglement, which have not been quantified before this work. We discuss some general properties of the form of the optimal witness operator and of the convex structure of mixed states, which are related to the symmetry and the rank of states.

Entanglement evolution of three-qubit mixed states in multipartite cavity—reservoir systems

We analyze the multipartite entanglement evolution of three-qubit mixed states composed of a GHZ state and a W state. For a composite system consisting of three cavities interacting with independent reservoirs, it is shown that the entanglement evolution is restricted by a set of monogamy relations. Furthermore, as quantified by the negativity, the entanglement dynamical property of the mixed entangled state of cavity photons is investigated. It is found that the three cavity photons can exhibit the phenomenon of entanglement sudden death (ESD). However, compared with the evolution of a generalized three-qubit GHZ state which has the equal initial entanglement, the ESD time of mixed states is later than that of the pure state. Finally, we discuss the entanglement distribution in the multipartite system, and point out the intrinsic relation between the ESD of cavity photons and the entanglement sudden birth of reservoirs.

Effect of atomic decay on purity, total correlations and entanglement of pure and mixed states

Abstract The atomic decay for a two level atom interacting with a single mode of electromagnetic field is considered. In particular for a coherent state or statistical mixture ( SM ) of two opposite coherent states as initial field states, the exact solution of the master equation is found. Effect of the atomic damping on the partial entropies of the atom or the field and the total entropy as a measures of the purity loss is investigated. The degree of entanglement by the negativity and the mutual information and the atomic coherence through the master equation is studied.

Nonlocal correlations for manifold quantum systems: Entanglement of two-spin states

In this paper, we study the bipartite entanglement of spin coherent states in the case of pure and mixed states. By a proper choice of the subsystem spins, the entanglement for large class of quantum systems is investigated. We generalize the result to the case of bipartite mixed states using a simplified expression of concurrence in Wootters’ measure of the bipartite entanglement. It is found that in some cases, the maximal entanglement of mixed states in the context of su(2) algebra can be detected. Our observations may have important implications in exploiting these states in quantum information theory.

Experimental simulation of a polarization-dispersion-fluctuating channel with photon pairs

We report on an experimental implementation of a tunable source of mixed two-photon entangled states. In contrast to previous implementations there is no correlation between the phase shift and spectral property of photons which would in principle allow local spectral filtration. The source provides genuinely mixed states that mimic various statistics of polarization-dispersion fluctuations. We believe that our source may be useful for testing robustness of quantum-information protocols against this specific form of noise. We demonstrate this function on a simple case of filtration by means of a balanced beam splitter.

Multipartite electronic entanglement purification using quantum-dot spin and microcavity system

This paper presents an entanglement purification protocol of multipartite electronic spin entangled state resorting to quantum-dot (QD) spin and micro cavity coupled system. The QD and microcavity coupling system is used to construct parity check detectors which provides a novel experimental platform of quantum information processing with photon and solid qubit. In this proposed protocol, the mixed multi-electron entangled state ensemble can be purified efficiently.

Entanglement behavior of quantum states of fermionic systems in an accelerated frame

In this paper, we investigate the behavior of bipartite entanglement of fermionic systems when one of the parties is traveling with a uniform acceleration. For the ordering problem in fermionic systems, we apply the recent result of Montero and Mart\'{\i}n-Mart\'{\i}nez [Phys. Rev. A 83, 052306 (2011)]. Based on the approach, we consider both pure and mixed entangled states, and we show that the behavior in terms of the entanglement measure (negativity) allows one to obtain physical results, i.e., its convergence in the infinite acceleration. The behavior shows that the ordering employed is relevant to derive physical results for fermionic entanglement. This also corrects the previous analysis of Mart\'{\i}n-Mart\'{\i}nez and Fuentes.

Beyond pure state entanglement for atomic ensembles

We analyze multipartite entanglement between atomic ensembles within quantum matter–light interfaces. In our proposal, a polarized light beam crosses sequentially several polarized atomic ensembles impinging on each of them at a given angle αi. These angles are crucial parameters for shaping the entanglement since they are directly connected to the appropriate combinations of the collective atomic spins that are squeezed. We exploit such a scheme to go beyond the pure state paradigm proposing realistic experimental settings to address multipartite mixed state entanglement in continuous variables.

Quantifying mixed-state quantum entanglement by optimal entanglement witnesses

We develop an approach of quantifying entanglement in mixed quantum states by the optimal entanglement witness operator. We identify the convex set of mixed states for which a single witness provides the exact value of an entanglement measure, and show that the convexity, properties, and symmetries of entanglement or of a target state considerably fix the form of the optimal witness. This greatly reduces difficulty in computing and experimentally determining entanglement measures. As an example, we show how to experimentally quantify bound entanglement in four-qubit noisy Smolin states and three-qubit Greenberger-Horne-Zeilinger (GHZ) entanglement under white noise. For general measures and states, we provide a numerical method to efficiently optimize witness.

Rescaling multipartite entanglement measures for mixed states

A relevant problem regarding entanglement measures is the following: Given an arbitrary mixed state, how does a measure for multipartite entanglement change if general local operations are applied to the state? This question is nontrivial as the normalization of the states has to be taken into account. Here we answer it for pure-state entanglement measures which are invariant under determinant 1 local operations and homogeneous in the state coefficients, and their convex-roof extension which quantifies mixed-state entanglement. Our analysis allows to enlarge the set of mixed states for which these important measures can be calculated exactly. In particular, our results hint at a distinguished role of entanglement measures which have homogeneous degree 2 in the state coefficients.

Entanglement of Three-Qubit Greenberger-Horne-Zeilinger–Symmetric States

The first characterization of mixed-state entanglement was achieved for two-qubit states in Werner's seminal work [Phys. Rev. A 40, 4277 (1989)]. A physically important extension concerns mixtures of a pure entangled state [such as the Greenberger-Horne-Zeilinger (GHZ) state] and the unpolarized state. These mixed states serve as benchmark for the robustness of multipartite entanglement. They share the symmetries of the GHZ state. We call such states GHZ symmetric. Here we give a complete description of the entanglement in the family of three-qubit GHZ-symmetric states and, in particular, of the three-qubit generalized Werner states. Our method relies on the appropriate parametrization of the states and on the invariance of entanglement properties under general local operations. An application is the definition of a symmetrization witness for the entanglement class of arbitrary three-qubit states.

Improvement on controlled-controlled-NOT operation-based entanglement purification protocol

We show that controlled-controlled-NOT (CCN) operation-based entanglement purification protocol can be further improved. CCN protocol requires Bell state measurements after performing the CCN operations. In the original CCN protocol, the measured states are assumed to be destroyed. However, if controlled-NOT gates are used to perform such Bell state measurements, in some unsuccessful situations of the CCN protocol, one can further purify the two mixed entangled states which are to be measured. In this way, the total efficiency of the CCN protocol is further increased.

New Aspects of Field Entropy Squeezing as an Indicator for Mixed State Entanglement in an Effective Two-Level System with Stark Shift

We present an effective two-level system in interaction through two-photon processes with a single mode quantized electromagnetic field, initially prepared in a coherent state. Field entropy squeezing as an indicator of the entanglement in a mixed state system is suggested. The temporal evolution of the negativity, Wehrl entropy, Wehrl phase distribution and field entropy squeezing are investigated. The results highlight the important roles played by both the Stark shift parameters and the mixed state setting in the dynamics of the Wehrl entropy, Wehrl phase distribution and field entropy squeezing.

Relativity of mixed entangled states

We obtain the necessary and sufficient separability and distillability conditions of mixtures of a maximally entangled state and the completely separable state in relativistic setting. In an inertial frame we study the entanglement under Wigner rotations induced by Lorentz transformations. We also investigate the mixed state entanglement of scalar and Dirac fields as seen by two relatively accelerated observers. For scalar field we show that in infinite acceleration limit the state has no longer distillable entanglement. For dirac field the entanglement in the infinite acceleration limit is finite. In both cases we show that there are states that will change from entangled into separable for a certain value of velocity or acceleration. We conclude that distillability is a relative concept, depending on the frame in which it is observed.

Relativity of mixed entangled states

We obtain the necessary and sufficient separability and distillability conditions of mixtures of a maximally entangled state and the completely separable state in relativistic setting. In an inerti...

Nonlocality and entanglement in qubit systems

Nonlocality and quantum entanglement constitute two special aspects of the quantum correlations existing in quantum systems, which are of paramount importance in quantum-information theory. Traditionally, they have been regarded as identical (equivalent, in fact, for pure two qubit states, that is, Gisin’s Theorem), yet they constitute different resources. Describing nonlocality by means of the violation of several Bell inequalities, we obtain by direct optimization those states of two qubits that maximally violate a Bell inequality, in terms of their degree of mixture as measured by either their participation ratio R = 1/Tr(ρ2) or their maximum eigenvalue λmax. This optimum value is obtained as well, which coincides with previous results. Comparison with entanglement is performed too. An example of an application is given in the XY model. In this novel approximation, we also concentrate on the nonlocality for linear combinations of pure states of two qubits, providing a closed form for their maximal nonlocality measure. The case of Bell diagonal mixed states of two qubits is also extensively studied. Special attention concerning the connection between nonlocality and entanglement for mixed states of two qubits is paid to the so-called maximally entangled mixed states. Additional aspects for the case of two qubits are also described in detail. Since we deal with qubit systems, we will perform an analogous study for three qubits, employing similar tools. Relation between distillability and nonlocality is explored quantitatively for the whole space of states of three qubits. We finally extend our analysis to four-qubit systems, where nonlocality for generalized Greenberger–Horne–Zeilinger states of arbitrary number of parties is computed.

Remote information concentration and multipartite entanglement in multilevel systems

Remote information concentration (RIC) in $d$-level systems (qudits) is studied. It is shown that the quantum information initially distributed in three spatially separated qudits can be remotely and deterministically concentrated to a single qudit via an entangled channel without performing any global operations. The entangled channel can be different types of genuine multipartite pure entangled states which are inequivalent under local operations and classical communication. The entangled channel can also be a mixed entangled state, even a bound entangled state which has a similar form to the Smolin state, but has different features from the Smolin state. A common feature of all these pure and mixed entangled states is found, i.e., they have $d^2$ common commuting stabilizers. The differences of qudit-RIC and qubit-RIC ($d=2$) are also analyzed.

Continuous variable entanglement in two-mode open quantum systems

in the framework of th. of open ss (OS) based oncompletely positive q. dyn. semigs - master eq. for 2independent h. os. interacting with an environmentPeres–Simon cond. for separability of 2-mode Gaussianstates - generation and evolution of entanglement in termsof covariance matrix for an arbitrary Gaussian input statedepending on values of diffusion and dissipation coeffsdescribing environment, the state keeps in time its initialtype: separable or entangled, or entanglement suddendeath or birth (collapse or revival of entanglement); theinitial state evolves asymptotically to an entangled orseparable equilibrium bipartite state, independent of thetype of the initial statelogarithmic negativity - degree of entanglementit is found a class of Gaussian maximally entangled mixedstates (GMEMS) and the maximally logarithmic negativity