Homogenization for a Class of Generalized Langevin Equations with an Application to Thermophoresis

We study a class of systems whose dynamics are described by generalized Langevin equations with state-dependent coefficients. We find that in the limit, in which all the characteristic time scales vanish at the same rate, the position variable of the system converges to a homogenized process, described by an equation containing additional drift terms induced by the noise. The convergence results are obtained using the main result in Hottovy et al. (Commun Math Phys 336(3):1259–1283, 2015), whose version is proven here under a weaker spectral assumption on the damping matrix. We apply our results to study thermophoresis of a Brownian particle in a non-equilibrium heat bath.

     

Improvement of Gao et al.’s semi-quantum secret sharing protocol

Recently, Yin and Fu (Int. J. Theor. Phys. 55(9), 4027–4035 (2016)) pointed out that Xie et al.’s semi-quantum secret sharing (SQSS) protocol (Int. J. Theor. Phys. 54(10), 3819–3824 (2015)) suffers from the intercept-resend attack from a dishonest party, and suggested an improved protocol accordingly. Later, Gao et al. (Int. J. Theor. Phys. 56(8), 2512–2520 (2017)) pointed out that Yin and Fu’s analysis on the intercept-resend attack from a dishonest party is incorrect. Moreover, they also pointed out that Yin and Fu’s improved protocol does not satisfy the condition of semi-quantum, and proposed an improved protocol. This paper is devoted to putting forward an improved version for Gao et al.’s protocol. Compared with Gao et al.’s protocol, the improved version has higher quantum efficiency and less classical communication cost.

     

Superadiabatic Shortcuts for Fast Generating Two-Atom Four-Dimensional Entanglement

We propose a scheme for rapidly generating two-atom four-dimensional entanglement based on superadiabatic shortcuts. In the scheme, the counterdiabatic Hamiltonian has the same form as that of the effective Hamiltonian, and the scheme avoids the disadvantage of the invariants-based scheme Dong et al. (Int. J. Theor. Phys. 57, 3149–3162, 2018), so the scheme is more feasible in experiment. In addition, numerical simulation results show that the scheme is robust against decoherence and variations in various parameters, and the two atoms four-dimensional entanglement can be generated with high fidelity.

     

Cryptanalysis and Improvement of Ye et al’s Quantum Private Comparison Protocol

Recently, Ye et al. (Int. J. Theor. Phys. 56, 1517–1529, 2017) proposed a quantum private comparison (QPC) protocol based on five-qubit entanglement state. Two parties can verify that their secret information is equal or not with the help of the semi-honest third party (TP). However, in this paper we will point out the Ye et al.’s initial protocol is not safe under a special participant attack. That is a malicious participant can get the other party’s secret input information illegally under the forgery attack. Furthermore, we give two possible improvement protocols, which can perform this protocol secure against this kind of attack.

     

Two-Dimensional Anisotropic Random Walks: Fixed Versus Random Column Configurations for Transport Phenomena

We consider random walks on the square lattice of the plane along the lines of Heyde (J Stat Phys 27:721–730, 1982, Stochastic processes, Springer, New York, 1993) and den Hollander (J Stat Phys 75:891–918, 1994), whose studies have in part been inspired by the so-called transport phenomena of statistical physics. Two-dimensional anisotropic random walks with anisotropic density conditions á  la Heyde (J Stat Phys 27:721–730, 1982, Stochastic processes, Springer, New York, 1993) yield fixed column configurations and nearest-neighbour random walks in a random environment on the square lattice of the plane as in den Hollander (J Stat Phys 75:891–918, 1994) result in random column configurations. In both cases we conclude simultaneous weak Donsker and strong Strassen type invariance principles in terms of appropriately constructed anisotropic Brownian motions on the plane, with self-contained proofs in both cases. The style of presentation throughout will be that of a semi-expository survey of related results in a historical context.     

Thermal Entanglement Properties in Two Qubits One-Axis Spin Squeezing Model with an External Magnetic Field

In a recent article in this journal Guo-Hui (Int. J. Theor. Phys. 56, 600, 2017) has investigated the quantum correlation properties in the two qubits one-axis spin squeezing model with an external magnetic field by means of concurrence (C) and quantum discord (QD) criteria. We are to reveal numerically and analytically that in the limiting case T→ 0 (ground state) the sudden disappearance phenomenon (SDP) does not occur in the behavior of C and the values obtained for C are incorrect.

     

Observable-Geometric Phases and Quantum Computation

This paper presents an alternative approach to geometric phases from the observable point of view. Precisely, we introduce the notion of observable-geometric phases, which is defined as a sequence of phases associated with a complete set of eigenstates of the observable. The observable-geometric phases are shown to be connected with the quantum geometry of the observable space evolving according to the Heisenberg equation. They are indeed distinct from Berry’s phase (Berry Proc. R. Soc. London Series A 392:45–57, 1984; Simon Phys. Rev. Lett. 51:2167–2170, 1983) as the system evolves adiabatically. It is shown that the observable-geometric phases can be used to realize a universal set of quantum gates in quantum computation. This scheme leads to the same gates as the Abelian geometric gates of Zhu and Wang (Phys. Rev. Lett. 89: 097902: 1–4, 2002, Phys. Rev. A 67: 022319: 1–9, 2003), but based on the quantum geometry of the observable space beyond the state space.

     

Tighter Weighted Polygamy Inequalities of Multipartite Entanglement in Arbitrary-Dimensional Quantum Systems

We investigate polygamy relations of multipartite entanglement in arbitrary-dimensional quantum systems. By improving an inequality and using the βth (0 ≤ β ≤ 1) power of entanglement of assistance, we provide a new class of weighted polygamy inequalities of multipartite entanglement in arbitrary-dimensional quantum systems. We show that these new polygamy relations are tighter than the ones given in Kim (Phys. Rev. A 97, 042332 2018).

     

Damping in the Interaction of a Two-Photon Field and a Two-Level Atom Through Quantized Caldirola-Kanai Hamiltonian

Following the lines of the recent papers (Daneshmand and Tavassoly, Int. J. Theor. Phys. 56, 1218 (2017)), we study quantum mechanical treatments of an interaction between a two-level atom with a single-mode field in the two-photon Jaynes-Cummings model, where the Hamiltonian of the field is considered to be the quantized Caldirola-Kanai (CK) Hamiltonian. As a result, we would expect that the quantum dynamics of the two-photon JCM in terms of the CK Hamiltonian is qualitatively different from that of the usual one-photon case. We analytically calculate the explicit form of the atom-field entangled state and numerically evaluate the dynamics of its physical properties. The degree of entanglement, atomic population as well as sub-Poissonian statistics and quadrature squeezing of the field are analyzed. We adjust the latter evolved parameters by appropriately tuning the damping parameter within the CK Hamiltonian and detuning factor. Finally, we report a field detuning asymmetry in the collective statistical behavior.

     

Using Inequalities as Tests for the Kochen-Specker Theorem for Multiparticle States

The Kochen-Specker theorem is investigated for n spin-1/2 systems by using an inequality proposed in Nagata (J. Math. Phys. 46, 102101, 2005) on the basis on binary logic. A measurement theory based on the truth values (binary logic), i.e., the truth T (1) for true and the falsity F (0) for false is used. The values of measurement outcome are either + 1 or 0 (in \(\hbar /2\) unit). The quantum predictions by n-multipartite states violate the inequality by an amount that grows exponentially with n. The measurement theory based on the binary logic provides an exponentially stronger refutation of the existence of hidden-variable when the number of parties of the state increases more. It turns out that the Kochen-Specker theorem becomes a quite strong theorem when the dimension of the multipartite state highly increases, regardless of entanglement properties.

     

Replica Bounds by Combinatorial Interpolation for Diluted Spin Systems

In two papers Franz et al. proved bounds for the free energy of diluted random constraints satisfaction problems, for a Poisson degree distribution (Franz and Leone in J Stat Phys 111(3–4):535–564, 2003) and a general distribution (Franz et al. in J Phys A 36(43), 10967, 2003). Panchenko and Talagrand (Probab Theo Relat Fields 130(3):319–336, 2004) simplified the proof and generalized the result of Franz and Leone (J Stat Phys 111(3–4):535–564, 2003) for the Poisson case. We provide a new proof for the general degree distribution case and as a corollary, we obtain new bounds for the size of the largest independent set (also known as hard core model) in a large random regular graph. Our proof uses a combinatorial interpolation based on biased random walks (Salez in Combin Probab Comput 25(03):436–447, 2016) and allows to bypass the arguments in Franz et al. (J Phys A 36(43):10967, 2003) based on the study of the Sherrington–Kirkpatrick (SK) model.     

Trade-Off Relations of CHSH Violations Based on Norms of Bloch Vectors

By considering the norms of Bloch vectors, we present an improved trade-off relation of CHSH violations of pairwise qubits systems for any multi-qubit system, which leads to restrictions on the distribution of non-locality among the pairwise qubits systems. Detailed examples are computed to show that our result improves the trade-off relation in Qin et al. (Phys. Rev. A 92, 062339 2015). Our bounds are given by the norms of the Bloch vectors. Thus the bounds give experimentally feasible way in describing trade-off relation of maximal violations of CHSH inequalities for any multipartite-qubit state.

     

Cryptanalysis and Improvement of a Multiparty Quantum Direct Secret Sharing of Classical Messages with Bell States and Bell Measurements

Recently, a multiparty quantum direct secret sharing protocol with Bell states was presented (Song et al., Int. J Theor. Phys. 57, 1559, 2018). In this protocol, the secret message of the dealer is directly encoding into the transmitted particles. All agents obtain their pieces of secret by making Bell state measurement on their receiving particles, then cooperate to recover the dealer’s secret. However, as we show, this protocol is insecure, because an outside attacker or two special dishonest agents can eavesdrop the secret fully. Furthermore, an improved version of this protocol is proposed, which can stand against the presented attacks.

     

Dynamic Properties for BEC in an Optical Cavity with Atom-Photon Nonlinear Interaction

In this paper we investigate the dynamics of physical properties of the system introduced in Dimer et al. (Phys. Rev. A 75, 013804, 2007) and Zhao et al. (Phys. Rev. A 90, 023622, 2014) consisting of an ensemble of four-level atoms in Bose-Einstein condensate (BEC) state and a single-mode quantized field in which nonlinear interaction is taken into account. In fact, we start with a four-level atom and then explain how this model can be reduced to an effective two-level one via the adiabatic elimination. Also, our presentation is free of any classical approximation and so it is fully quantized. In this regard, we introduce the dynamical Hamiltonian of the system in terms of angular momentum operators and use the Dicke model to achieve the state of atomic sub-system. After obtaining the analytical solution of the state vector associated with the quantized BEC-field system, various physical properties such as atomic population inversion, quantum statistics of the field, squeezing in atomic and field subsystems as well as the degree of entanglement between the “BEC atoms” and the “photons” are numerically evaluated. It is shown that, the nonlinear interaction and other involved parameters in the presented model can dramatically affect the dynamics of the system. The collapse-revival phenomenon in the population inversion, Mandel parameter and atomic squeezing is a superb feature of the system which can be controlled by tuning the chosen parameters. Meanwhile, we propose an efficient way for the generation of sub-Poissonian and squeezed fields as well as squeezed atoms via nonlinear interaction of quantized filed with atomic BEC. In addition, it is found that, after the onset of interaction the system is always entangled. Altogether, under particular conditions, the approximated sudden death and then revival of entanglement can be observed.

     

Incompatibility of New Symmetry Reductions in U(1) × U(2) × U(3) Gauge Group with Higgs Mechanism

Noncommutative (NC) space-time leads to some strong constraints on the possible choices of gauge groups and allowed representations of matter and gauge fields. The standard model based on U(3) × U(2) × U(1) can be transcribed to NC space-time consistently with these constraints (Chaichian et al., Eur. Phys. J. C29:413, 1). In fact, through two new symmetry reduction mechanisms, this gauge group is reduced to the usual standard model one. In this paper, we show that, on the contrary to the usual standard model, the Goldestone boson equivalence theorem is violated due to the incompatibility of the new symmetry reduction mechanisms with the electroweak Higgs mechanism.

     

There are no nice interfaces in (2+1)-dimensional SOS models in random media

We prove that in dimensiond2 translation-covariant Gibbs states describing rigid interfaces in a disordered solid-on-solid (SOS) cannot exist for any value of the temperature, in contrast to the situation ind3. The proof relies on an adaptation of a theorem of Aizenman and Wehr.     

Cryptanalysis of Zhang et al’s Quantum Private Comparison and the Improvement

Based on EPR pairs, Zhang et al. analyzed the security of Yang and Tseng et al’s two QPC protocols, and proposed some new improvement strategies (Zhang and Zhang, Quantum Inform. Process. 12(5):1981–1990 2013). This paper points that Zhang et al’s protocol is insecure under a special attack, i.e. Trojan-horse attacks. To avoid this attack, we present an improved QPC protocol based on single particle encryption. Through security analysis of presented protocol, the improved protocol can resist Trojan horse attack (THA). We give a suggestion that non-orthogonal quantum states can be used to transmit information for reducing the leakage in a QPC protocol.

     

Long-Ranged Correlations in Bounded Nonequilibrium Fluids

In a recent paper, Liu and Oppenheim [J. Stat. Phys. 86:179 (1997)] solve the fluctuating heat diffusion equation for a bounded system with a temperature gradient. This note demonstrates that, contrary to their claims, their solution for the temperature correlation function is indeed long-ranged and reduces to that of Garcia et al.[J. Stat. Phys. 47:209 (1987)].     

A Pearson Random Walk with Steps of Uniform Orientation and Dirichlet Distributed Lengths

A constrained diffusive random walk of n steps in ℝ ^d and a random flight in ℝ ^d , which are equivalent, were investigated independently in recent papers (J. Stat. Phys. 127:813, 2007; J. Theor. Probab. 20:769, 2007, and J. Stat. Phys. 131:1039, 2008). The n steps of the walk are independent and identically distributed random vectors of exponential length and uniform orientation. Conditioned on the sum of their lengths being equal to a given value l, closed-form expressions for the distribution of the endpoint of the walk were obtained altogether for any n for d=1,2,4. Uniform distributions of the endpoint inside a ball of radius l were evidenced for a walk of three steps in 2D and of two steps in 4D.     

Central Limit Theorems for Open Quantum Random Walks on the Crystal Lattices

We consider the open quantum random walks on the crystal lattices and investigate the central limit theorems for the walks. On the integer lattices the open quantum random walks satisfy the central limit theorems as was shown by Attal et al (Ann Henri Poincaré 16(1):15–43, 2015). In this paper we prove the central limit theorems for the open quantum random walks on the crystal lattices. We then provide with some examples for the Hexagonal lattices. We also develop the Fourier analysis on the crystal lattices. This leads to construct the so called dual processes for the open quantum random walks. It amounts to get Fourier transform of the probability densities, and it is very useful when we compute the characteristic functions of the walks. In this paper we construct the dual processes for the open quantum random walks on the crystal lattices providing with some examples.