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arXiv2007

Quantify Entanglement for Multipartite Quantum States

In this paper, we consider the problem of how to quantify entanglement for any multipartite quantum states. For bipartite pure states partial entropy is a good entanglement measure. By using partial entropy, we firstly introduce the Combinatorial Entropy of Fully entangled states (CEF) which can be used to quantify entanglement for any fully entangled pure states. In order to quantify entanglement for any multipartite states we also need another concept the Entanglement Combination (EC) which can be used to completely describe the entanglement between any parties of the given quantum states. Combining CEF with EC, we define the Combinatorial Entropy (CE) for any multipartite pure states and present some nice properties which indicate CE is a good entanglement measure. Finally, we point out the feasibility of extending these three concepts to mixed quantum states.

quant-ph↗
arXiv2008

Quantum Markovian Subsystems: Invariance, Attractivity, and Control

We characterize the dynamical behavior of continuous-time, Markovian quantum systems with respect to a subsystem of interest. Markovian dynamics describes a wide class of open quantum systems of relevance to quantum information processing, subsystem encodings offering a general pathway to faithfully represent quantum information. We provide explicit linear-algebraic characterizations of the notion of invariant and noiseless subsystem for Markovian master equations, under different robustness assumptions for model-parameter and initial-state variations. The stronger concept of an attractive quantum subsystem is introduced, and sufficient existence conditions are identified based on Lyapunov's stability techniques. As a main control application, we address the potential of output-feedback Markovian control strategies for quantum pure state-stabilization and noiseless-subspace generation. In particular, explicit results for the synthesis of stabilizing semigroups and noiseless subspaces in finite-dimensional Markovian systems are obtained.

quant-ph↗
arXiv2007

Non-Computability of Consciousness

With the great success in simulating many intelligent behaviors using computing devices, there has been an ongoing debate whether all conscious activities are computational processes. In this paper, the answer to this question is shown to be no. A certain phenomenon of consciousness is demonstrated to be fully represented as a computational process using a quantum computer. Based on the computability criterion discussed with Turing machines, the model constructed is shown to necessarily involve a non-computable element. The concept that this is solely a quantum effect and does not work for a classical case is also discussed.

quant-ph↗
arXiv2008

The Resolvent Algebra: A New Approach to Canonical Quantum Systems

The standard C*-algebraic version of the algebra of canonical commutation relations, the Weyl algebra, frequently causes difficulties in applications since it neither admits the formulation of physically interesting dynamical laws nor does it incorporate pertinent physical observables such as (bounded functions of) the Hamiltonian. Here a novel C*-algebra of the canonical commutation relations is presented which does not suffer from such problems. It is based on the resolvents of the canonical operators and their algebraic relations. The resulting C*-algebra, the resolvent algebra, is shown to have many desirable analytic properties and the regularity structure of its representations is surprisingly simple. Moreover, the resolvent algebra is a convenient framework for applications to interacting and to constrained quantum systems, as we demonstrate by several examples.

math.OA↗
arXiv2007

Some geometric features of Berry's phase

In this letter, we elaborate on the identification and construction of the differential geometric elements underlying Berry's phase. Berry bundles are built generally from the physical data of the quantum system under study. We apply this construction to typical and recently investigated systems presenting Berry's phase to explore their geometric features.

math-ph↗
arXiv2009

Non-Markovian decoherence dynamics of entangled coherent states

We microscopically model the decoherence dynamics of entangled coherent states under the influence of vacuum fluctuation. We derive an exact master equation with time-dependent coefficients reflecting the memory effect of the environment, by using the Feynman-Vernon influence functional theory in the coherent-state representation. Under the Markovian approximation, our master equation recovers the widely used Lindblad equation in quantum optics. We then investigate the non-Markovian entanglement dynamics of the quantum channel in terms of the entangled coherent states under noise. Compared with the results in Markovian limit, it shows that the non-Markovian effect enhances the disentanglement to the initially entangled coherent state. Our analysis also shows that the decoherence behaviors of the entangled coherent states depend sensitively on the symmetrical properties of the entangled coherent states as well as the interactions between the system and the environment.

quant-ph↗
arXiv2007

The tripartite separability of density matrices of graphs

The density matrix of a graph is the combinatorial laplacian matrix of a graph normalized to have unit trace. In this paper we generalize the entanglement properties of mixed density matrices from combinatorial laplacian matrices of graphs discussed in Braunstein {\it et al.} Annals of Combinatorics, {\bf 10}(2006)291 to tripartite states. Then we proved that the degree condition defined in Braunstein {\it et al.} Phys. Rev. A {\bf 73}, (2006)012320 is sufficient and necessary for the tripartite separability of the density matrix of a nearest point graph.

quant-ph↗
arXiv2007

Quantum protocols for transference of proof of zero-knowledge systems

Zero-knowledge proof system is an important protocol that can be used as a basic block for construction of other more complex cryptographic protocols. An intrinsic characteristic of a zero-knowledge systems is the assumption that is impossible for the verifier to show to a third part that he has interacted with the prover. However, it has been shown that using quantum correlations the impossibility of transferring proofs can be successfully attacked. In this work we show two new protocols for proof transference, being the first one based on teleportation and the second one without using entangled states.

quant-ph↗
arXiv2009

Multiparty-controlled teleportation of an arbitrary m-qudit state with pure entangled quantum channel

We present a general scheme for multiparty-controlled teleportation of an arbitrary m-qudit ($d$-dimensional quantum system) state by using non-maximally entangled states as the quantum channel. The sender performs m generalized Bell-state measurements on her 2$m$ particles, the controllers take some single-particle measurements with the measuring basis $X_{d}$ and the receiver only need to introduce one auxiliary two-level particle to extract quantum information probabilistically with the fidelity unit if he cooperates with all the controllers. All the parties can use some decoy photons to set up their quantum channel securely, which will forbid some a dishonest party to eavesdrop freely. This scheme is optimal as the probability that the receiver obtains the originally unknown m-qudit state equals to the entanglement of the quantum channel.

quant-ph↗
arXiv2008

Realism violates quantum mechanics

Recently, [{arXiv:0810.3134}] is accepted and published. We show that local realistic theories violate separability of $N$-qubit quantum states by a factor of $3^N$. Thus we have a violation factor of 3 when N=1. Realistic theories violate a proposition of a single qubit (a state with two-dimensional space) system, the Bloch sphere machinery of quantum mechanics. Our method uses the ratio of each of the scalar products. The maximal possible value of the scalar product in local realistic theories grows exponentially larger than one in $N$-qubit separable states when the number of qubits increases. We find the violation factor $3^N$ when the measurement setup is entire range of settings for each of the local observers.

quant-ph↗
arXiv2007

Origin of which-way information and generalization of the Born rule

The possibility to recover the which-way information, for example in the two slit experiment, is based on a natural but implicit assumption about the position of a particle {\it before} a position measurement is performed on it. This assumption cannot be deduced from the standard postulates of quantum mechanics. In the present paper this assumption is made explicit and formally postulated as a new rule, the {\it quantum typicality rule}. This rule correlates the positions of the particles at two different times, thus defining their trajectories. Unexpectedly, this rule is also equivalent to the Born rule with regard to the explanation of the results of statistical experiments. For this reason it can be considered a generalization of the Born rule. The existence of the quantum typicality rule strongly suggests the possibility of a new trajectory-based formulation of quantum mechanics. According to this new formulation, a closed quantum system is represented as a {\it quantum process}, which corresponds to a canonical stochastic process in which the probability measure is replaced by the wave function and the usual frequentist interpretation of probability is replaced by the quantum typicality rule.

quant-ph↗
arXiv2007

Absolute Calibration of Analog Detectors by using Parametric Down Conversion

In this paper we report our systematic study of a promising absolute calibration technique of analog photo-detectors, based on the properties of parametric down conversion. Our formal results and a preliminary uncertainty analysis show that the proposed method can be effectively developed with interesting applications to metrology.

quant-ph↗
arXiv2008

Entanglement and separability of quantum harmonic oscillator systems at finite temperature

In the present paper we study the entanglement properties of thermal (a.k.a. Gibbs) states of quantum harmonic oscillator systems as functions of the Hamiltonian and the temperature. We prove the physical intuition that at sufficiently high temperatures the thermal state becomes fully separable and we deduce bounds on the critical temperature at which this happens. We show that the bound becomes tight for a wide class of Hamiltonians with sufficient translation symmetry. We find, that at the crossover the thermal energy is of the order of the energy of the strongest normal mode of the system and quantify the degree of entanglement below the critical temperature. Finally, we discuss the example of a ring topology in detail and compare our results with previous work in an entanglement-phase diagram.

quant-ph↗
arXiv2007

Halting in quantum Turing computation

The paper considers the halting scheme for quantum Turing machines. The scheme originally proposed by Deutsch appears to be correct, but not exactly as originally intended. We discuss the result of Ozawa as well as the objections raised by Myers, Kieu and Danos and others. Finally, the relationship of the halting scheme to the quest for a universal quantum Turing machine is considered.

quant-ph↗
arXiv2007

Non-Positive Semigroup Dynamics in Continuous Variable Models

Non-positive, Markovian semigroups are sometimes used to describe the time evolution of subsystems immersed in an external environment. A widely adopted prescription to avoid the appearance of negative probabilities is to eliminate from the admissible initial conditions those density matrices that would not remain positive by the action of the semigroup dynamics. Using a continuous variable model, we show that this procedure leads to physical inconsistencies when two subsystems are considered and their initial state is entangled.

quant-ph↗
arXiv2009

Nonclassicality in phase space and nonclassical correlation

Continuous variable entanglement is a manifestation of nonclassicality of quantum states. In this paper we attempt to analyze whether and under which conditions nonclassicality can be used as an entanglement criterion. We adopt the well-accepted definition of nonclassicality in the form of lack of well-defined positive Glauber Sudarshan P-function describing the state. After demonstrating that the classicality of subsystems is not sufficient for the nonclassicality of the overall state to be identifiable with entanglement, we focus on Gaussian states and find specific local unitary transformations required to arrive at this equivalency. This is followed by the analysis of quantitative relation between nonclassicality and entanglement.

quant-ph↗