Concurrence-based Entanglement Measure For True $4$-way Entanglement
An entanglement monotone, which is invariant under the determinant 1 SLOCC operations and measures the true quadripartite entanglement, is explicitly constructed.
quant-ph↗
arXiv subjects
Eylee Jung
Publications and source records attributed to Eylee Jung.
Entanglement Classification of extended Greenberger-Horne-Zeilinger-Symmetric States
In this paper we analyze entanglement classification of extended Greenberger-Horne-Zeilinger-symmetric states $ρ^{ES}$, which is parametrized by four real parameters $x$, $y_1$, $y_2$ and $y_3$. The condition for separable states of $ρ^{ES}$ 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 $ρ^{ES}$ 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.
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Three-Tangle in Non-inertial Frame
Let Alice, Bob, and Charlie initially share an arbitrary fermionic three-qubit pure state, whose three-tangle is $τ_3^{(0)}$. It is shown within the single-mode approximation that if one party among the three of them moves with a uniform acceleration with respect to the other parties, the three-tangle reduces to $τ_3^{(0)} \cos^2 r$, where $r$ denotes a statistical factor in Fermi-Dirac statistics.
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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.
hep-th↗
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 $λ_c$. 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 $λ_c$ freely.
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Aharonov-Bohm-Coulomb Problem in Graphene Ring
We study the Aharonov-Bohm-Coulomb problem in a graphene ring. We investigate, in particular, the effects of a Coulomb type potential of the form $ξ/r$ on the energy spectrum of Dirac electrons in the graphene ring in two different ways: one for the scalar coupling and the other for the vector coupling. It is found that, since the potential in the scalar coupling breaks the time-reversal symmetry between the two valleys as well as the effective time-reversal symmetry in a single valley, the energy spectrum of one valley is separated from that of the other valley, demonstrating a valley polarization. In the vector coupling, however, the potential does not break either of the two symmetries and its effect appears only as an additive constant to the spectrum of Aharonov-Bohm potential. The corresponding persistent currents, the observable quantities of the symmetry-breaking energy spectra, are shown to be asymmetric about zero magnetic flux in the scalar coupling, while symmetric in the vector coupling.
cond-mat.mes-hall↗
Test of Common Sense in Quantum Copying Process
It is believed that the more we have {\it a priori} information on input states, the better we can make the quality of clones in quantum cloning machines. This common sense idea was confirmed several years ago by analyzing a situation, where the input state is either one of two non-orthogonal states. If the {\it a priori} information is measured by the Shannon entropy, common sense predicts that the quality of the clone becomes poorer with increasing $N$, where $N$ is the number of possible input states. We show, however, that the {\it a priori} information measured by the Shannon entropy does not affect the quality of the clones. Instead the no-cloning theorem and `denseness' of the possible input states play important roles in determining the quality. Specifically, the factor `denseness' plays a more crucial role than the no-cloning theorem when $N \geq 3$.
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Tripartite Entanglement in Noninertial Frame
The tripartite entanglement is examined when one of the three parties moves with a uniform acceleration with respect to other parties. As Unruh effect indicates, the tripartite entanglement exhibits a decreasing behavior with increasing the acceleration. Unlike the bipartite entanglement, however, the tripartite entanglement does not completely vanish in the infinite acceleration limit. If the three parties, for example, share the Greenberger-Horne-Zeilinger or W-state initially, the corresponding $π$-tangle, one of the measures for tripartite entanglement, is shown to be $π/6 \sim 0.524$ or 0.176 in this limit, respectively. This fact indicates that the tripartite quantum information processing may be possible even if one of the parties approaches to the Rindler horizon. The physical implications of this striking result are discussed in the context of black hole physics.
hep-th↗
Difficulties in analytic computation for relative entropy of entanglement
It is known that relative entropy of entanglement for entangled state $ρ$ is defined via its closest separable (or positive partial transpose) state $σ$. Recently, it has been shown how to find $ρ$ provided that $σ$ is given in two-qubit system. In this paper we study on the inverse process, i.e. how to find $σ$ provided that $ρ$ is given. It is shown that if $ρ$ is one of Bell-diagonal, generalized Vedral-Plenio and generalized Horodecki states, one can always find $σ$ from a geometrical point of view. This is possible due to the following two facts: (i) The Bloch vectors of $ρ$ and $σ$ are identical with each other (ii) The qubit-interaction vector of $σ$ can be computed from a crossing point between minimal geometrical object, in which all separable states reside in the presence of Bloch vectors, and a straight line, which connects the point corresponding to the qubit-interaction vector of $ρ$ and the nearest vertex of the maximal tetrahedron, where all two-qubit states reside. It is shown, however, that these nice properties are not maintained for the arbitrary two-qubit states.
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Toward an understanding of entanglement for generalized n-qubit W-states
We solve stationarity equations of the geometric measure of entanglement for multi-qubit W-type states. In this way we compute analytically the maximal overlap of one-parameter $n$-qubit and two-parameter four-qubit W-type states and their nearest product states. Possible extensions to arbitrary W-type states and geometrical interpretations of these results are discussed in detail.
quant-ph↗
Does three-tangle properly quantify the three-party entanglement for Greenberger-Horne-Zeilinger-type states?
Some mixed states composed of only GHZ states can be expressed in terms of only W-states. This fact implies that such states have vanishing three-tangle. One of such rank-3 states, $Π_{GHZ}$, is explicitly presented in this paper. These results are used to compute analytically the three-tangle of a rank-4 mixed state $σ$ composed of four GHZ states. This analysis with considering Bloch sphere $S^{16}$ of $d=4$ qudit system allows us to derive the hyper-polyhedron. It is shown that the states in this hyper-polyhedron have vanishing three-tangle. Computing the one-tangles for $Π_{GHZ}$ and $σ$, we prove the monogamy inequality explicitly. Making use of the fact that the three-tangle of $Π_{GHZ}$ is zero, we try to explain why the W-class in the whole mixed states is not of measure zero contrary to the case of pure states.
quant-ph↗
Three-Party Entanglement in Tripartite Teleportation Scheme through Noisy Channels
We have tried to interpret the physical role of the three-tangle and $π$-tangle in the real physical information process. For the model calculation we adopt the three-party teleportation scheme through the various noisy channels. The three parties consist of sender, accomplice and receiver. It is shown that the $π$-tangles for the X- and Z-noisy channels vanish at $κt \to \infty$ limit, where $κt$ is a parameter introduced in the master equation of Lindblad form. In this limit the receiver's maximum fidelity reduces to the classical limit 2/3. However, this nice feature is not maintained at the Y- and isotropy-noise channels. For Y-noise channel the $π$-tangle vanishes at $0.61 \leq κt$. At $κt = 0.61$ the receiver's maximum fidelity becomes 0.57, which is much less than the classical limit. Similar phenomenon occurs at the isotropic noise channel. We also computed the three-tangles analytically for the X- and Z-noise channels. The remarkable fact is that the three-tangle for Z-noise channel is exactly same with the corresponding $π$-tangle. In the X-noise channel the three-tangle vanishes at $0.10 \leq κt$. At $κt = 0.10$ the receiver's fidelity can be reduced to the classical limit provided that the accomplice performs the measurement appropriately. However, the receiver's maximum fidelity becomes 8/9, which is much larger than the classical limit. Since the Y- and isotropy-noise channels are rank-8 mixed states, their three-tangles are not computed explicitly. Instead, we have derived their upper bounds with use of the analytical three-tangles for other noisy channels. Our analysis strongly suggests that we need different three-party entanglement measure whose value is between three-tangle and $π$-tangle.
quant-ph↗
Attack of Many Eavesdroppers via Optimal Strategy in Quantum Cryptography
We examine a situation that $n$ eavesdroppers attack the Bennett-Brassard cryptographic protocol via their own optimal and symmetric strategies. Information gain and mutual information with sender for each eavesdropper are explicitly derived. The receiver's error rate for the case of arbitrary $n$ eavesdroppers can be derived using a recursive relation. Although first eavesdropper can get mutual information without disturbance arising due to other eavesdroppers, subsequent eavesdropping generally increases the receiver's error rate. Other eavesdroppers cannot gain information on the input signal sufficiently. As a result, the information each eavesdropper gains becomes less than optimal one.
quant-ph↗
Quantum Resonance near Optimal Eavesdropping in Quantum Cryptography
We find a resonance behavior in the disturbance when an eavesdropper chooses a near-optimal strategy intentionally or unintentionally when the usual Bennett-Brassard cryptographic scheme is performed between two trusted parties. This phenomenon tends to disappear when eavesdropping strategy moves far from the optimal one. Therefore, we conjecture that this resonant effect is a characteristic for the eavesdropping strategy near to optimal one. We argue that this effect makes the quantum cryptography more secure against the eavesdropper's attack.
quant-ph↗
Three-Tangle for Rank-3 Mixed States: mixture of Greenberger-Horne-Zeilinger, W and flipped W states
Three-tangle for the rank-three mixture composed of Greenberger-Horne-Zeilinger, W and flipped W states is analytically calculated. The optimal decompositions in the full range of parameter space are constructed by making use of the convex-roof extension. We also provide an analytical technique, which determines whether or not an arbitrary rank-3 state has vanishing three-tangle. This technique is developed by making use of the Bloch sphere S^8 of the qutrit system. The Coffman-Kundu-Wootters inequality is discussed by computing one-tangle and concurrences. It is shown that the one-tangle is always larger than the sum of squared concurrences and three-tangle. The physical implication of three-tangle is briefly discussed.
quant-ph↗
GHZ versus W : Quantum Teleportation through Noisy Channels
Which state does lose less quantum information between GHZ and W states when they are prepared for two-party quantum teleportation through noisy channel? We address this issue by solving analytically a master equation in the Lindbald form with introducing the noisy channels which makes the quantum channels to be mixed states. It is found that the answer of the question is dependent on the type of the noisy channel. If, for example, the noisy channel is ($L_{2,x}$, $L_{3,x}$, $L_{4,x}$)-type where $L's$ denote the Lindbald operators, GHZ state is always more robust than W state, i.e. GHZ state preserves more quantum information. In, however, ($L_{2,y}$, $L_{3,y}$, $L_{4,y}$)-type channel the situation becomes completely reversed. In ($L_{2,z}$, $L_{3,z}$, $L_{4,z}$)-type channel W state is more robust than GHZ state when the noisy paramter ($κ$) is comparatively small while GHZ state becomes more robust when $κ$ is large. In isotropic noisy channel we found that both states preserve equal amount of quantum information. A relation between the average fidelity and entanglement for the mixed state quantum channels are discussed.
quant-ph↗
Three-Qubit Groverian Measure
The Groverian measures are analytically computed in various types of three-qubit states. The final results are also expressed in terms of local-unitary invariant quantities in each type. This fact reflects the manifest local-unitary invariance of the Groverian measure. It is also shown that the analytical expressions for various types have correct limits to other types. For some types (type 4 and type 5) we failed to compute the analytical expression of the Groverian measure in this paper. However, from the consideration of local-unitary invariants we have shown that the Groverian measure in type 4 should be independent of the phase factor $ϕ$, which appear in the three-qubit state $|ψ>$. This fact with geometric interpretation on the Groverian measure may enable us to derive the analytical expressions for general arbitrary three-qubit states in near future.
quant-ph↗
Reduced State Uniquely Defines Groverian Measure of Original Pure State
Groverian and Geometric entanglement measures of the n-party pure state are expressed by the (n-1)-party reduced state density operator directly. This main theorem derives several important consequences. First, if two pure n-qudit states have reduced states of (n-1)-qudits, which are equivalent under local unitary(LU) transformations, then they have equal Groverian and Geometric entanglement measures. Second, both measures have an upper bound for pure states. However, this upper bound is reached only for two qubit systems. Third, it converts effectively the nonlinear eigenvalue problem for three qubit Groverian measure into linear eigenvalue equations. Some typical solutions of these linear equations are written explicitly and the features of the general solution are discussed in detail.
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