A step in this direction has been made in Ref. , where the author considers quasi- thermal states, namely mixedstates whose logarithm is a local Hamiltonian. Similarly to the Gaussian case he can identify some kind of purity gap, as the gap of such local Hamiltonian. In the case of a closed system, with the dynamics governed by a local Hamiltonian, the author defines states to be in the same phases iff they are connected by a local unitary transformation and studies the robustness of this definition under weak and strong local perturbations. He also considers the case of open systems whose dynamics are governed by local Lindbladians. Also in this case he defines phases through local unitary transformations. In an appendix, he comments on the possibility of defining phases via a non unitary evolution, in a similar fashion to what we do in this work. However, he concludes that this approach is unsuccessful because it would generate a single trivial phase. This seems in contrast with what we find here, and the reason is that in  the author considers only fixed points of globally fast Lindbladians. In such case of course all states could be obtained very fast from the product state and one obtains a single trivial phase. In this work instead we allow for Lindbladians whose time of convergence from the initial to the final state may scale with the system size. As commented in detail in this section, we define two states to be in the same phase if such scaling is less than linear (say poly-logarithmic). As already mentioned, this allows for a very rich structure of the phase diagram.
Entanglement is an essential ingredient in many appli- cations in quantum information processing and quan- tum computation [NC00, HHHH09]. Mixedstates which are not entangled are called separable, and they may contain only classical correlations—in contrast to entangled states, which contain quantum correla- tions. As many other problems in theoretical physics and elsewhere, the problem of determining whether a state is entangled or not is NP-hard [Gur03, Gha10]. This does not prevent the existence of multiple sepa- rability criteria [HHHH09]. One example are criteria based on the rank of a bipartite mixed state 0 6 ρ ∈ M d 1 ⊗ M d 2 (where M d denotes the set of complex
This quantification of entanglement leads to an interesting result about mixedstates. All mixedstates have non-zero entropy, and they can be purified by extending to a larger system. The entropy of entanglement therefore tells us that every mixed state is entangled to its purifying subsystem. If you have a pure entangled state that undergoes loss to the environment, the entanglement will decay and eventually disappear. But since the remaing state is mixed, it must be entangled to the subsystem that purifies it. The entanglement has not disappeared, it has simply spread out to a larger system. If all the losses could be recovered the entanglement could be restored. Practically, of course, this is impossible, but it does raise an interesting question about entanglement. Most of what we see is in a mixed state, so does that mean that almost everything is entangled to something, and if we could observe its purification by possessing everything that it has interacted with, we would see that entanglement is much more prevalent than it first appears? The study of mixedstates could help us understand how to use this spread-out entanglement effectively. In mixedstates it is much more difficult to quantify the entanglement of a given state, largely because every mixed state has an infinite number of possible pure-state decompositions. This has led to numerous different methods to quantify entanglement in mixedstates, each best suited to a different purpose. Some important properties that a good entanglement measure must satisfy are given below .
Bipolar mixedstates remain a nosologic dilemma, diagnostic challenge and neglected area of therapeutic research. Mixed episodes are reported to occur in up to 40% of acute bipolar admissions and are associated with more severe manic and general psychopathology, more catatonic symptoms, more co- morbidity, a higher risk of suicide and a poorer outcome than pure manic episodes. Kraepelin was the first to emphasize the clinical relevance of mixedstates. In recent years, several au- thors have contributed to promove a greater awareness of this issue, considering the (DSM-IV-TR) definition of mixedstates extremely narrow and inadequate. The nomenclature for the co- occurrence of manic and depressive symptoms has been revised in the new DSM-5 version to accommodate a mixed categori- cal–dimensional concept. The new classification will capture subthreshold non-overlapping symptoms of the opposite pole using a “with mixed features” specifier to be applied to manic episodes in bipolar disorder I, hypomanic, and major depressive episodes experienced in bipolar disorder I, bipolar disorder II, bipolar disorder not otherwise specified, and major depressive disorder. The revision will have a substantial impact in several fields: epidemiology, diagnosis, treatment, research, education, and regulations.
In order to provide a new, timely and concise mini-review of asenapine in the treatment of manic and mixedstates associated with BD disorder, we performed careful MedLine, Excerpta Medica and PsycInfo searches to identify papers published in English over the past 7 years. Search terms were “asenapine”, “manic”, “mixedstates”, “bipolar I disorder”. Each term was also cross-referenced with the others using the MeSH method (Medical Subjects Headings).
The revival of the concept of mixedstates will be hopeful- ly fostered by changes in the DSM-5 definition, and is also a consequence of the renewed interest on this subtype of bipolar disorder. Of course, the current criteria of mixedstates are not equivalent to the classical, Kraepelinian no- tion of mixedstates and could have been improved. Both DSM-IV-TR definition of mixedstates and the DSM-5 mixed features specifier show clear troubles, in particular in recognising severe mixedstates, while the combina- tory model shows a greater sensitivity for the definition of less severe varieties of mixedstates characterised by clearly identifiable symptoms. Moreover, the mixed cate- gorical-dimensional concept used in the DSM-5 does not adequately reflect some overlapping mood criteria, such as mood lability, irritability and psychomotor agitation, considered among the most common features of mixed depression. The significant changes made in the DSM-5 will help researchers in studying the clinical characteris- tics of this subtype of bipolar disorder and in implement- ing effective treatment strategies. Guidelines for the treat- ment of mixedstates, in fact, do not give clear indications for pharmacological or non-pharmacological treatments of mixedstates, and the few available data are limited to post-hoc analyses and subanalyses performed in bipolar, mostly manic, patients.
However, it is known that for a number of mixedstates, the distillable entanglement is not equal to the entanglement cost 关 28 兴 . One has irreversibility. It has generally been assumed that this is because one is making transformations between pure states 共 in this case, singlets 兲 , and the mixed state AB . One therefore expects some information loss. However, as we have seen here, one can make transformations between pure and mixedstates completely reversible, provided one has access to noise. And indeed, in the paradigm of entangle- ment theory, there is no reason why two distant parties could not share some initial noisy resource. There is no special a priori reason for irreversibility in entanglement theory. It is therefore interesting to compare the situation discussed here with that of entanglement theory. This comparison is sum- merized in the following table, and described below.
a change in the way we have moods, not as a change from one kind of mood to another. Fourth, I return to the phenomenon of mixedstates and argue that the affective dimension of depres- sion and mania, when conceived along the phenomenological lines I set forth in the previous sections, dissolves the paradox of mixedstates by showing that the essential characteristics of depression and mania cannot and do not coincide. Many cases of mixedstates are diagnosed because moods that we take to be essential features of either depression or mania arise within the context of what is considered to be the opposite kind of epi- sode (e.g. dysphoria, typically associated with depression, often arises in what is otherwise considered a manic state). However, if we conceive of the affective dimension of depression as a decrease in the degree to which one is situated in and attune to the world through moods, and the affective dimension of mania as an increase in the degree to which one is situated in and at- tuned to the world through moods, then the particular mood one finds oneself in is simply irrelevant to the diagnosis of either depression or mania. As a result, the manifestation of any par- ticular moods in what otherwise seems to be a pure manic or depressive episode does not constitute a mixed state.
Lithium is still recommended as a first-choice treatment for acute bipolar mania, especially in pure euphoric mania of mild to moderate severity. Despite the large quantity of evidence supporting the efficacy of lithium, in clinical practice its use has often been limited because of management issues related to its narrow therapeutic index. International guidelines suggest com- bining lithium with a second mood stabilizer (anticonvulsant or atypical antipsychotic) for treatment of mixedstates, rapid cycling and severe forms of mania with atypical features, which are classically considered to be poorly responsive to lithium alone. To date, however, the specific modalities of these associ- ations on the basis of different clinical presentations have been poorly investigated in clinical trials. In this study, we aimed to evaluate the modalities of use of lithium in a naturalistic setting of manic and mixed bipolar patients, and to investigate the ef- fects of its combination with valproate on the clinical course.
no stati presi in considerazione tutti gli studi presenti su Medline (Medical Literature Analysis and Retrieval Sy- stem Online), utilizzando il motore di ricerca PUBMED, selezionati in base alle seguenti keywords: mixed state(s) treatment/therapy o mixed episode(s) treatment/the- rapy. Considerando i pur pochi dati esistenti, lo scritto che segue cerca di tracciarne le conclusioni in modo critico nel tentativo di dare qualche elemento di utilità clinico-pratica. Verrà considerata prima la gestione e la cura degli episodi maniacali con elementi misti e suc- cessivamente la gestione e la cura degli episodi depres- sivi con elementi misti.
state is extended but the mixing on the links couples it to other states that are localized at the given energy. As long as the critical energies of the mixedstates are close, the localization length of the admixed state is large, and the overall effect of the mixing results in the appearance of a finite energy region of delocalized states. This is the case for relatively small exchange couplings . In the regime of small , the coefficients 2 of the mixing
In this paper, we use the quantum Jensen-Shannon divergence as a means of measuring the in- formation theoretic dissimilarity of graphs and thus develop a novel graph kernel. In quantum mechanics, the quantum Jensen-Shannon divergence can be used to measure the dissimilarity of quantum systems specified in terms of their density matrices. We commence by computing the density matrix associated with a continuous-time quantum walk over each graph being compared. In particular, we adopt the closed form solution of the density matrix introduced in [27, 28] to re- duce the computational complexity and to avoid the cumbersome task of simulating the quantum walk evolution explicitly. Next, we compare the mixedstates represented by the density matrices using the quantum Jensen-Shannon divergence. With the quantum states for a pair of graphs de- scribed by their density matrices to hand, the quantum graph kernel between the pair of graphs is defined using the quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets from both bioinformat- ics and computer vision. The experimental results demonstrate the effectiveness of the proposed quantum graph kernel.
In this paper, we investigate this type of sampling procedure in detail. Several challenges arise in the analysis of this protocol. First, defining what we mean when we say that the sampling works is not trivial. In the case of regular quantum sampling, we usually want to say that the state has a very small probability of being outside of a low-error subspace that corresponds to the statistics that we have observed. For mixedstates, this definition fails completely: every subspace contains pure states, which we would want to exclude since they are very far from the ideal mixed state. We might then be tempted to include the purifying systems in the definition of the low-error subspace, but then we have no guarantee that an adversarial prover will respect the structure we want to impose on his part of the state—we don’t even know that it consists of n subsystems. A second difficulty comes from the fact that the prover might not necessarily want to provide the state that gives him the best chance of passing the test, even if he has it. If we again look at the case of certifying uniformly random qubits, even if Sam has the ideal state before the sampling begins, Paul might want to bias the outcome, for example by passing the test if he measures |0i on all of the non-sampled qubits, and failing on purpose otherwise. Because of these difficulties, our main result does not follow from traditional sampling theorems.
At this point we would like to make a few comments that are crucial in order to evaluate the claims regarding the capacity of decoherence to solve foundational prob- lems. These comments have to do with similarities and differences regarding mixedstates and reduced density matrices. Regarding similarities, it is clear that, mathe- matically speaking, they are identical. That is, they are both generically represented by matrices with trace equal to one. As a result, entangled subsystems and ensembles are often described with matrices of identical form. Regarding differences, it is central to keep in mind that the physical situations described by mixtures (or proper mix- tures) and reduced density matrices (or improper mixtures) are extremely different. In the first case, the systems described always possess well-defined quantum states, even though these might not be known to us. In the second case, if the subsystem one wants to describe is entangled, it simply does not possess a well-defined state. As a result, ρ A cannot be considered to represent the state of the system, so it becomes merely a
Like a silver thread, quantum entanglement  runs through the foundations and breakthrough applications of quantum information theory. It cannot arise from local operations and classical communication (LOCC) and therefore represents a more intimate relationship among physical systems than we may encounter in the classical world. The ‘‘nonlocal’’ character of entanglement mani- fests itself through a number of counterintuitive phe- nomena encompassing the Einstein-Podolsky-Rosen paradox [2,3], steering , Bell nonlocality , or nega- tivity of entropy [6,7]. Furthermore, it extends our abilities to process information. Here, entanglement is used as a resource which needs to be shared between remote parties. However, entanglement is not the only manifestation of quantum correlations. Notably, separable quantum states can also be used as a shared resource for quantum commu- nication. The experiment presented in this Letter highlights the quantumness of correlations in separable mixedstates and the role of classical information in quantum commu- nication by demonstrating entanglement distribution using merely a separable ancilla mode.
As quantum information science develops towards quantum information technology, the question of the efficient use and optimization of resources becomes a burning issue. So far, quantum information processing (QIP) has been mostly thought of as entanglement-enabled technology. Quantum cryptography is an exception, but even there the so-called effective entanglement between the parties plays a decisive role [1,2]. With the advent of new quantum computation paradigms  interest in more generic and even nonentangled QIP resources has emerged . Unlike entanglement, the new resources, commonly dubbed as quantum correlations, reside in all states which do not diagonalize in any local product basis. Entanglement and quantum correlations are equivalent notions only for pure states. Quantumness of correlations in separable states is fundamentally related to the noncommutativity of observables, nonorthogonality of states, and properties of quantum measurements, whereas entanglement can be seen as a consequence of the quantum superposition principle. Correlated mixedstates are a lucid illustration of the fact that the quantum-classical divide is actually purpose-oriented and that such states, long considered unsuitable for QIP, may become a robust and efficient quantum tool.
The variational method is a versatile tool for classical simulation of a variety of quantum systems. Great efforts have recently been devoted to its extension to quantum computing for efficiently solving static many-body problems and simulating real and imaginary time dynamics. In this work, we first review the conventional variational principles, including the Rayleigh-Ritz method for solving static problems, and the Dirac and Frenkel variational principle, the McLachlan’s variational principle, and the time-dependent variational prin- ciple, for simulating real time dynamics. We focus on the simulation of dynamics and discuss the connections of the three variational principles. Previous works mainly focus on the unitary evolution of pure states. In this work, we introduce variational quantum simulation of mixedstates under general stochastic evolution. We show how the results can be reduced to the pure state case with a correction term that takes accounts of global phase alignment. For variational simulation of imaginary time evolution, we also extend it to the mixed state scenario and discuss variational Gibbs state preparation. We further elaborate on the design of ansatz that is compatible with post-selection measurement and the implementation of the generalised variational algorithms with quantum circuits. Our work completes the theory of variational quantum simulation of general real and imaginary time evolution and it is applicable to near-term quantum hardware.
In practice we deal with mixedstates rather than pure states due to decoherence effects and hence it is of great importance to study mixed separable states. There exists many important papers [6–14] for mixedstates in the literature; classification of local unitary equivalent classes of symmetric N-qubit mixedstates and an algorithm to identify pure separable states based on the geometrical Multiaxial Representation (MAR) of the density matrix have been investigated. Makhlin has presented a complete set of 18 local polynomial invariants of two qubit mixedstates and demonstrated the usefulness of these invariants to study entanglement. Also, detection of multipartite entanglement has been studied in depth(see for example [18–20]). Geometric entanglement properties of pure symmetric N qubit states are studied in detail. To this day, no generally
Ignoring the connected part of the quantum network in Fig. 9, is what one does in discarding the mathematical formalism of interactions in QFT, as often happens in constructivist formulations of QFT: only free fields in input and output are taken into account. If virtual states and mixedstates were absent in the quantum network of Fig. 9, the computational speed would be much lower. In fact, in this case, the quantum network would be reduced to a 2 n Boolean lattice (n = 0,1,2, ....) represented by the regular tree graph (a binary tree) in Fig. 10.