Quantum phase transition,quantum fidelity and fidelity susceptibility in the Yang–Baxter system

In this paper, we investigate the ground-state fidelity and fidelity susceptibility in the many-body Yang–Baxter system and analyze their connections with quantum phase transition. The Yang–Baxter system was perturbed by a twist of \( e^{i\varphi } \) at each bond, where the parameter \( \varphi \) originates from the q-deformation of the braiding operator U with \(q = e^{-i\varphi }\) (Jimbo in Yang–Baxter equations in integrable systems, World Scientific, Singapore, 1990), and \( \varphi \) has a physical significance of magnetic flux (Badurek et al. in Phys. Rev. D 14:1177, 1976). We test the ground-state fidelity related by a small parameter variation \(\varphi \) which is a different term from the one used for driving the system toward a quantum phase transition. It shows that ground-state fidelity develops a sharp drop at the transition. The drop gets sharper as system size N increases. It has been verified that a sufficiently small value of \(\varphi \) used has no effect on the location of the critical point, but affects the value of \( F(g_{c},\varphi ) \). The smaller the twist \(\varphi \), the more the value of \( F(g_{c},\varphi ) \) is close to 0. In order to avoid the effect of the finite value of \( \varphi \), we also calculate the fidelity susceptibility. Our results demonstrate that in the Yang–Baxter system, the quantum phase transition can be well characterized by the ground-state fidelity and fidelity susceptibility in a special way.     

Yang–Baxter equations and quantum entanglements

In this paper some results associated with a new type of Yang–Baxter equation (YBE) are reviewed. The braiding matrix of Kauffman–Lomonaco has been extended to the solution (called type-II) of Yang–Baxter equation (YBE) and the related chain Hamiltonian is given. The Lorentz additivity for spectral parameters is found, rather than the Galilean rule for the familiar solutions (called type-I) of YBE associated with the usually exact solvable models. Based on the topological basis, the N-dimensional solution of YBE is found to be the Wigner D-functions. The explicit examples for spin-\(\frac{1}{2}\) and spin-1 have been shown. The extremes of \(\ell _1\)-norm of \(D\)-functions are introduced to distinguish the type-I from type-II of braiding matrices that also correspond to those of von Neumann entropy for quantum information.     

Quantum teleportation and Birman–Murakami–Wenzl algebra

In this paper, we investigate the relationship of quantum teleportation in quantum information science and the Birman–Murakami–Wenzl (BMW) algebra in low-dimensional topology. For simplicity, we focus on the two spin-1/2 representation of the BMW algebra, which is generated by both the Temperley–Lieb projector and the Yang–Baxter gate. We describe quantum teleportation using the Temperley–Lieb projector and the Yang–Baxter gate, respectively, and study teleportation-based quantum computation using the Yang–Baxter gate. On the other hand, we exploit the extended Temperley–Lieb diagrammatical approach to clearly show that the tangle relations of the BMW algebra have a natural interpretation of quantum teleportation. Inspired by this interpretation, we construct a general representation of the tangle relations of the BMW algebra and obtain interesting representations of the BMW algebra. Therefore, our research sheds a light on a link between quantum information science and low-dimensional topology.     

Quantum Arthur–Merlin games

This paper studies quantum Arthur–Merlin games, which are Arthur–Merlin games in which Arthur and Merlin can perform quantum computations and Merlin can send Arthur quantum information. As in the classical case, messages from Arthur to Merlin are restricted to be strings of uniformly generated random bits. It is proved that for one-message quantum Arthur–Merlin games, which correspond to the complexity class QMA, completeness and soundness errors can be reduced exponentially without increasing the length of Merlins message. Previous constructions for reducing error required a polynomial increase in the length of Merlins message. Applications of this fact include a proof that logarithmic length quantum certificates yield no increase in power over BQP and a simple proof that Other facts that are proved include the equivalence of three (or more) message quantum Arthur–Merlin games with ordinary quantum interactive proof systems and some basic properties concerning two-message quantum Arthur–Merlin games.     

Quantum steering and entanglement in three-mode triangle Bose–Hubbard system

We consider the possibility of generation steerable states in Bose–Hubbard system composed of three interacting wells in the form of a triangle. We show that although our system still fulfills the monogamy relations, the presence of additional coupling which transforms a chain of wells onto triangle gives a variety of new possibilities for the generation of steerable quantum states. Deriving analytical formulas for the parameters describing steering and bipartite entanglement, we show that interplay between two couplings influences quantum correlations of various types. We compare the time evolution of steering parameters to those describing bipartite entanglement and find the relations between the appearance of maximal entanglement and disappearance of steering effect.     

Classical and Quantum Complexity of the Sturm–Liouville Eigenvalue Problem

We study the approximation of the smallest eigenvalue of a Sturm–Liouville problem in the classical and quantum settings. We consider a univariate Sturm–Liouville eigenvalue problem with a nonnegative function q from the class C² ([0,1]) and study the minimal number n() of function evaluations or queries that are necessary to compute an -approximation of the smallest eigenvalue. We prove that n()=(^–1/2) in the (deterministic) worst case setting, and n()=(^–2/5) in the randomized setting. The quantum setting offers a polynomial speedup with bit queries and an exponential speedup with power queries. Bit queries are similar to the oracle calls used in Grovers algorithm appropriately extended to real valued functions. Power queries are used for a number of problems including phase estimation. They are obtained by considering the propagator of the discretized system at a number of different time moments. They allow us to use powers of the unitary matrix exp((1/2) iM), where M is an n× n matrix obtained from the standard discretization of the Sturm–Liouville differential operator. The quantum implementation of power queries by a number of elementary quantum gates that is polylog in n is an open issue. In particular, we show how to compute an -approximation with probability (3/4) using n()=(^–1/3) bit queries. For power queries, we use the phase estimation algorithm as a basic tool and present the algorithm that solves the problem using n()=(log ^–1) power queries, log ^2–1 quantum operations, and (3/2) log ^–1 quantum bits. We also prove that the minimal number of qubits needed for this problem (regardless of the kind of queries used) is at least roughly (1/2) log ^–1. The lower bound on the number of quantum queries is proven in Bessen (in preparation). We derive a formula that relates the Sturm–Liouville eigenvalue problem to a weighted integration problem. Many computational problems may be recast as this weighted integration problem, which allows us to solve them with a polylog number of power queries. Examples include Grovers search, the approximation of the Boolean mean, NP-complete problems, and many multivariate integration problems. In this paper we only provide the relationship formula. The implications are covered in a forthcoming paper (in preparation).PACS: 03.67.Lx, 02.60.-x.     

Universal access in the information Society (2001–2021): knowledge,experience, challenges and new perspectives

Universal Access in the Information Society -     

Quantum speed limits—primer,perspectives, and potential future directions

Fundamental physical limits on the speed of state evolution in quantum systems exist in the form of the Mandelstam–Tamm and the Margolus–Levitin inequalities. We give an expository review of the development of these quantum speed limit (QSL) inequalities, including extensions to different energy statistics and generalizations to mixed system states and open and multipartite systems. The QSLs expressed by these various inequalities have implications for quantum computation, quantum metrology, and control of quantum systems. These connections are surveyed, and some important open questions are noted.     

Quantum measurement and the Aharonov–Bohm effect with superposed magnetic fluxes

We consider the magnetic flux in a quantum mechanical superposition of two values and find that the Aharonov–Bohm effect interference pattern contains information about the nature of the superposition, allowing information about the state of the flux to be extracted without disturbance. The information is obtained without transfer of energy or momentum and by accumulated nonlocal interactions of the vector potential $\varvec{A}$ with many charged particles forming the interference pattern, rather than with a single particle. We suggest an experimental test using already experimentally realized superposed currents in a superconducting ring and discuss broader implications.     

Entanglement and Berry phase in a 9 × 9 Yang–Baxter system

A M-matrix which satisfies the Hecke algebraic relations is presented. Via the Yang–Baxterization approach, we obtain a unitary solution \breveR(q,j₁,j₂){\breve{R}(\theta,\varphi_{1},\varphi_{2})} of Yang–Baxter equation. It is shown that any pure two-qutrit entangled states can be generated via the universal \breveR{\breve{R}}-matrix assisted by local unitary transformations. A Hamiltonian is constructed from the \breveR{\breve{R}}-matrix, and Berry phase of the Yang–Baxter system is investigated. Specifically, for j₁ = j₂{\varphi_{1}\,{=}\,\varphi_{2}}, the Hamiltonian can be represented based on three sets of SU(2) operators, and three oscillator Hamiltonians can be obtained. Under this framework, the Berry phase can be interpreted.     

Quantum computing and communications – Introduction and challenges

Computer engineers are continuously seeking new solutions to increase available processing speed, achievable transmission rates, and efficiency in order to satisfy users’ expectations. While multi-core systems, computing clouds, and other parallel processing techniques dominate current technology trends, elementary particles governed by quantum mechanics have been borrowed from the physicists’ laboratory and applied to computer engineering in the efforts to solve sophisticated computing and communications problems. In this paper, we review the quantum mechanical background of quantum computing from an engineering point of view and describe the possibilities offered by quantum-assisted and quantum-based computing and communications. In addition to the currently available solutions, the corresponding challenges will also be surveyed.     

Quantum holonomies for displaced Landau–Aharonov–Casher states

We construct displaced Fock states for a Landau–Aharonov–Casher system for neutral particles. Abelian and non-Abelian geometric phases can be obtained in an adiabatic cyclic evolution using this displaced states. Moreover, we show that a possible logical base related to the angular momenta of the neutral particle with permanent magnetic dipole moment can be defined, and then quantum holonomies for specific paths can be built and used to implement one-qubit quantum gates.     

Colored Simultaneous Geometric Embeddings and?Universal Pointsets

Universal pointsets can be used for visualizing multiple relationships on the same set of objects or for visualizing dynamic graph processes. In simultaneous geometric embeddings, the same point in the plane is used to represent the same object as a way to preserve the viewer??s mental map. In colored simultaneous embeddings this restriction is relaxed, by allowing a given object to map to a subset of points in the plane. Specifically, consider a set of graphs on the same set of n vertices partitioned into k colors. Finding a corresponding set of k-colored points in the plane such that each vertex is mapped to a point of the same color so as to allow a straight-line plane drawing of each graph is the problem of colored simultaneous geometric embedding. For n-vertex paths, we show that there exist universal pointsets of size n, colored with two or three colors. We use this result to construct colored simultaneous geometric embeddings for a 2-colored tree together with any number of 2-colored paths, and more generally, a?2-colored outerplanar graph together with any number of 2-colored paths. For n-vertex trees, we construct small near-universal pointsets for 3-colored caterpillars of size n, 3-colored radius-2 stars of size n+3, and 2-colored spiders of size n. For n-vertex outerplanar graphs, we show that these same universal pointsets also suffice for 3-colored K ₃-caterpillars, 3-colored K ₃-stars, and 2-colored fans, respectively. We also present several negative results, showing that there exist a 2-colored planar graph and pseudo-forest, three 3-colored outerplanar graphs, four 4-colored pseudo-forests, three 5-colored pseudo-forests, five 5-colored paths, two 6-colored biconnected outerplanar graphs, three 6-colored cycles, four 6-colored paths, and three 9-colored paths that cannot be simultaneously embedded.     

Quantum correlations and decoherence dynamics for a qutrit–qutrit system under random telegraph noise

We analyze the effect of a classical random telegraph noise on the dynamics of quantum correlations and decoherence between two non-interacting spin-qutrit particles, initially entangled, and coupled either to independent sources or to a common source of noise. Both Markovian and non-Markovian environments are considered. For the Markov regime, as the noise switching rate decreases, a monotonic decay of the initial quantum correlations is found and the loss of coherence increases monotonically with time up to the saturation value. For the non-Markov regime, evident oscillations of correlations and decoherence are observed due to the noise regime, but correlations, however, avoid sudden death phenomena. The oscillatory behavior is more and more prominent as the noise switching rate decreases in this regime, thus enhancing robustness of correlations. Similarly to the qubits case, independent environments coupling is more effective than a common environment coupling in preserving quantum correlations and coherence of the system for a Markovian noise; meanwhile, the opposite is found for the non-Markovian one.     

Critical thermodynamic evaluation and optimization of the Pb–Pr,Pb–Nd,Pb–Tb and Pb–Dy systems

All available experimental data on phase equilibria and thermodynamic properties of the Pb–Pr, Pb–Nd, Pb–Tb and Pb–Dy binary systems were reviewed and critically examined. A thermodynamic optimization of these systems is presented for the first time. A set of optimized model parameters for all solid stoichiometric compounds, terminal solid solutions and liquid phase was built to reproduce all available reliable thermodynamic properties and phase diagram data within experimental error limits. The Modified Quasichemical Model in the pair approximation was used to describe the thermodynamic properties of the liquid solution accurately. In view of the limited experimental phase diagram and thermodynamic data available for these systems, trends in the rare earth-lead and rare earth–tin systems were examined to estimate the missing information and evaluate whether the predictions are reasonable. Based on these trends, a predicted phase diagram for the Pb–Nd and Pb–Tb systems, which are not established to date, is presented.     

Critical evaluation and thermodynamic optimization of the Al–Ce,Al–Y,Al–Sc and Mg–Sc binary systems

New critical evaluations and optimizations of the Al–Ce, Al–Y, Al–Sc and Mg–Sc systems are presented. The Modified Quasichemical Model is used for the liquid phases which exhibit a high degree of short-range ordering. A number of solid solutions in the binary systems are modelled using the Compound Energy Formalism. All available and reliable experimental data such as enthalpies of mixing in liquid alloys, heats of formation of intermetallic phases, phase diagrams, etc. are reproduced within experimental error limits. It is shown that the Modified Quasichemical Model reproduces the partial enthalpy of mixing data in the liquid alloys better than the Bragg–Williams random mixing model which does not take short-range ordering into account.