Mixed states

Top PDF Mixed states:

Classification of phases for mixed states via fast dissipative evolution

Classification of phases for mixed states via fast dissipative evolution

A step in this direction has been made in Ref. [20], where the author considers quasi- thermal states, namely mixed states 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 [20] 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.
Show more

46 Read more

Separability for mixed states with operator Schmidt rank two

Separability for mixed states with operator Schmidt rank two

Entanglement is an essential ingredient in many appli- cations in quantum information processing and quan- tum computation [NC00, HHHH09]. Mixed states 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
Show more

14 Read more

Quantum correlations in continuous variable mixed states : from discord to signatures

Quantum correlations in continuous variable mixed states : from discord to signatures

This quantification of entanglement leads to an interesting result about mixed states. All mixed states 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 mixed states could help us understand how to use this spread-out entanglement effectively. In mixed states 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 mixed states, each best suited to a different purpose. Some important properties that a good entanglement measure must satisfy are given below [206].
Show more

149 Read more

Bipolar mixed states: evolution of the concept and implications for the treatment and research

Bipolar mixed states: evolution of the concept and implications for the treatment and research

Bipolar mixed states 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 mixed states. In recent years, several au- thors have contributed to promove a greater awareness of this issue, considering the (DSM-IV-TR) definition of mixed states 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.
Show more

16 Read more

The role of asenapine in the treatment of manic or mixed states associated with bipolar I disorder

The role of asenapine in the treatment of manic or mixed states associated with bipolar I disorder

In order to provide a new, timely and concise mini-review of asenapine in the treatment of manic and mixed states 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”, “mixed states”, “bipolar I disorder”. Each term was also cross-referenced with the others using the MeSH method (Medical Subjects Headings).

7 Read more

Mixed states: still a modern psychopathological syndrome?

Mixed states: still a modern psychopathological syndrome?

The revival of the concept of mixed states 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 mixed states are not equivalent to the classical, Kraepelinian no- tion of mixed states and could have been improved. Both DSM-IV-TR definition of mixed states and the DSM-5 mixed features specifier show clear troubles, in particular in recognising severe mixed states, while the combina- tory model shows a greater sensitivity for the definition of less severe varieties of mixed states 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 mixed states, in fact, do not give clear indications for pharmacological or non-pharmacological treatments of mixed states, and the few available data are limited to post-hoc analyses and subanalyses performed in bipolar, mostly manic, patients.
Show more

9 Read more

Reversible transformations from pure to mixed states and the unique measure of information

Reversible transformations from pure to mixed states and the unique measure of information

However, it is known that for a number of mixed states, 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 mixed states 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.
Show more

9 Read more

Reconsidering the affective dimension of depression and mania: towards a phenomenological dissolution of the paradox of mixed states

Reconsidering the affective dimension of depression and mania: towards a phenomenological dissolution of the paradox of mixed states

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 mixed states 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 mixed states by showing that the essential characteristics of depression and mania cannot and do not coincide. Many cases of mixed states 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.
Show more

9 Read more

Lithium and valproate in manic and mixed states: a naturalistic prospective study

Lithium and valproate in manic and mixed states: a naturalistic prospective study

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 mixed states, 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.
Show more

5 Read more

Management and care of mixed states

Management and care of mixed states

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.
Show more

10 Read more

Spin Flip Scattering at Quantum Hall Transition

Spin Flip Scattering at Quantum Hall Transition

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 mixed states 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

7 Read more

A quantum Jensen-Shannon graph kernel for unattributed graphs

A quantum Jensen-Shannon graph kernel for unattributed graphs

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 mixed states 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.
Show more

33 Read more

Clifford algebras and geometry of entanglement

Clifford algebras and geometry of entanglement

For the single qubit case, both pure and mixed states are discussed explicitly in terms of the Clifford algebra description along with the `mixedness' of a single qubit state, and the Ri[r]

90 Read more

Secure  Certification  of  Mixed  Quantum  States  with  Application  to  Two-Party  Randomness  Generation

Secure Certification of Mixed Quantum States with Application to Two-Party Randomness Generation

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 mixed states, 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.
Show more

33 Read more

Less Decoherence and More Coherence in Quantum Gravity, Inflationary Cosmology and Elsewhere

Less Decoherence and More Coherence in Quantum Gravity, Inflationary Cosmology and Elsewhere

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 mixed states 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
Show more

37 Read more

Distributing entanglement with separable states

Distributing entanglement with separable states

Like a silver thread, quantum entanglement [1] 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 [4], Bell nonlocality [5], 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 mixed states and the role of classical information in quantum commu- nication by demonstrating entanglement distribution using merely a separable ancilla mode.
Show more

5 Read more

Quantum nature of Gaussian discord : experimental evidence and role of system environment correlations

Quantum nature of Gaussian discord : experimental evidence and role of system environment correlations

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 [3] interest in more generic and even nonentangled QIP resources has emerged [4]. 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 mixed states 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.
Show more

6 Read more

Theory of variational quantum simulation

Theory of variational quantum simulation

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 mixed states 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.
Show more

41 Read more

Geometric multiaxial representation of N qubit mixed symmetric separable states

Geometric multiaxial representation of N qubit mixed symmetric separable states

In practice we deal with mixed states 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 mixed states in the literature; classification of local unitary equivalent classes of symmetric N-qubit mixed states and an algorithm to identify pure separable states[15] based on the geometrical Multiaxial Representation (MAR) of the density matrix[16] have been investigated. Makhlin[17] has presented a complete set of 18 local polynomial invariants of two qubit mixed states 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[21]. To this day, no generally
Show more

8 Read more

Quantum Information Hidden in Quantum Fields

Quantum Information Hidden in Quantum Fields

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 mixed states 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.
Show more

30 Read more

Show all 10000 documents...