arXiv subjects

Mi-Ra Hwang

Publications and source records attributed to Mi-Ra Hwang.

29 records · Page 2Linked to original sources

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.

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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.

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arXiv2009

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.

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arXiv2009

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.

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arXiv2008

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.

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arXiv2008

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.

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arXiv2008

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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arXiv2008

Perfect Quantum Teleportation and Superdense coding with $P_{max} = 1/2$ states

We conjecture that criterion for perfect quantum teleportation is that the Groverian entanglement of the entanglement resource is $1/\sqrt{2}$. In order to examine the validity of our conjecture we analyze the quantum teleportation and superdense coding with $|Φ> = (1/\sqrt{2}) (|00q_1> + |11q_2>)$, where $|q_1>$ and $|q_2>$ are arbitrary normalized single qubit states. It is shown explicitly that $|Φ>$ allows perfect two-party quantum teleportation and superdense coding scenario. Next we compute the Groverian measures for $|ψ>=\sqrt{1/2 - b^2}|100>+b |010>+a|001> +\sqrt{1/2-a^2}|111>$ and $|\tildeψ>=a|000>+b|010>+\sqrt{1/2 - (a^2+b^2)}|100> + (1/\sqrt{2}) |111>$, which also allow the perfect quantum teleportation. It is shown that both states have $1/\sqrt{2}$ Groverian entanglement measure, which strongly supports that our conjecture is valid.

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arXiv2008

Mixed-State Entanglement and Quantum Teleportation through Noisy Channels

The quantum teleportation with noisy EPR state is discussed. Using an optimal decomposition technique, we compute the concurrence, entanglement of formation and Groverian measure for various noisy EPR resources. It is shown analytically that all entanglement measures reduce to zero when $\bar{F} \leq 2/3$, where $\bar{F}$ is an average fidelity between Alice and Bob. This fact indicates that the entanglement is a genuine physical resource for the teleportation process. This fact gives valuable clues on the optimal decomposition for higher-qubit mixed states. As an example, the optimal decompositions for the three-qubit mixed states are discussed by adopting a teleportation with W-state

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arXiv2007

Amplitude Damping for single-qubit System with single-qubit mixed-state Environment

We study a generalized amplitude damping channel when environment is initially in the single-qubit mixed state. Representing the affine transformation of the generalized amplitude damping by a three-dimensional volume, we plot explicitly the volume occupied by the channels simulatable by a single-qubit mixed-state environment. As expected, this volume is embedded in the total volume by the channels which is simulated by two-qubit enviroment. The volume ratio is approximately 0.08 which is much smaller than 3/8, the volume ratio for generalized depolarizing channels.

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arXiv2007

Quantum Teleportation and Von Neumann Entropy

The single qubit quantum teleportation (sender and receiver are Alice and Bob respectively) is analyzed from the aspect of the quantum information theories. The various quantum entropies are computed at each stage, which ensures the emergence of the entangled states in the intermediate step. The mutual information $S(B:C)$ becomes non-zero before performing quantum measurement, which seems to be consistent to the original purpose of the quantum teleportation. It is shown that if the teleported state $|ψ>$ is near the computational basis, the quantum measurement in $C$-system is dominantly responsible for the joint entropy $S(A,C)$ at the final stage. If, however, $|ψ>$ is far from the computational basis, this dominant responsibility is moved into the quantum measurement of system $A$. A possible extension of our results are briefly discussed.

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