arXiv subjects

Jin-Woo Son

Publications and source records attributed to Jin-Woo Son.

15 recordsLinked to original sources

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↗

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

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

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↗

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.

quant-ph↗

arXiv2008

Role of Three-Qubit Mixed-States Entanglement in Teleportation Scheme

The bipartite quantum teleportation with a three-qubit mixture of GHZ and W states as a quantum channel is discussed. When the quantum channel is a mixed state consisting of the GHZ state plus small perturbed W state, the entanglement of the channel becomes zero when the average fidelity $\bar{F}_{GHZ}$ is less than 0.775. This means that the mixed state cannot play an any role as a quantum channel at $\bar{F}_{GHZ} \leq 0.775$. For the case of the mixed state consisting of the W state plus small perturbed GHZ state it turn out that this mixed state cannot play a role as a quantum channel at $\bar{F}_W \leq 0.833$.

quant-ph↗

arXiv2008

Geometric Measure of Entanglement and Shared Quantum States

We give an explicit expression for the geometric measure of entanglement for three qubit states that are linear combinations of four orthogonal product states. It turns out that the geometric measure for these states has three different expressions depending on the range of definition in parameter space. Each expression of the measure has its own geometrically meaningful interpretation. Such an interpretation allows oneself to take one step toward a complete understanding for the general properties of the entanglement measure. The states that lie on joint surfaces separating different ranges of definition, designated as shared states, seem to have particularly interesting features. The properties of the shared states are fully discussed.

quant-ph↗

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.

quant-ph↗

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.

quant-ph↗

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.

quant-ph↗

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

quant-ph↗

arXiv2007

On A two-variable p-adic l_q function

We prove that a two-variable p-adic l_q-function has the series p-adic expansion which interpolates a linear combinations of terms of the generalized q-Euler polynomials at non positive integers. The proof of this original construction is due to Kubota and Leopoldt in 1964, although the method given this note is due to Washington

math.NT↗

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.

quant-ph↗

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.

quant-ph↗