arXiv subjects

DaeKil Park

Publications and source records attributed to DaeKil Park.

At least 55 records · Page 3Linked to original sources

arXiv2013

Entanglement Degradation in the presence of $(4+n)$-dimensional Schwarzschild Black Hole

In this short paper we compute the various bipartite quantum correlations in the presence of the $(4+n)$-dimensional Schwarzschild black hole. In particular, we focus on the $n$-dependence of various bosonic bipartite entanglements. For the case between Alice and Rob, where the former is free falling observer and the latter is at the near-horizon region, the quantum correlation is degraded compared to the case in the absence of the black hole. The degradation rate increases with decreasing $n$. We also compute the physically inaccessible correlations. It is found that there is no creation of quantum correlation between Alice and AntiRob. For the case between Rob and AntiRob the quantum entanglement is created although they are separated in the causally disconnected regions. It is found that contrary to the physically accessible correlation the entanglement between Rob and AntiRob decreases with decreasing $n$.

hep-th↗

arXiv2012

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 $π$-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.

quant-ph↗

arXiv2012

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.

quant-ph↗

arXiv2012

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↗

arXiv2012

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.

quant-ph↗

arXiv2012

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↗

arXiv2010

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 $N \geq 3$.

quant-ph↗

arXiv2010

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↗

arXiv2010

Relative Entropy of Entanglement for Two-Qubit State with $z$-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.

quant-ph↗

arXiv2010

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.

quant-ph↗

arXiv2009

Maximally entangled three-qubit states via geometric measure of entanglement

Bipartite maximally entangled states have the property that the largest Schmidt coefficient reaches its lower bound. However, for multipartite states the standard Schmidt decomposition generally does not exist. We use a generalized Schmidt decomposition and the geometric measure of entanglement to characterize three-qubit pure states and derive a single-parameter family of maximally entangled three-qubit states. The paradigmatic Greenberger-Horne-Zeilinger (GHZ) and W states emerge as extreme members in this family of maximally entangled states. This family of states possess different trends of entanglement behavior: in going from GHZ to W states the geometric measure and the relative entropy of entanglement and the bipartite entanglement all increase monotonically whereas the three-tangle and bi-partition negativity both decrease monotonically.

quant-ph↗

arXiv2009

Effect of Phase Factor in the Geometric Entanglement Measure of Three-Qubit States

Any pure three-qubit state is uniquely characterized by one phase and four positive parameters. The geometric measure of entanglement as a function of state parameters can have different expressions. Each of expressions has its own applicable domain and thus the whole state parameter space is divided into subspaces that are ranges of definition for corresponding expressions. The purpose of this paper is to examine the applicable domains for the most general qubit-interchange symmetric three-qubit states. First, we compute the eigenvalues of the non-linear eigenvalue equations and the nearest separable states for the permutation invariant three-qubit states with a fixed phase. Next, we compute the geometric entanglement measure, deduce the boundaries of all subspaces, and find allocations of highly and slightly entangled states. It is shown that there are three applicable domains when the phase factor is $π/2$ while other cases have only two domains. The emergence of the three domains is due to the appearance of the additional W-state. We show that most of highly entangled states reside near the boundaries of the domains and states located far from the boundaries become less-entangled and eventually go to the product states. The neighbors of W-state are generally more entangled than the neighbors of Greenberger-Horne-Zeilinger(GHZ) state from the aspect of the geometric measure. However, the range of the GHZ-neighbors is much more wider than the range of the W-neighbors.

quant-ph↗

arXiv2009

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↗

arXiv2009

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↗

arXiv2009

Effect of Decoherence in Ekert-Protocol

We have examined the effect of the decoherence in the Ekert91 quantum cryptographic protocol. In order to explore this issue we have introduced two major decoherences, the depolarizing channel and the generalized amplitude damping, between the singlet source and one of the legitimate users. It is shown that the depolarizing channel disentangles the quantum channel more easily than the generalized amplitude damping. This fact indicates that the Ekert protocol is more robust to the generalized amplitude damping. We also have computed the Bell inequality to check the robustness or weakness of the Ekert91 protocol. Computation of the Bell inequality also confirms the robustness of the Ekert91 protocol to the generalized amplitude damping compared to the depolarizing channel.

quant-ph↗

arXiv2009

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↗

arXiv2009

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↗

arXiv2009

Generalized Schmidt decomposition based on injective tensor norm

We present a generalized Schmidt decomposition for a pure system with any number of two-level subsystems. The basis is symmetric under the permutation of the parties and is derived from the product state defining the injective tensor norm of the state. The largest coefficient quantifies the quantum correlation of the state. Other coefficients have a lot of information such as the unentangled particles as well as the particles whose reduced states are completely mixed. The decomposition clearly distinguishes the states entangled in inequivalent ways and have an information on the applicability to the teleportation and superdense coding when the given quantum state is used as a quantum channel.

quant-ph↗