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operations and measures the true quadripartite entanglement, is explicitly constructed.Comment: This paper has been withdrawn by the author due to a crucial calculational error in (AD)-(BC) partitio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

REE From EOF

It is well-known that entanglement of formation (EOF) and relative entropy of entanglement (REE) are exactly identical for all two-qubit pure states even though their definitions are completely different. We think this fact implies that there is a veiled connection between EOF and REE. In this context, we suggest a procedure, which enables us to compute REE from EOF without relying on the converse procedure. It is shown that the procedure yields correct REE for many symmetric mixed states such as Bell-diagonal, generalized Vedral-Plenino, and generalized Horodecki states. It also gives a correct REE for less symmetric Vedral-Plenio-type state. However, it is shown that the procedure does not provide correct REE for arbitrary mixed states.Comment: 17 pages, 1 figure, several typos corrected, final version to appear in Quantum Information Processin

Mixedness and Entanglement in the presence of Localized Closed Timelike Curves

We examine mixedness and entanglement of the chronology-respecting (CR) system with assuming that quantum mechanical closed timelike curves (CTCs) exist in nature and by introducing the qubit system and applying the general controlled operations between CR and CTC systems. We use the magnitude of Bloch vector as a measure of mixedness. While Deutschian-CTC (D-CTC) either preserves or decreases the magnitude, postselected-CTC (P-CTC) can increases it. Nonintuitively, even the completely mixed CR-qubit can be converted into a pure state after CTC-qubit travels around the P-CTC. It is also shown that while D-CTC cannot increase the entanglement of CR system, P-CTC can increase it. Surprisingly, any partially entangled state can be maximally entangled pure state if P-CTC exists. Thus, distillation of P-CTC-assisted entanglement can be easily achieved without preparing the multiple copies of the partially entangled state.Comment: 10 pages, 1 figure; V2 12 pages, references added, will appear in QI

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

Uncertainties in Gapped Graphene

Motivated by graphene-based quantum computer we examine the time-dependence of the position-momentum and position-velocity uncertainties in the monolayer gapped graphene. The effect of the energy gap to the uncertainties is shown to appear via the Compton-like wavelength $\lambda_c$. The uncertainties in the graphene are mainly contributed by two phenomena, spreading and zitterbewegung. While the former determines the uncertainties in the long-range of time, the latter gives the highly oscillation to the uncertainties in the short-range of time. The uncertainties in the graphene are compared with the corresponding values for the usual free Hamiltonian $\hat{H}_{free} = (p_1^2 + p_2^2) / 2 M$. It is shown that the uncertainties can be under control within the quantum mechanical law if one can choose the gap parameter $\lambda_c$ freely.Comment: 12 pages, 11 figures V2: 21 pages, one more author is added. will appear in PR

GUP and Point Interaction

The non-relativistic quantum mechanics with the generalized uncertainty principle (GUP) is examined when the potential is one-dimensional $\delta-$function. It is shown that unlike usual quantum mechanics, the Schr\"{o}dinger and Feynman's path-integral approaches are inequivalent at the first order of GUP parameter.Comment: 9 pages, no figure V2: will appear in PR

Sum Rule of Quantum Uncertainties: Coupled Harmonic Oscillator System with Time-Dependent Parameters

Uncertainties $(\Delta x)^2$ and $(\Delta p)^2$ are analytically derived in an $N$-coupled harmonic oscillator system when spring and coupling constants are arbitrarily time-dependent and each oscillator is in an arbitrary excited state. When $N = 2$, those uncertainties are shown as just arithmetic average of uncertainties of two single harmonic oscillators. We call this property as "sum rule of quantum uncertainty". However, this arithmetic average property is not generally maintained when $N \geq 3$, but it is recovered in $N$-coupled oscillator systems if and only if $(N-1)$ quantum numbers are equal. The generalization of our results to a more general quantum system is briefly discussed.Comment: 15 pages, 2 figures v2: 17 pages, will appear in QI

Comment on "Path integral action of a particle with the generalized uncertainty principle and correspondence with noncommutativity"

Recently in [Phys. Rev. D $99$ $(2019)$ 104010] the non-relativistic Feynman propagator for harmonic oscillator system is presented when the generalized uncertainty principle is employed. In this short comment it is shown that the expression is incorrect. We also derive the correct expression of it.Comment: 5 pages, will appear in PRD (comment

Quantum Discord and Quantum Entanglement in the Background of an Asymptotically Flat Static Black Holes

The quantum discord and tripartite entanglement are discussed in the presence of an asymptotically flat static black holes. The total correlation, quantum discord and classical correlation exhibit decreasing behavior with increasing Hawking temperature. It is shown that the classical correlation is less than the quantum discord in the full range of Hawking temperature. The tripartite entanglements for Greenberger-Horne-Zeilinger and W-states also exhibit decreasing behavior with increasing Hawking temperature. At the infinite limit of Hawking temperature the tripartite entanglements for Greenberger-Horne-Zeilinger and W-states reduce to 52% and 33% of the corresponding values in the flat space limit, respectively.Comment: 13pages,5figure