负值量子条件熵与双量子系统一类混合态纠缠量度

运用负值量子条件熵研究了双量子系统一类混合态的纠缠量度.给出了负值量子条件作为条件熵纠缠度的定义，证明了条件熵纠缠满足作为2×2系统一类混合纠缠态量度的四个基本条件.当双量子系统处于纯态时，条件熵纠缠度即为部分熵纠缠度.应用条件熵纠缠度研究了真空腔场中两全同二能级原子之间纯态和一类混合态纠缠的时间演化，比较了相同条件下两全同原子系统concurrence纠缠度的时间演化.结果表明，两纠缠度演化规律完全一致，验证了负值量子条件熵可以作为双量子系统纯态和一类混合态的纠缠量度. 关键词： 双量子系统 负值量子条件熵 条件熵纠缠度 混合态纠缠度     

Map for Simultaneous Measurements for a Quantum Logic

In this paper we will study a function of simultaneous measurements for quantum events (s-map) which will be compared with the conditional states on an orthomodular lattice as a basic structure for quantum logic. We will show the connection between s-map and a conditional state. On the basis of the Rényi approach to the conditioning, conditional states, and the independence of events with respect to a state are discussed. Observe that their relation of independence of events is not more symmetric contrary to the standard probabilistic case. Some illustrative examples are included.     

量子条件振幅算子性质的研究

分析量子条件振幅算子的性质，该算子起一个类似于在经典信息理论中的条件概率的作用.论证表示一个量子双组元系统的条件算子的频谱在局域幺正变换下是不变的，并且表明它的不可分性.证明一个可分态的条件振幅算子不能有一个超过1的本征值.得出一个在von Neumann条件熵的非负性基础上的相关的可分性条件. 关键词： 条件概率 条件振幅算子 von Neumann条件熵 可分性条件     

Conditional entropy in algebraic statistical physics

The notion of conditional entropy as entropy of conditional state on C^*-algebra with respect to its C^*-subalgebra ₁ is introduced. It is proved that for a compatible state σ on (which admits the conditional expectation of Umegaki-Takesaki) the mean conditional entropy in an a priori state σ₁ on ₁ is equal to the difference of the entropy of the state σ on and the entropy of the state σ₁ on ₁. The conditional entropy enables us to define the input-output information of a quantum communication channel in analogy to the classical Shannon formula.     

Remarks on Concrete Orthomodular Lattices

An orthomodular lattice (OML) is called concrete if it is isomorphic to a collection of subsets of a set with partial ordering given by set inclusion, orthocomplementation given by set complementation, and finite orthogonal joins given by disjoint unions. Interesting examples of concrete OMLs are obtained by applying Kalmbach's construction K(L) to an arbitrary bounded lattice L. This note provides several results regarding Kalmbach's construction, concrete OMLs, and the relationship between the notions. First, we provide order-theoretic and categorical characterizations of the OML K(L) in terms of the bounded lattice L. Second, we provide an identity satisfied by each OML K(L), but not valid in every concrete OML. This shows that the class of OMLs of the form K(L) do not generate the variety of all concrete OMLs. Finally, we show that every concrete OML can be embedded into a concrete OML in which every element is a join of two or fewer atoms.     

Spectral Automorphisms in Quantum Logics

In quantum mechanics, the Hilbert space formalism might be physically justified in terms of some axioms based on the orthomodular lattice (OML) mathematical structure (Piron in Foundations of Quantum Physics, Benjamin, Reading, 1976). We intend to investigate the extent to which some fundamental physical facts can be described in the more general framework of OMLs, without the support of Hilbert space-specific tools. We consider the study of lattice automorphisms properties as a “substitute” for Hilbert space techniques in investigating the spectral properties of observables. This is why we introduce the notion of spectral automorphism of an OML. Properties of spectral automorphisms and of their spectra are studied. We prove that the presence of nontrivial spectral automorphisms allow us to distinguish between classical and nonclassical theories. We also prove, for finite dimensional OMLs, that for every spectral automorphism there is a basis of invariant atoms. This is an analogue of the spectral theorem for unitary operators having purely point spectrum.     

Unitary bounds and controllability of quantum evolution in NMR spectroscopy

The effect of restricted control of unitary quantum evolution is investigated with specific attention to NMR spectroscopy. It is demonstrated that in cases where the Hamiltonian through commutation fails to span the entire Lie algebra su(n) for an n-level quantum system, the maximum transfer efficiency may be reduced significantly relative to previously known unitary bounds on spin dynamics. The paper describes methods to determine the degree of controllability and the conditional unitary bounds induced by restricted control. These features are exemplified in relation to heteronuclear coherence transfer by planar and isotropic mixing in liquid state NMR.     

Quantum State Merging and Negative Information

We consider a quantum state shared between many distant locations, and define a quantum information processing primitive, state merging, that optimally merges the state into one location. As announced in [Horodecki, Oppenheim, Winter, Nature 436, 673 (2005)], the optimal entanglement cost of this task is the conditional entropy if classical communication is free. Since this quantity can be negative, and the state merging rate measures partial quantum information, we find that quantum information can be negative. The classical communication rate also has a minimum rate: a certain quantum mutual information. State merging enabled one to solve a number of open problems: distributed quantum data compression, quantum coding with side information at the decoder and sender, multi-party entanglement of assistance, and the capacity of the quantum multiple access channel. It also provides an operational proof of strong subadditivity. Here, we give precise definitions and prove these results rigorously.     

On the Orthocomplementation of State–Property–Systems of Contextual Systems

We adopt an operational approach to quantum mechanics in which a physical system is defined by the mathematical structure of its set of states and properties. We present a model in which the maximal change of state of the system due to interaction with the measurement context is controlled by a parameter which corresponds with the number N of possible outcomes in an experiment. In the case N=2 the system reduces to a model for the spin measurements on a quantum spin-1/2 particle. In the limit N→∞ the system is classical, i.e. the experiments are deterministic and its set of properties is a Boolean lattice. For intermediate situations the change of state due to measurement is neither ‘maximal’ (i.e. quantum) nor ‘zero’ (i.e. classical). We show that two of the axioms used in Piron’s representation theorem for quantum mechanics are violated, namely the covering law and weak modularity. Next, we discuss a modified version of the model for which it is even impossible to define an orthocomplementation on the set of properties. Another interesting feature for the intermediate situations of this model is that the probability of a state transition in general not only depends on the two states involved, but also on the measurement context which induces the state transition.     

Stability and equilibrium states

For an infinite dynamical quantum system idealized as aC*-algebra acted upon by time-translations automorphisms in an asymptotically abelian way, we propose to characterize equilibrium states by the three properties of stationarity, stability for local perturbations of the dynamics, and relative purity. We show that a state with these properties either gives rise to a one-sided energy spectrum or is a KMS- (i.e. essentially a limit Gibbs-) state.     

Growing Classical and Quantum Entropies in the Early Universe

Following the idea that the global and local arrow of time has a cosmological origin, we define an entropy in the classical and in the quantum periods of the universe evolution. For the quantum period a semi-classical approach is adopted, modelling the universe with Wheeler-De Witt equation and using WKB. By applying the self-induced decoherence to the state of the universe it is proved that the quantum universe becomes a classical one. This allows us to define a conditional entropy which, in our simplified model, is proportional to e ^{2γ t} where γ is the dumping factor associated with the interaction potential of the scalar fields. Finally we find both Gibbs and thermodynamical entropy of the universe based in the conditional entropy.     

Generation of a displaced qubit and entangled displaced photon state via conditional measurement and their properties

We study optical schemes for generating both a displaced photon and a displaced qubit via conditional measurement. Combining one mode prepared in different microscopic states (one-mode qubit, single photon, vacuum state) and another mode in macroscopic states (coherent state, single photon added coherent state), a conditional state in the other output mode exhibits properties of a superposition of the displaced vacuum and a single photon. We propose to use the displaced qubit and entangled states composed of the displaced photon as components for quantum information processing. Basic states of such a qubit are distinguishable from each other with high fidelity. We show that the qubit reveals both microscopic and macroscopic properties. Entangled displaced states with a coherent phase as an additional degree of freedom are introduced. We show that additional degree of freedom enables to implement complete Bell state measurement of the entangled displaced photon states.     

The Quantum Harmonic Oscillator in the ESR Model

The ESR model proposes a new theoretical perspective which incorporates the mathematical formalism of standard (Hilbert space) quantum mechanics (QM) in a noncontextual framework, reinterpreting quantum probabilities as conditional on detection instead of absolute. We have provided in some previous papers mathematical representations of the physical entities introduced by the ESR model, namely observables, properties, pure states, proper and improper mixtures, together with rules for calculating conditional and overall probabilities, and for describing transformations of states induced by measurements. We study in this paper the relevant physical case of the quantum harmonic oscillator in our mathematical formalism. We reinterpret the standard quantum rules for probabilities, provide new expressions for absolute probabilities, and show how the standard state transformations must be modified according to the ESR model.     

Optical matching layer structures in evanescent coupling photodiodes at a wavelength of 1.55μm： physics,design and simulation

We have studied the optical matching layers (OMLs) and external quantum efficiency in the evanescent coupling photodiodes (ECPDs) integrating a diluted waveguide as a fibre-to-waveguide coupler, by using the semi-vectorial beam propagation method (BPM). The physical basis of OML has been identified, thereby a general designing rule of OML is developed in such a kind of photodiode. In addition, the external quantum efficiency and the polarization sensitivity versus the absorption and coupling length are analysed. With an optical matching layer, the absorption medium with a length of 30μm could absorb 90% of the incident light at 1.55μm wavelength, thus the total absorption increases more than 7 times over that of the photodiode without any optical matching layer.     

Quantum melting of mesoscopic clusters

The phase diagram of a two-dimensional mesoscopic system of charges or dipoles, whose realizations could be electrons in a semiconductor quantum dot or indirect excitons in a system of two vertically coupled quantum dots, is investigated. Quantum calculations using ab initio Monte Carlo integration along trajectories determine the properties of such objects in the temperature-quantum de-Boer-parameter plane. At zero (sufficiently low) temperature, as the quantum fluctuations of the particles increase, two types of quantum disordering phenomena occur with increasing quantum de Boer parameter q: first, for q∼10⁻⁵ the systems transform into a radially ordered but orientationally disordered state wherein various shells of the “atom” rotate relative to one another. For much larger q∼0.1, a transition occurs to a disordered state (a superfluid in the case of a system of bosons). Fiz. Tverd. Tela (St. Petersburg) 41, 1856–1862 (October 1999)     

Conditional Entropy and the Rokhlin Metric on an Orthomodular Lattice with Bayessian State

The present paper deals with the study of conditional entropy and its properties in a quantum space (L,s), where L is an orthomodular lattice and s is a Bayessian state on L. First, we obtained a pseudo-metric on the family of all partitions of the couple (B,s), where B is a Boolean algebra and s is a state on B. This pseudo-metric turns out to be a metric (called the Rokhlin metric) by using a new notion of s-refinement and by identifying those partitions of (B,s) which are s-equivalent. The present theory has then been extended to the quantum space (L,s), where L is an orthomodular lattice and s is a Bayessian state on L. Applying the theory of commutators and Bell inequalities, it is shown that the couple (L,s) can be equivalently replaced by a couple (B,s ₀), where B is a Boolean algebra and s ₀ is a state on B.     

Local anharmonic vibrations strong correlations and superconductivity: A quantum simulation study

We investigate the importance of local anharmonic vibrations of the bridging oxygen in the copper oxide high-T _c materials in the context of superconductivity. For the numerical simulation we employ the projector quantum Monte Carlo method to study the ground state properties of the coupled electron-phonon system. The quantum Monte Carlo simulation allows an accurate treatment of electronic interactions which investigates the influence of strong correlations on superconductivity mediated by additional quantum degrees of freedom. As a generic model for such a system, we study the two-dimensional single band Hubbard model coupled to local pseudo spins (bridging oxygen), which mediate an effective attractive electron-electron interaction leading to superconductivity. The results are compared to those of an effective negativeU model.     

Realization of Quantum Maxwell's Demon with Solid-State Spins

We report experimental realization of a quantum version of Maxwell's demon using solid state spins where the information acquiring and feedback operations by the demon are achieved through conditional quantum gates.A unique feature of this implementation is that the demon can start in a quantum superposition state or in an entangled state with an ancilla observer. Through quantum state tomography, we measure the entropy in the system, demon, and the ancilla, showing the influence of coherence and entanglement on the result. A quantum implementation of Maxwell's demon adds more controllability to this paradoxical thermal machine and may find applications in quantum thermodynamics involving microscopic systems.     

基于交叉相位调制制备四光子偏振纠缠态及其在隐形传态上的运用

利用克尔介质、偏振分束器、半波片和对强相干探测场的零拍探测,呈现了一个关于制备四光子偏振Diche态、GHZ态和W态的方案,当前量子光学实验技术条件均能有效满足该方案的要求.强的探测模相继和多个信号模光子相互作用,每次对于探测模而言,都会产生一个相位旋转.接下来,对探测模利用零拍探测,信号模可以投影得到想要的光子偏振纠缠态.此外,为了展现所制备的纠缠态作为重要的量子信息资源的价值,基于交叉相位调制进一步提出了一个隐形传送三光子偏振纠缠态的实验方案.