On entanglement distillation and quantum error correction for unknown states and channels

We consider the problem of invariance of distillable entanglement D and quantum capacities Q under erasure of information about single copy of quantum state or channel respectively. We argue that any 2 ⊗N two-way distillable state is still two-way distillable after erasure of single copy information. For some known distillation protocols the obtained two-way distillation rate is the same as if Alice and Bob knew the state from the very beginning. The isomorphism between quantum states and quantum channels is also investigated. In particular it is pointed out that any transmission rate down the channel is equal to distillation rate with formal LOCC-like superoperator that uses in general nonphysical Alice actions. This allows to we prove that if given channel Λ has nonzero capacity (Q _→ or Q _⟺) then the corresponding quantum state ϱ(Λ) has nonzero distillable entanglement (D _→ or D _⟺). Follwoing the latter arguments are provided that any channel mapping single qubit into N level system allows for reliable two-way transmission after erasure of information about single copy. Some open problems are discussed.     

Quasi-Hopf Deformations of Quantum Groups

The search for elliptic quantum groups leads to a modified quantum Yang–Baxter relation and to a special class of quasi-triangular quasi-Hopf algebras. This Letter calculates deformations of standard quantum groups (with or without spectral parameter) in the category of quasi-Hopf algebras. An earlier investigation of the deformations of quantum groups, in the category of Hopf algebras, showed that quantum groups are generically rigid: Hopf algebra deformations exist only under some restrictions on the parameters. In particular, affine Kac–Moody algebras are more rigid than their loop algebra quotients and only the latter (in the case of sl(n)) can be deformed to elliptic Hopf algebras. The generalization to quasi-Hopf deformations lifts this restriction. The full elliptic quantum groups (with central extension) associated with sl(n) are thus quasi-Hopf algebras. The universal R-matrices satisfy a modified Yang–Baxter relation and are calculated more or less explicitly. The modified classical Yang–Baxter relation is obtained and the elliptic solutions are worked out explicitly.The same method is used to construct the Universal R-matrices associated with Felder's quantization of the Knizhnik–Zamolodchikov–Bernard equation, to throw some light on the quasi-Hopf structure of conformal field theory and (perhaps) the Calogero–Moser models.     

Sur les intégrales de mouvement du système de sinus-Gordon discret – On Integrals of Motion of the discrete sine-Gordon System

We give explicit formulas for some densities of integrals of motion for the discrete sine-Gordon system (quantum or not). The generating function for the densities of integrals of motion may be seen as the expansion of the logarithm of a certain continued fraction (possibly quantum). In the case of q root of the unity, we show that these integrals of motion can be identified to the classical integrals of motion.     

Properties of 2 × 2 h-Deformed Quantum (Super)Matrices

We investigate the h-deformed quantum (super)group of 2 × 2 matrices and use a kind of contraction procedure to prove that the n-th power of this deformed quantum (super)matrix is quantum (super)matrix with the deformation parameter nh.     

利用三粒子纠缠态建立量子隐形传态网络的探讨

利用W态纠缠源可以产生三纠缠粒子，用这些相互纠缠的粒子作为量子信道，再辅以经典信道传送Bell基联合测量信息和von Neumann测量信息，便可实现量子隐形传态网络.基于上述思想，研究了三纠缠粒子量子隐形传态网络的物理基础，得到了基于三粒子W 关键词： 量子通信 量子隐形传态 W态')" href="#">W态     

Quantum simulation of the t–J model

Computer simulation of a many-particle quantum system is bound to reach the inevitable limits of its ability as the system size increases. The primary reason for this is that the memory size used in a classical simulator grows polynomially whereas the Hilbert space of the quantum system does so exponentially. Replacing the classical simulator by a quantum simulator would be an effective method of surmounting this obstacle. The prevailing techniques for simulating quantum systems on a quantum computer have been developed for purposes of computing numerical algorithms designed to obtain approximate physical quantities of interest. The method suggested here requires no numerical algorithms; it is a direct isomorphic translation between a quantum simulator and the quantum system to be simulated. In the quantum simulator, physical parameters of the system, which are the fixed parameters of the simulated quantum system, are under the control of the experimenter. A method of simulating a model for high-temperature superconducting oxides, the t–J model, by optical control, as an example of such a quantum simulation, is presented.     

Calculating the C Operator in PT-symmetric Quantum Mechanics

It has recently been shown that a non-Hermitian Hamiltonian H possessing an unbroken PT symmetry (i) has a real spectrum that is bounded below, and (ii) defines a unitary theory of quantum mechanics with positive norm. The proof of unitarity requires a linear operator C, which was originally defined as a sum over the eigenfunctions of H. However, using this definition it is cumbersome to calculate C in quantum mechanics and impossible in quantum field theory. An alternative method is devised here for calculating C directly in terms of the operator dynamical variables of the quantum theory. This new method is general and applies to a variety of quantum mechanical systems having several degrees of freedom. More importantly, this method can be used to calculate the C operator in quantum field theory. The C operator is a new time-independent observable in PT-symmetric quantum field theory.     

Bound and Scattering States of Extended Calogero Model with an Additional PT Invariant Interaction

Here we discuss two many-particle quantum systems, which are obtained by adding some nonhermitian but PT (i.e. combined parity and time reversal) invariant interaction to the Calogero model with and without confining potential. It is shown that the energy eigenvalues are real for both of these quantum systems. For the case of extended Calogero model with confining potential, we obtain discrete bound states satisfying generalised exclusion statistics. On the other hand, the extended Calogero model without confining term gives rise to scattering states with continuous spectrum. The scattering phase shift for this case is determined through the exchange statistics parameter. We find that, unlike the case of usual Calogero model, the exclusion and exchange statistics parameters differ from each other in the presence of PT invariant interaction.     

A Study of the Efficiency of the Class of <Emphasis Type="Italic">W</Emphasis>-States as a Quantum Channel

Recently, a new class of W-states has been defined by Agarwal and Pati (Phys. Rev. A 74:062320, 2006) and it has been shown that they can be used as a quantum channel for teleportation and superdense coding. In this work, we identify those three-qubit states from the set of the new class of W-states which are most efficient or suitable for quantum teleportation. We show that with some probability is best suited for teleportation channel in the sense that it does not depend on the input state.     

Discord under the influence of a quantum phase transition

This paper studies the discord of a bipartite two-level system coupling to an XY spin-chain environment in a transverse field and investigates the relationship between the discord property and the environment’s quantum phase transition.The results show that the quantum discord is also able to characterize the quantum phase transitions.We also discuss the difference between discord and entanglement,and show that quantum discord may reveal more general information than quantum entanglement for characterizing the environment’s quantum phase transition.     

A new quantum mechanical photon counting distribution formula

By virtue of the density operator's P-representation in the coherent state representation, we derive a new quantum mechanical photon counting distribution formula. As its application, we calculate photon counting distributions for some given light fields. It is found that the pure squeezed state's photon counting distribution is related to the Legendre function, which is a new result.     

铁磁/半导体/铁磁结构的双量子环自旋输运的特性

研究了与铁磁/半导体/铁磁结构相关的双量子环自旋输运的规律,研究结果表明：总磁通为零条件下,铁磁电极磁化方向反平行时,双量子环与单量子环相比提高了自旋电子透射概率的平均值.铁磁电极磁化方向平行时,双量子环对提高自旋向下电子平均透射概率的效果更明显;双量子环受到Rashba自旋轨道耦合作用影响时,自旋电子的平均透射概率明显高于单量子环,即使再加上外加磁场的影响,透射概率较高这一特征依然存在;双量子环所含的δ势垒具有阻碍自旋电子输运的作用,随δ势垒强度Z的增大透射概率 关键词： 双量子环 Rashba自旋轨道耦合 透射概率 δ势垒')" href="#">δ势垒     

The C Operator in iϕ 3 Field Theory

The C operator defines a dynamically-determined positive-definite metric in PT-symmetric theories. We show how the operator formalism for the perturbative calculation of C can be extended from quantum mechanics to quantum field theory with a cubic self interaction.     

Quantum and classical correlations for a two-qubit X structure density matrix

We derive explicit expressions for quantum discord and classical correlation for an X structure density matrix. Based on the characteristics of the expressions, the quantum discord and the classical correlation are easily obtained and compared under different initial conditions using a novel analytical method. We explain the relationships among quantum discord, classical correlation, and entanglement, and further find that the quantum discord is not always larger than the entanglement measured by concurrence in a general two-qubit X state. The new method, which is different from previous approaches, has certain guiding significance for analysing quantum discord and classical correlation of a two-qubit X state, such as a mixed state.     

Quantum de Sitter algebra and some possible applications in cosmology

I summarize results recently obtained in collaboration with Amelino-Camelia, Bruno and Mandanici (preprint University of Rome “La Sapienza”, August, 2005) that concern an analysis of the path of a massless particle in a q-de Sitter space-time and an approximation scheme suitable for the corresponding analysis in a quantum FRW Universe. On the basis of some arguments in the quantum-gravity literature, the q deformation parameter is assumed to depend on both the Planck scale and the curvature, leading to results that are significantly different from those of other studies of Planck-scale effects in cosmology, where the possibility of an interplay between curvature and Planck scale was ignored. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Super Universality of the Quantum Hall Effect and the?“Large N Picture” of the ? Angle

It is shown that the “massless chiral edge excitations” are an integral and universal aspect of the low energy dynamics of the ϑ vacuum that has historically gone unnoticed. Within the SU(M+N)/S(U(M)×U(N)) non-linear sigma model we introduce an effective theory of “edge excitations” that fundamentally explains the quantum Hall effect. In sharp contrast to the common beliefs in the field our results indicate that this macroscopic quantization phenomenon is, in fact, a super universal strong coupling feature of the ϑ angle with the replica limit M=N=0 only playing a role of secondary importance. To demonstrate super universality we revisit the large N expansion of the CP ^N−1 model. We obtain, for the first time, explicit scaling results for the quantum Hall effect including quantum criticality of the quantum Hall plateau transition. Consequently a scaling diagram is obtained describing the cross-over between the weak coupling “instanton phase” and the strong coupling “quantum Hall phase” of the large N theory. Our results are in accordance with the “instanton picture” of the ϑ angle but fundamentally invalidate all the ideas, expectations and conjectures that are based on the historical “large N picture.”     

PT-symmetric Quantum Mechanics: A Precise and Consistent Formulation

The physical condition that the expectation values of physical observables are real quantities is used to give a precise formulation of PT-symmetric quantum mechanics. A mathematically rigorous proof is given to establish the physical equivalence of PT-symmetric and conventional quantum mechanics. The results reported in this paper apply to arbitrary PT-symmetric Hamiltonians with a real and discrete spectrum. They hold regardless of whether the boundary conditions defining the spectrum of the Hamiltonian are given on the real line or a complex contour.     

PT Symmetry in Quantum Field Theory

The Hamiltonian H specifies the energy levels and the time evolution of a quantum theory. It is an axiom of quantum mechanics that H be Hermitian. The Hermiticity of H guarantees that the energy spectrum is real and that the time evolution is unitary (probability preserving). In this talk we investigate an alternative formulation of quantum mechanics in which the mathematical requirement of Hermiticity is replaced by the more physically transparent condition of space-time reflection (PT) symmetry. We show that if the PT symmetry of a Hamiltonian H is not broken, then the spectrum of H is real. Examples of PT-symmetric non-Hermitian Hamiltonians are H=p ²+ix ³ and H=p ²-x ⁴. The crucial question is whether PT-symmetric Hamiltonians specify physically acceptable quantum theories in which the norms of states are positive and the time evolution is unitary. The answer is that a Hamiltonian that has an unbroken PT symmetry also possesses a physical symmetry that we call C. Using C, we show how to construct an inner product whose associated norm is positive definite. The result is a new class of fully consistent complex quantum theories. Observables exhibit CPT symmetry, probabilities are positive, and the dynamics is governed by unitary time evolution.