Local transformation of mixed states of two qubits to Bell diagonal states

The optimal entanglement manipulation for a single copy of mixed states of two qubits is to transform it to a Bell diagonal state. In this paper we derive an explicit form of the local operation that can realize such a transformation. The result obtained is universal for arbitrary entangled two-qubit states and it discloses that the corresponding local filter is not unique for density matrices with rank n = 2 and can be exclusively determined for that with n = 3 and 4. As illustrations, a four-parameter family of mixed states are explored, the local filter as well as the transformation probability are given explicitly, which verify the validity of the general result.

Dissipative scheme to approach the boundary of two-qubit entangled mixed states

We discuss the generation of states close to the boundary family of maximally entangled mixed states as defined by the use of concurrence and linear entropy. The coupling of two qubits to a dissipation-affected bosonic mode is able to produce a bipartite state having, for all practical purposes, the entanglement and mixedness properties of one of such boundary states. We thoroughly study the effects that thermal and squeezed characters of the bosonic mode have in such a process and we discuss tolerance to qubit phase-damping mechanisms. The nondemanding nature of the scheme makes it realizable in a matter-light-based physical setup, which we address in some details.

Bipolar missed states : the diagnosis and clinical salience of bipolar mixed states

Objective: To explore diagnostic and treatment issues concerning bipolar mixed states.

Method: Bipolar mixed states are described and concerns about diagnostic and treatment difficulties are summarized and discussed.

Result: Mixed states can present with equal admixtures of depressive or manic symptoms, or more commonly one component predominates. There is fair consensus, although little data, regarding the management of manic mixed states. However depressive mixed states are far more complex both in terms of recognition and management. People suffering from mixed states characteristically present with complaints of depression.

Conclusions: The boundaries between depressive mixed states and agitated depression are vague, yet carry substantial therapeutic implications. Bipolar mixed states are often difficult to treat, and tend to take much longer to settle than either pure mania or depression.  Furthermore there is data that treatment with antidepressants can worsen the course of mixed states. Hence missed diagnoses can potentially have negative clinical implications.  Therefore in this paper the clinical presentation, diagnosis and therapy of mixed states is reviewed with a view to improving management.

A prospective study of the impact of subthreshold mixed states on the 24-month clinical outcomes of bipolar I disorder or schizoaffective disorder

Objectives: Subthreshold mixed states are common, yet their clinical significance is unclear. This study investigated the clinical outcomes of subthreshold mixed states in participants with bipolarI disorder or schizoaffective disorder, using the Cassidy and Benazzi criteria for manic and depressive mixed states, respectively.

Methods: The Bipolar Comprehensive Outcomes Study (BCOS) is a prospective observational study of treatment and outcomes for patients with bipolar I or schizoaffective disorder, bipolar type. Participants (N=239) were grouped based on study entry clinical presentation as having pure depression (n=63) if they satisfied DSM-IV-TR criteria for a Major Depressive Episode (MDE), depressive mixed state (DMX) if they also had at least three concurrent hypomanic symptoms (n=33), or not depressed (n=143) if they did not satisfy the criteria for MDE. Participants were similarly grouped as having pure mania (n=3) if they satisfied DSM-IV criteria for a Manic Episode, manic mixed state (MMX) if they also had at least two concurrent depressive symptoms (n=33), or not manic (n=203). Clinical data were collected by interview every 3-months over a 24-month period.

Results: Measures of quality of life, mental and physical health over the 24-month period were significantly worse for participants who were classified as having mixed states at study entry on most outcome measures compared to participants who were not in an illness episode at study entry. DMX was predictive of greater manic symptomatology over the 24 months compared to participants with pure depression.

Conclusion: In participants with a current episode of mood disorder, the presence of subthreshold symptoms of opposite polarity was associated with poorer clinical outcomes over a 24-month period.

Continuum of depressive and manic mixed states in patients with bipolar disorder: quantitative measurement and clinical features.

Bipolar mixed states combine depressive and manic features, presenting diagnostic and treatment challenges and reflecting a severe form of the illness. DSM-IV criteria for a mixed state require combined depressive and manic syndromes, but a range of mixed states has been described clinically. A unified definition of mixed states would be valuable in understanding their diagnosis, mechanism and treatment implications. We investigated the manner in which depressive and manic features combine to produce a continuum of mixed states. In 88 subjects with bipolar disorder (DSM-IV), we evaluated symptoms and clinical characteristics, and compared depression-based, mania-based, and other published definitions of mixed states. We developed an index of the extent to which symptoms were mixed (Mixed State Index, MSI) and characterized its relationship to clinical state. Predominately manic and depressive mixed states using criteria from recent literature, as well as Kraepelinian mixed states, had similar symptoms and MSI scores. Anxiety correlated significantly with depression scores in manic subjects and with mania scores in depressed subjects. Discriminant function analysis associated mixed states with symptoms of hyperactivity and negative cognitions, but not subjective depressive or elevated mood. High MSI scores were associated with severe course of illness. For depressive or manic episodes, characteristics of mixed states emerged with two symptoms of the opposite polarity. This was a cross-sectional study. Mixed states appear to be a continuum. An index of the degree to which depressive and manic symptoms combine appears useful in identifying and characterizing mixed states. We propose a depressive or manic episode with three or more symptoms of the opposite polarity as a parsimonious definition of a mixed state.

Entanglement measure for rank-2 mixed states

We provide an easily computable formula for a bipartite mixed-state entanglement measure. Our formula can be applied to readily calculate the entanglement for any rank-2 mixed state of a bipartite system. We use this formula to provide a tight upper bound for the entanglement of formation for rank-2 states of a qubit and a qudit. We also outline situations where our formula could be applied to study the entanglement properties of complex quantum systems.

Purification of entangled coherent states

We suggest an entanglement purification scheme for mixed entangled coherent states using 50-50 beam splitters and photodetectors. This scheme is directly applicable for mixed entangled coherent states of the Werner type, and can be useful for general mixed states using additional nonlinear interactions. We apply our scheme to entangled coherent states decohered in a vacuum environment and find the decay time until which they can be purified.

Entanglement of mixed macroscopic superpositions: An entangling-power study

We investigate entanglement properties of a recently introduced class of macroscopic quantum superpositions in two-mode mixed states. One of the tools we use in order to infer the entanglement in this non-Gaussian class of states is the power to entangle a qubit system. Our study reveals features which are hidden in a standard approach to entanglement investigation based on the uncertainty principle of the quadrature variables. We briefly describe the experimental setup corresponding to our theoretical scenario and a suitable modification of the protocol which makes our proposal realizable within the current experimental capabilities.

Teleporting bipartite entanglement using maximally entangled mixed channels

The ability to teleport entanglement through maximally entangled mixed states as defined by concurrence and linear entropy is studied. We show how the teleported entanglement depends on the quality of the quantum channel used, as defined through its entanglement and mixedness, as well as the form of the target state to be teleported. We present new results based on the fidelity of the teleported state as well as an experimental setup that is immediately implementable with currently available technology.

Faithful nonclassicality indicators and extremal quantum correlations in two-qubit states

The state disturbance induced by locally measuring a quantum system yields a signature of nonclassical correlations beyond entanglement. Here, we present a detailed study of such correlations for two-qubit mixed states. To overcome the asymmetry of quantum discord and the unfaithfulness of measurement-induced disturbance (severely overestimating quantum correlations), we propose an ameliorated measurement-induced disturbance as nonclassicality indicator, optimized over joint local measurements, and we derive its closed expression for relevant two-qubit states. We study its analytical relation with discord, and characterize the maximally quantum-correlated mixed states, that simultaneously extremize both quantifiers at given von Neumann entropy: among all two-qubit states, these states possess the most robust quantum correlations against noise.

Extremal quantum correlations: Experimental study with two-qubit states

We explore experimentally the space of two-qubit quantum-correlated mixed states, including frontier states as defined by the use of quantum discord and von Neumann entropy. Our experimental setup is flexible enough to allow for high-quality generation of a vast variety of states. We address quantitatively the relation between quantum discord and a recently suggested alternative measure of quantum correlations.