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We study the role of average concurrence in entanglement swapping in quantum networks. We begin with qubit pure states, and there is a very simple rule governing the propagation of average concurrence in multiple swaps. We look at examples of mixed qubit states, and find the relation for pure states gives an upper bound on what is possible with mixed states. We then move on to qudits, where we make use of the I-concurrence. Here the situation is not as simple as for qubits, but in some cases relatively straightforward results can be obtained., Comment: Comments welcome

Background and Objectives: Unstable mixed episodes or rapid switching between opposite affective poles within the scope of short cycles was first characterized in 1967 by S. Mentzos as complex polymorphous states with chaotic overlap of manic and depressive symptoms. Well-known examples include antidepressant-induced mania/hypomania and rapid/ultra-rapid/ultradian cycling, when clinicians observe an almost continuous mixed state with a constant change of preponderance of manic or depressive symptoms. Achieving stable remission in these cases is challenging with almost no data on evidence-based treatment. When mood stabilizers are ineffective, electroconvulsive therapy (ECT) has been suggested. Objectives: After reviewing the evidence from available literature, this article presents our own clinical experience of ECT efficacy and tolerability in patients with ultra-rapid cycling bipolar disorder (BD) and unstable mixed states. Materials and Methods: We conducted an open, one-year observational prospective study with a “mirror image” design, including 30 patients with rapid and ultra-rapid cycling BD on long-term mood stabilizer treatment (18 received lithium carbonate, 6 on valproate and 6 on carbamazepine) with limited effectiveness. A bilateral ECT course (5–10 sessions) was prescribed for regaining mood stability. Results: ECT was very effective in 12 patients (40%) with a history of ineffective mood stabilizer treatment who achieved and maintained remission, all of them received lithium except for 1 patient who received carbamazepine and 2 with valproate. Nine patients (30%) showed partial response (one on carbamazepine and two on valproate) and nine patients (30%) had no improvement at all (four on carbamazepine and two on valproate). For the whole sample, the duration of affective episodes was significantly reduced from 36.05 ± 4.32 weeks in the year prior to ECT to 21.74 ± 12.14 weeks in the year post-ECT (p &lt, 0.001). Depressive episodes with mixed and/or catatonic features according to DSM-5 specifiers were associated with a better acute ECT response and/or long-term mood stabilizer treatment outcome after ECT. Conclusions: ECT could be considered as a useful option for getting mood instability under control in rapid and ultra-rapid cycling bipolar patients. Further randomized trials are needed to confirm these results.

We introduce the focused confinement method, a reaction coordinate-free simulation approach for the calculation of conformational free energies. These are obtained in a series of restrained simulations that transform part of the molecule of interest to independent harmonic oscillators resulting in mixed harmonic-anharmonic states. It is shown that the free energy difference between these mixed states can be readily calculated through the construction of chimeric trajectories. By focusing the confinement to the conformationally active region, the method requires fewer restrained simulations than the traditional confinement method, which eases the treatment of large systems. The accuracy and efficiency of the method is demonstrated for implicitly and explicitly solvated systems.

We introduce QuEST, the Quantum Exact Simulation Toolkit, and compare it to ProjectQ, qHipster and a recent distributed implementation of Quantum++. QuEST is the first open source, OpenMP and MPI hybridised, GPU accelerated simulator of universal quantum circuits. Embodied as a C library, it is designed so that a user's code can be deployed seamlessly to any platform from a laptop to a supercomputer. QuEST is capable of simulating generic quantum circuits of general single-qubit gates and multi-qubit controlled gates, on pure and mixed states, represented as state-vectors and density matrices, and under the presence of decoherence. Using the ARCUS Phase-B and ARCHER supercomputers, we benchmark QuEST's simulation of random circuits of up to 38 qubits, distributed over up to 2048 compute nodes, each with up to 24 cores. We directly compare QuEST's performance to ProjectQ's on single machines, and discuss the differences in distribution strategies of QuEST, qHipster and Quantum++. QuEST shows excellent scaling, both strong and weak, on multicore and distributed architectures., 8 pages, 8 figures; fixed typos; updated QuEST URL and fixed typo in Fig. 4 caption where ProjectQ and QuEST were swapped in speedup subplot explanation; added explanation of simulation algorithm, updated bibliography; stressed technical novelty of QuEST; mentioned new density matrix support

Our current conceptualisation of mixed states, defined as co-occurring manic and depressive symptoms, is unlikely to advance our knowledge or inform clinical practice. Episodes of mixed states can no longer be coded in the Diagnostic and Statistical Manual of Mental Disorders (DSM-5), and the 'mixed features specifier' fails to capture the most common mixed state presentations. This reflects a lack of understanding of both the importance of mixed states and their underlying pathophysiology. Indeed, research into the nature of mixed states is scarce and uninformative, and most clinical practice guidelines fail to provide advice regarding their management. In this paper, we proffer a reconceptualisation of mixed states that provides a framework for informing clinical practice and research. It is based on the ACE model, which deconstructs mood disorders into three domains of symptoms: activity, cognition, and emotion. Symptoms within each domain vary independently over time and in different directions (towards either excitation or inhibition). By deconstructing mood disorders into component domains, mixed states can be explained as the product of different domains varying 'out of sync'. In most cases, the aetiology of mixed states is unknown. Alongside such idiopathic mixed states, we describe three potential causes of mixed states that are important to consider when formulating management: transitions, ultradian cycling, and treatment-emergent affective switches. In addition to providing guidance on the identification of various kinds of mixed states, we discuss practical strategies for their management, including the monitoring of ACE domains and functioning, to inform the use of psychoeducation and lifestyle changes, psychotherapy, pharmacology, and electroconvulsive therapy.

Evaporation characteristics of various droplets on superhydrophobized Si micro-pillar (SiμP) substrate have been investigated experimentally. Especially, the unique characteristics of evaporating mixed drop have been elucidated for the first time, to the best of the authors’ knowledge. Processes for forming different droplets, i.e., Cassie, Wenzel, and mixed ones, are developed. Exposure to humidifier mist has enabled the formation of Cassie droplets, droplets sitting on pillars top with entrapped air underneath. Water vapor condensation has led to the formation of mixed droplets, that is, Cassie droplet with impaled plugs. The mixed droplets have been converted into Wenzel ones by simply adding additional water and applying pressure to them. These droplets have shown different evaporation characteristics. As expectedly, mixed droplets have shown evaporation time in-between of those for Cassie and Wenzel ones. Further, compared to the well-known constant contact angle (CCA) mode of evaporation for Cassie and constant contact radius (CCR) mode of evaporation for Wenzel droplets, respectively, the evaporation of the mixed droplet has been found to be pseudo-CCA mode, where the contact angle decreases/recovers with stepwise decrease in contact radius. This evaporation behavior is quite similar to the stick-slip motion of droplet evaporation on superhydrophobic surface. Finally, spontaneous droplet movement, depending on the droplet type, has been traced during the evaporation. While the Cassie drop moves rather randomly during evaporation, the mixed droplet showed predictable movement depending on the size and location of Wenzel plugs. The evaporation characteristics of different droplets can be a valuable help for a wide variety of applications such as self-cleaning, dewing, fog-basking, dropwise/filmwise condensation, etc.

We construct inequalities between R\'enyi $\ensuremath{\alpha}$-entropy and the indexes of coincidence of probability distributions, based on which we obtain improved state-dependent entropic uncertainty relations for general symmetric informationally complete positive operator-valued measures (SIC-POVMs) and mutually unbiased measurements (MUMs). We show that our uncertainty relations for general SIC-POVMs and MUMs can be tight for sufficiently mixed states, and, moreover, comparisons to the numerically optimal results are made via information diagrams.

We analyze the relationship between qubit-environment entanglement that can be created during the pure dephasing of the qubit and the effectiveness of the spin echo protocol. We focus here on mixed states of the environment. We show that while the echo protocol can obviously counteract classical environmental noise, it can also undo dephasing associated with qubit-environment entanglement, and there is no obvious difference in its efficiency in these two cases. Additionally, we show that qubit-environment entanglement can be generated at the end of the echo protocol even when it is absent at the time of application of the local operation on the qubit (the {\pi} pulse). We prove that this can occur only at isolated points in time, after fine-tuning of the echo protocol duration. Finally, we discuss the conditions under which the observation of specific features of the echo signal can serve as a witness of the entangling nature of the joint qubit-environment evolution., Comment: 10 pages, 1 figure

We present a systematic approach for obtaining lower bounds on the failure probability of unambiguous state discrimination by introducing an ancillary degree of freedom. Specifically, the lower bounds are obtained by introducing a suitable homogeneous function of the off-diagonal entries of the reduced matrix in the ancillary degree of freedom. A series of lower bounds on the failure probability of unambiguous discrimination of both pure states and mixed states are derived using the ${l}_{r}$-norm of the off-diagonal entries. Our method adds insights into the problem of unambiguous state discrimination. In particular, since we have related the lower bound with off-diagonal entries of density matrices, e.g., the ${l}_{1}$-norm coherence, our work suggests that unambiguous state discrimination may provide further applications in quantifying coherence, and vise versa.

We present a theoretical scheme for the generation of stationary entangled states. To achieve the purpose we consider an open quantum system consisting of a two-qubit plunged in a thermal bath, as the source of dissipation, and then analytically solve the corresponding quantum master equation. We generate two classes of stationary entangled states including the Werner-like and maximally entangled mixed states. In this regard, since the solution of the system depends on its initial state, we can manipulate it and construct robust Bell-like state. In the continuation, we analytically obtain the population and coherence of the considered two-qubit system and show that the residual coherence can be maintained even in the equilibrium condition. Finally, we successfully encode our two-qubit system to solve a binary classification problem. We demonstrate that, the introduced classifiers present high accuracy without requiring any iterative method. In addition, we show that the quantum based classifiers beat the classical ones.

Bipolar disorder is a disabling psychiatric disorder which causes premature death and loss of quality of life. Despite the developments, novel treatments are partially effective and insufficient responses to treatment may cause loss of quality of life. Contemporary approaches to treatment planning involve taking the current symptoms and the personal treatment history of the patient into account and tailoring them for the treatment of each patient, i.e. individualized treatment. In this article, effects and side effects of antipsychotics, mood stabilizers and sedative hypnotic medications are reviewed and presented briefly for clinicians. Although novel developments have been observed in the literature about mixed states and psychotic symptoms, evidence-based options are still limited. Efficacy of mood stabilizers may be prolonged and additional medications may also be needed frequently in patients treated with mood stabilizers. Antipsychotics may cause several side effects and cannot be maintained for a long time in some of those patients. These factors may limit the use of mood stabilizers or antipsychotics. Therefore, the experience of the clinician and personal history of the patient still have importance in the procedure.

The notion of "mixity" of the dysphoric phases of the bipolarity includes the most insidious symptoms of the bipolar spectrum of mood disorders: the overlapping between depression-restlessness-irritability-grief-tension-anxiety can cause worsening of the mood disorders and in the most acute phases may cause increased risk of major behavioural disruption including murder and suicide. The "mixity" is a dynamic notion describing the presence of overlapping symptoms of mixed states, in an increasing intensity level. The early utilization of the rating scale on mixed states, "GT-MSRS",which can demonstrate the level of "mixity"of the mood disorder, can prevent this. Mixed states occur in an average of 40% of bipolar patients over a lifetime;when considering bipolarity the notion of the "mixity" becomes the conceptual reference point of the diagnostic process.

In this paper, we will discuss the possibility of increasing the Holevo value when measuring with post-selection. By measurement with post-selection we mean that some of the outcomes of the measurement are discarded, and then we work with the resulting states. Using the example of two mixed states, it will be shown that mutual information after performing post-selection is greater than their initial Holevo value. An increase in the Holevo value follows from the monotonicity property of the quantum relative entropy.

Animal models are essential tools for studying the biological basis and testing new substances for any disease. However, the development of animal models for psychiatric disorders is a challenge because there is no precise etiology and physiopathology, and the diagnosis is performed by behavioral analysis. On the other hand, animal models are even more important in psychiatry because animal models allow us to test the hypotheses related to the etiology and pathophysiology of disorders. The development of animal models of bipolar disorder is particularly complicated by its clinical course, which involves mania, depression, mixed states, and euthymia. In this chapter, we will discuss the main animal models used to study the neurobiology of bipolar disorder and the model evolution along time.

Unambiguous quantum state discrimination is a strategy where the conclusive result can always be trusted. This strategy is very important, since it can be used for various quantum information protocols, including quantum key distribution. However, in the view of quantumness, it is not clear what is going on in performing unambiguous quantum state discrimination. To answer the question, we investigate coherence distribution when unambiguous discrimination is performed by generalized measurement. Specially, we study coherence distribution in three cases, which consist of unambiguous quantum state discrimination, sequential quantum state discrimination, and assisted optimal discrimination, which are considered to be a family of unambiguous quantum state discrimination. In this investigation, we show that the structure of generalized measurements performing various types of unambiguous quantum state discrimination can be understood in terms of coherence distribution. Our result is not limited to the discrimination of two pure quantum states, but it is extended to the discrimination of two mixed states.

Lifetime calculations of Th II J = 1.5 and 2.5 odd states are performed with configuration&ndash, interaction many-body perturbation theory (CI-MBPT). For many J = 2.5 states, lifetimes are quite accurate, but two pairs of J = 2.5 odd states and many groups of J = 1.5 states are strongly mixed, making theoretical predictions unreliable. To solve this problem, a method based on intensities is used. To relate experimental intensities to lifetimes, two parameters, one an overall coefficient of proportionality for transition rates and one temperature of the Boltzmann distribution of populations, are introduced and fitted to minimize the deviation between theoretical and intensity-derived lifetimes. For strongly mixed groups of states, the averaged lifetimes obtained from averaged transition rates were used instead of individual lifetimes in the fit. Close agreement is obtained. Then intensity branching ratios are used to extract individual lifetimes for the strongly mixed states. The resulting lifetimes are compared to available directly measured lifetimes and reasonable agreement is found, considering limited accuracy of intensity measurements. The method of intensity-based lifetime calculations with fit to theoretical lifetimes is quite general and can be applied to many complex atoms where strong mixing between multiple states exists.