scholarly journals Twisted and untwisted negativity spectrum of free fermions

2019 ◽  
Vol 7 (3) ◽  
Author(s):  
Hassan Shapourian ◽  
Paola Ruggiero ◽  
Shinsei Ryu ◽  
Pasquale Calabrese

A basic diagnostic of entanglement in mixed quantum states is known as the positive partial transpose (PT) criterion. Such criterion is based on the observation that the spectrum of the partially transposed density matrix of an entangled state contains negative eigenvalues, in turn, used to define an entanglement measure called the logarithmic negativity. Despite the great success of logarithmic negativity in characterizing bosonic many-body systems, generalizing the operation of PT to fermionic systems remained a technical challenge until recently when a more natural definition of PT for fermions that accounts for the Fermi statistics has been put forward. In this paper, we study the many-body spectrum of the reduced density matrix of two adjacent intervals for one-dimensional free fermions after applying the fermionic PT. We show that in general there is a freedom in the definition of such operation which leads to two different definitions of PT: the resulting density matrix is Hermitian in one case, while it becomes pseudo-Hermitian in the other case. Using the path-integral formalism, we analytically compute the leading order term of the moments in both cases and derive the distribution of the corresponding eigenvalues over the complex plane. We further verify our analytical findings by checking them against numerical lattice calculations.

2021 ◽  
Author(s):  
Xiao-Fang Liu ◽  
Dong-Fen Li ◽  
Yun-Dan Zheng ◽  
Xiao-Long Yang ◽  
Jie Zhou ◽  
...  

Abstract Quantum controlled teleportation is the transmission of the quantum state under the supervision of a third party. This paper presents a theoretical and experimental combination of an arbitrary two-qubit quantum controlled teleportation scheme. In the scheme, the sender Alice only needs to perform two Bell state measurements, and the receiver Bob can perform the appropriate unitary operation to reconstruct arbitrary two-qubit states under the control of the supervisor Charlie. We verified the operation process of the scheme on the IBM Quantum Experience platform and further checked the accuracy of the transmitted quantum state by performing quantum state tomography. Meanwhile, good fidelity is obtained by calculating the theoretical density matrix and the experimental density matrix. We also introduced a sequence of photonic states to analyze the possible intercept-replace-resend, intercept-measure-resend, and entanglement-measure-resend attacks on this scheme. The results proved that our scheme is highly secure.


Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 149-167 ◽  
Author(s):  
Andrea Prunotto ◽  
Wanda Maria Alberico ◽  
Piotr Czerski

Abstract The rooted maps theory, a branch of the theory of homology, is shown to be a powerful tool for investigating the topological properties of Feynman diagrams, related to the single particle propagator in the quantum many-body systems. The numerical correspondence between the number of this class of Feynman diagrams as a function of perturbative order and the number of rooted maps as a function of the number of edges is studied. A graphical procedure to associate Feynman diagrams and rooted maps is then stated. Finally, starting from rooted maps principles, an original definition of the genus of a Feynman diagram, which totally differs from the usual one, is given.


2012 ◽  
Vol 15 (01) ◽  
pp. 1250001 ◽  
Author(s):  
JIM GATHERAL ◽  
TAI-HO WANG

In this article, we derive a new most-likely-path (MLP) approximation for implied volatility in terms of local volatility, based on time-integration of the lowest order term in the heat-kernel expansion. This new approximation formula turns out to be a natural extension of the well-known formula of Berestycki, Busca and Florent. Various other MLP approximations have been suggested in the literature involving different choices of most-likely-path; our work fixes a natural definition of the most-likely-path. We confirm the improved performance of our new approximation relative to existing approximations in an explicit computation using a realistic S&P500 local volatility function.


2021 ◽  
Vol 36 (Supplement_1) ◽  
Author(s):  
Davide Viggiano ◽  
Giovambattista Capasso

Abstract Background and Aims The term "inflammation" is undoubtedly one of the oldest medical terms and yet in use. However, its meaning has changed over the centuries. This work gives a historical and critical view of the concept of inflammation, with particular reference to kidney diseases. Method The term "inflammation" was used in Galenic medicine to specify a collection of symptoms. Celsus (c. 25 BC – c. 50 AD) described "rubor et tumor cum calor et dolor", but the list became much longer in subsequent Galenic scholars. It is interesting to note that one of the inflammation symptoms, "tumor," was then used to indicate cancer (tumor=swelling due to a mass or due to edema). Virchow (1821 –1902) is often quoted for introducing a fifth symptom, "function Lasa", but his significant contribution relies on introducing the microscope to study diseases: thanks to this instrument, the paradigm of inflammation was undergoing a revolution. Thereby, the definition of inflammation shifted from a pure collection of symptoms to a histopathological classification, characterized by the tissue "inflammatory infiltrates" with subcategories according to the cell types involved. Numerous authors added their names to pathology textbooks when describing a new kind of cellular infiltration. Overall, the tremendous success of the histopathologic paradigm of inflammation or "inflammatory infiltrates" was the possibility to contain and revert this phenomenon with corticosteroids (with few exceptions). Subsequently, specific drugs were proposed for each inflammatory infiltrate. This type of paradigm is still used today to define, e.g., tubulointerstitial nephritis or intra- and peri-glomerular inflammations. The subsequent classification of inflammatory infiltrates using immunohistochemistry did not modify our classification system (the distinction of, e.g., CD20 lymphocytes from CD4 T-cells is not used, unfortunately, in today's classification system). Results Towards the 1940s, Avery et al. recognize that some plasma proteins (specifically the famous C-reactive protein) increase during acute infection, which is a typical inflammatory state. This observation led to a new "molecular definition of inflammation". The idea to identify the presence of inflammatory infiltrates in tissues just by looking at plasma constituents had great success: after all, the histological processing of tissues was no longer needed. Even though many authors were alerting that these plasma constituents are often increased even in the absence of any "inflammatory infiltrate", the plasma proteins were so easily accessible that the new direction was not modifiable. A modern generalization of this type of approach is called "liquid biopsy, " even though it is not limited to the inflammatory states, but to a larger number of identifiable diseases today only histologically. The effect of the new "molecular" definition of inflammation was that a large number of diseases without significant inflammatory infiltrates (such as obesity, atherosclerosis, aging, dialysis, and chronic kidney disease) are notwithstanding accompanied by the increase of plasma proteins labeled as "inflammatory". Therefore, the list of "inflammatory" diseases (in the new terms) is now much more extensive. The price for such enlargement of conditions is that most new entries do not respond to steroids or other anti-inflammatory drugs. Conclusion The new definition of" inflammatory disease" comprises classical steroid-dependent disorders characterized by inflammatory infiltrates and new conditions with minimal inflammatory infiltrates plus the presence of "inflammatory" plasma proteins plus little response to steroids. It might be beneficial to distinguish these types of inflammation.


Author(s):  
Wolfgang Schmickler

In this chapter we introduce and discuss a number of concepts that are commonly used in the electrochemical literature and in the remainder of this book. In particular we will illuminate the relation of electrochemical concepts to those used in related disciplines. Electrochemistry has much in common with surface science, which is the study of solid surfaces in contact with a gas phase or, more commonly, with ultrahigh vacuum (uhv). A number of surface science techniques has been applied to electrochemical interfaces with great success. Conversely, surface scientists have become attracted to electrochemistry because the electrode charge (or equivalently the potential) is a useful variable which cannot be well controlled for surfaces in uhv. This has led to a laudable attempt to use similar terminologies for these two related sciences, and to introduce the concepts of the absolute scale of electrochemical potentials and the Fermi level of a redox reaction into electrochemistry. Unfortunately, there is some confusion of these terms in the literature, even though they are quite simple. Electrochemical interfaces are sometimes referred to as electrified interfaces, meaning that potential differences, charge densities, dipole moments, and electric currents occur. It is obviously important to have a precise definition of the electrostatic potential of a phase. There are two different concepts. The outer or Volta potential ψα of the phase a is the work required to bring a unit point charge from infinity to a point just outside the surface of the phase. By "just outside" we mean a position very close to the surface, but so far away that the image interaction with the phase can be ignored; in practice, that means a distance of about 10-5 — 10-3 cm from the surface. Obviously, the outer potential ψα is a measurable quantity. In contrast, the inner or Galvani potential ϕα is defined as the work required to bring a unit point charge from infinity to a point inside the phase α; so this is the electrostatic potential which is actually experienced by a charged particle inside the phase. Unfortunately, the inner potential cannot be measured: If one brings a real charged particle - as opposed to a point charge - into the phase, additional work is required due to the chemical interaction of this particle with other particles in the phase. For example, if one brings an electron into a metal, one has to do not only electrostatic work, but also work against the exchange and correlation energies.


1993 ◽  
Vol 48 (1-2) ◽  
pp. 390-397 ◽  
Author(s):  
M. Peter ◽  
T. Jarlborg ◽  
A. A. Manuel ◽  
B. Barbiellini

Abstract The positron annihilation technique has made well-known contributions to the study of Fermi surfaces in "classical" superconductors, including A15 phases where the definition of the Fermi surface has been questioned on the grounds of Anderson localization. In the case of the superconducting oxides, even more far out models were proposed, which made the clear imaging of the Fermi surface by positrons desirable. The difficulties due to the predicted weakness of the signal, and the large possibility for trapping have now been surmounted and the Fermi surface has been seen; what more can we learn from positrons?After presenting the actual situation with experiment, we will comment on enhancement and correlation and their effect on ACAR and lifetime studies. Then we explain the picture of Jarlborg and Singh of enhancement, with its recent tests for many substances. We conclude by asking the question of sensitivity of positrons to many-body effects. Ferromagnetism, antiferromagnetism, possibly charge density waves have been seen -superconductors, heavy fermions and spinons-holons would pose a problem.Stephan Berko (1924-1991) was interested in these problems and knew that better machines and better detectors would open new possibilities.


2017 ◽  
Vol 529 (7) ◽  
pp. 1600356 ◽  
Author(s):  
Soumya Bera ◽  
Thomas Martynec ◽  
Henning Schomerus ◽  
Fabian Heidrich-Meisner ◽  
Jens H. Bardarson

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1002
Author(s):  
José J. Gil

The information contained in an n-dimensional (nD) density matrix ρ is parametrized and interpreted in terms of its asymmetry properties through the introduction of a family of components of purity that are invariant with respect to arbitrary rotations of the nD Cartesian reference frame and that are composed of two categories of meaningful parameters of different physical nature: the indices of population asymmetry and the intrinsic coherences. It is found that the components of purity coincide, up to respective simple coefficients, with the intrinsic Stokes parameters, which are also introduced in this work, and that determine two complementary sources of purity, namely the population asymmetry and the correlation asymmetry, whose weighted square average equals the overall degree of purity of ρ. A discriminating decomposition of ρ as a convex sum of three density matrices, viz. the pure, the fully random (maximally mixed) and the discriminating component, is introduced, which allows for the definition of the degree of nonregularity of ρ as the distance from ρ to a density matrix of a system composed of a pure component and a set of 2D, 3D,… and nD maximally mixed components. The chiral properties of a state ρ are analyzed and characterized from its intimate link to the degree of correlation asymmetry. The results presented constitute a generalization to nD systems of those established and exploited for polarization density matrices in a series of previous works.


Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 434
Author(s):  
F. Hadi Madjid ◽  
John M. Myers

Entangled states of light exhibit measurable correlations between light detections at separated locations. These correlations are exploited in entangled-state quantum key distribution. To do so involves setting up and maintaining a rhythm of communication among clocks at separated locations. Here, we try to disentangle our thinking about clocks as used in actual experiments from theories of time, such as special relativity or general relativity, which already differ between each other. Special relativity intertwines the concept of time with a particular definition of the synchronization of clocks, which precludes synchronizing every clock to every other clock. General relativity imposes additional barriers to synchronization, barriers that invite seeking an alternative depending on any global concept of time. To this end, we focus on how clocks are actually used in some experimental situations. We show how working with clocks without worrying about time makes it possible to generalize some designs for quantum key distribution and also clarifies the need for alternatives to the special-relativistic definition of synchronization.


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