Generalized uncertainty principle and DD-dimensional quantum mechanics

The non-relativistic quantum mechanics with a generalized uncertainty principle (GUP) is examined in $D$-dimensional free particle and harmonic oscillator systems. The Feynman propagators for these systems are exactly derived within the first order of the GUP parameter.Comment: 13 pages, 1 figure, will appear in PR

Tripartite Entanglement-Dependence of Tripartite Non-locality in Non-inertial Frame

The three-tangle-dependence of $S_{max} = \max$, where $S$ is Svetlichny operator, are explicitly derived when one party moves with an uniform acceleration with respect to other parties in the generalized Greenberger-Horne-Zeilinger and maximally slice states. The $\pi$-tangle-dependence of $S_{max}$ are also derived implicitly. From the dependence we conjecture that the multipartite entanglement is not the only physical resource for quantum mechanical multipartite non-locality.Comment: 13 pages,6 figures, V2, 14 pages, 6 figures, will appear in JPHYS

Four-Qubit Monogamy and Four-Way Entanglement

We examine the various properties of the three four-qubit monogamy relations, all of which introduce the power factors in the three-way entanglement to reduce the tripartite contributions. On the analytic ground as much as possible we try to find the minimal power factors, which make the monogamy relations hold if the power factors are larger than the minimal powers. Motivated to the three-qubit monogamy inequality we also examine whether those four-qubit monogamy relations provide the SLOCC-invariant four-way entanglement measures or not. Our analysis indicate that this is impossible provided that the monogamy inequalities are derived merely by introducing weighting power factors.Comment: 18 pages, 6 figure

Protection of Entanglement in the presence of Markovian or Non-Markovian Environment via particle velocity : Exact Results

On the analytic ground we examine a physical mechanism how particle velocity can protect an entanglement when quantum system is embedded in Markovian or non-Markovian environment. In particular the effect of particle velocity is examined in the entanglement sudden death (ESD) and revival of entanglement (ROE) phenomena. Even though particles move fast, the ESD phenomenon does not disappear if it occurs at zero velocity. However the time domain $0 \leq t \leq t_*$ for nonvanishing entanglement becomes larger and larger with increasing velocity. When ROE phenomenon occurs at zero velocity, even small velocity can make this phenomenon not to occur although the oscillatory behavior of entanglement in time is maintained. For comparatively large velocity the amplitude of the oscillatory behavior becomes extremely small. In this way the entanglement can be protected by particle velocity. The protection of entanglement via velocity is compared with that via the detuning parameter.Comment: 15 pages, 12 figure

Tripartite Entanglement Dynamics in the presence of Non-Markovian Environment

We study on the tripartite entanglement dynamics when each party is initially entangled with other parties, but they locally interact with their own non-Markovian environment. First, we consider three GHZ-type initial states, all of which have GHZ symmetry provided that the parameters are chosen appropriately. However, this symmetry is broken due to the effect of environment. The corresponding $\pi$-tangles, one of the tripartite entanglement measure, are analytically computed at arbitrary time. The revival phenomenon of entanglement occurs after complete disappearance of entanglement. We also consider two W-type initial states. The revival phenomenon also occurs in this case. On the analytical ground the robustness issue against the effect of environment is examined for both GHZ-type and W-type initial states.Comment: 19pages, 7 pdf figures V2: 24 pages, 11 figures, will appear in QI

Thermal Entanglement and Thermal Discord in two-qubit Heisenberg XYZ Chain with Dzyaloshinskii-Moriya Interactions

In order to explore the effect of external temperature $T$ in quantum correlation we compute thermal entanglement and thermal discord analytically in the Heisenberg $X$ $Y$ $Z$ model with Dzyaloshinskii-Moriya Interaction term ${\bm D} \cdot \left( {\bm \sigma}_1 \times {\bm \sigma}_2 \right)$. For the case of thermal entanglement it is shown that quantum phase transition occurs at $T = T_c$ due to sudden death phenomenon. For antiferromagnetic case the critical temperature $T_c$ increases with increasing $|{\bm D}|$. For ferromagnetic case, however, $T_c$ exhibits different behavior in the regions $|{\bm D}| \geq |{\bm D_*}|$ and $|{\bm D}| < |{\bm D_*}|$, where ${\bm D_*}$ is particular value of ${\bm D}$. It is shown that $T_c$ becomes zero at $|{\bm D}| = |{\bm D_*}|$. We explore the behavior of thermal discord in detail at $T \approx T_c$. For antiferromagnetic case the external temperature makes the thermal discord exhibit exponential damping behavior, but it never reaches to exact zero. For ferromagnetic case the thermal entanglement and thermal discord are shown to be zero simultaneously at $T_c = 0$ and $|{\bm D}| = |{\bm D_*}|$. This is unique condition for simultaneous disappearance of thermal entanglement and thermal discord in this model.Comment: 24 pages, 16 figures, several typos corrected, V2: 29 pages, 19 figures, will appear in QIP, V3: mistake in figure number is correcte

Relative Entropy of Entanglement for Two-Qubit State with zz-directional Bloch Vectors

So far there is no closed formula for relative entropy of entanglement of arbitrary two-qubit states. In this paper we present a method, which guarantees the derivation of the relative entropy of entanglement for most states that have $z$-directional Bloch vectors. It is shown that the closest separable states for those states also have $z$-directional Bloch vectors though there are few exceptions.Comment: 12pages, no figure, will appear in IJQ

Entanglement Classification of extended Greenberger-Horne-Zeilinger-Symmetric States

In this paper we analyze entanglement classification of extended Greenberger-Horne-Zeilinger-symmetric states $\rho^{ES}$, which is parametrized by four real parameters $x$, $y_1$, $y_2$ and $y_3$. The condition for separable states of $\rho^{ES}$ is analytically derived. The higher classes such as bi-separable, W, and Greenberger-Horne-Zeilinger classes are roughly classified by making use of the class-specific optimal witnesses or map from the extended Greenberger-Horne-Zeilinger symmetry to the Greenberger-Horne-Zeilinger symmetry. From this analysis we guess that the entanglement classes of $\rho^{ES}$ are not dependent on $y_j \hspace{.2cm} (j=1,2,3)$ individually, but dependent on $y_1 + y_2 + y_3$ collectively. The difficulty arising in extension of analysis with Greenberger-Horne-Zeilinger symmetry to the higher-qubit system is discussed.Comment: 16 pages, 6 figure

Concurrence-based Entanglement Measure For True 44-way Entanglement

An entanglement monotone, which is invariant under the determinant 1 SLOCC operations and measures the true quadripartite entanglement, is explicitly constructed.Comment: This paper has been withdrawn by the author due to a crucial calculational error in (AD)-(BC) partitio

Entanglement of Four-Qubit Rank-22 Mixed States

It is known that there are three maximally entangled states $\ket{\Phi_1} = (\ket{0000} + \ket{1111}) / \sqrt{2}$, $\ket{\Phi_2} = (\sqrt{2} \ket{1111} + \ket{1000} + \ket{0100} + \ket{0010} + \ket{0001}) / \sqrt{6}$, and $\ket{\Phi_3} = (\ket{1111} + \ket{1100} + \ket{0010} + \ket{0001}) / 2$ in four-qubit system. It is also known that there are three independent measures ${\cal F}^{(4)}_j \hspace{.2cm} (j=1,2,3)$ for true four-way quantum entanglement in the same system. In this paper we compute ${\cal F}^{(4)}_j$ and their corresponding linear monotones ${\cal G}^{(4)}_j$ for three rank-two mixed states \rho_j = p \ket{\Phi_j}\bra{\Phi_j} + (1 - p) \ket{\mbox{W}_4} \bra{\mbox{W}_4}, where \ket{\mbox{W}_4} = (\ket{0111} + \ket{1011} + \ket{1101} + \ket{1110}) / 2. We discuss the possible applications of our results briefly.Comment: 20 pages, 5 eps figures, will appear in Quantum Information Processin