arXiv subjects

Soojoon Lee

Publications and source records attributed to Soojoon Lee.

71 records · Page 4Linked to original sources

arXiv2009

Any multipartite entangled state violating Mermin-Klyshko inequality can be distilled for almost all bipartite splits

We study the explicit relation between violation of Bell inequalities and bipartite distillability of multi-qubit states. It has been shown that even though for $N\ge 8$ there exist $N$-qubit bound entangled states which violates a Bell inequality [Phys. Rev. Lett. {\bf 87}, 230402 (2001)], for all the states violating the inequality there exists at least one splitting of the parties into two groups such that pure-state entanglement can be distilled [Phys. Rev. Lett. {\bf 88}, 027901 (2002)]. We here prove that for all $N$-qubit states violating the inequality the number of distillable bipartite splits increases exponentially with $N$, and hence the probability that a randomly chosen bipartite split is distillable approaches one exponentially with $N$, as $N$ tends to infinity. We also show that there exists at least one $N$-qubit bound entangled state violating the inequality if and only if $N\ge 6$.

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arXiv2008

Quantum states for perfectly secure secret sharing

In this work, we investigate what kinds of quantum states are feasible to perform perfectly secure secret sharing, and present its necessary and sufficient conditions. We also show that the states are bipartite distillable for all bipartite splits, and hence the states could be distillable into the Greenberger-Horne-Zeilinger state. We finally exhibit a class of secret-sharing states, which have an arbitrarily small amount of bipartite distillable entanglement for a certain split.

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arXiv2008

Monogamy equality in $2\otimes 2 \otimes d$ quantum systems

There is an interesting property about multipartite entanglement, called the monogamy of entanglement. The property can be shown by the monogamy inequality, called the Coffman-Kundu-Wootters inequality [Phys. Rev. A {\bf 61}, 052306 (2000); Phys. Rev. Lett. {\bf 96}, 220503 (2006)], and more explicitly by the monogamy equality in terms of the concurrence and the concurrence of assistance, $\mathcal{C}_{A(BC)}^2=\mathcal{C}_{AB}^2+(\mathcal{C}_{AC}^a)^2$, in the three-qubit system. In this paper, we consider the monogamy equality in $2\otimes 2 \otimes d$ quantum systems. We show that $\mathcal{C}_{A(BC)}=\mathcal{C}_{AB}$ if and only if $\mathcal{C}_{AC}^a=0$, and also show that if $\mathcal{C}_{A(BC)}=\mathcal{C}_{AC}^a$ then $\mathcal{C}_{AB}=0$, while there exists a state in a $2\otimes 2 \otimes d$ system such that $\mathcal{C}_{AB}=0$ but $\mathcal{C}_{A(BC)}>\mathcal{C}_{AC}^a$.

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arXiv2007

Three-party d-level quantum secret sharing protocol

We develop a three-party quantum secret sharing protocol based on arbitrary dimensional quantum states. In contrast to the previous quantum secret sharing protocols, the sender can always control the state, just using local operations, for adjusting the correlation of measurement directions of three parties and thus there is no waste of resource due to the discord between the directions. Moreover, our protocol contains the hidden value which enables the sender to leak no information of secret key to the dishonest receiver until the last steps of the procedure.

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arXiv2007

Teleportation capability, distillability, and nonlocality on three-qubit states

In this paper, we consider teleportation capability, distillability, and nonlocality on three-qubit states. In order to investigate some relations among them, we first find the explicit formulas of the quantities about the maximal teleportation fidelity on three-qubit states. We show that if any three-qubit state is useful for three-qubit teleportation then the three-qubit state is distillable into a Greenberger-Horne-Zeilinger state, and that if any three-qubit state violates a specific form of Mermin inequality then the three-qubit state is useful for three-qubit teleportation.

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arXiv2007

Bound entangled states with nonzero distillable key rate

In this paper, we present sufficient conditions for states to have positive distillable key rate. Exploiting the conditions, we show that the bound entangled states given by Horodecki et al. [Phys. Rev. Lett. 94, 160502 (2005), quant-ph/0506203] have nonzero distillable key rate, and finally exhibit a new class of bound entangled states with positive distillable key rate, but with negative Devetak-Winter lower bound of distillable key rate for the ccq states of their privacy squeezed versions.

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arXiv2006

Notes on the hidden subgroup problem on some semi-direct product groups

We consider the hidden subgroup problem on the semi-direct product of cyclic groups $\Z_{N}\rtimes\Z_{p}$ with some restriction on $N$ and $p$. By using the homomorphic properties, we present a class of semi-direct product groups in which the structures of subgroups can be easily classified. Furthermore, we show that there exists an efficient quantum algorithm for the hidden subgroup problem on the class.

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arXiv2005

Quantum algorithms without initializing the auxiliary qubits

In this Letter, we construct the quantum algorithms for the Simon problem and the period-finding problem, which do not require initializing the auxiliary qubits involved in the process of functional evaluation but are as efficient as the original algorithms. In these quantum algorithms, one can use any arbitrarily mixed state as the auxiliary qubits, and furthermore can recover the state of the auxiliary qubits to the original one after completing the computations. Since the recovered state can be employed in any other computations, we obtain that a single preparation of the auxiliary qubits in an arbitrarily mixed state is sufficient to implement the iterative procedure in the Simon algorithm or the period-finding algorithm.

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arXiv2005

Entanglement of three-qubit pure states in terms of teleportation capability

We define an entanglement measure, called the partial tangle, which represents the residual two-qubit entanglement of a three-qubit pure state. By its explicit calculations for three-qubit pure states, we show that the partial tangle is closely related to the faithfulness of a teleportation scheme over a three-qubit pure state.

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arXiv2004

Secure quantum cryptographic network based on quantum key distribution

We present a protocol for quantum cryptographic network consisting of a quantum network center and many users, in which any pair of parties with members chosen from the whole users on request can secure a quantum key distribution by help of the center. The protocol is based on the quantum authentication scheme given by Barnum et al. [Proc. 43rd IEEE Symp. FOCS'02, p. 449 (2002)]. We show that exploiting the quantum authentication scheme the center can safely make two parties share nearly perfect entangled states used in the quantum key distribution. This implies that the quantum cryptographic network protocol is secure against all kinds of eavesdropping.

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arXiv2003

Faithful sharing of multipartite entanglement over noisy quantum channels

We present a protocol in which two or more parties can share multipartite entanglement over noisy quantum channels. The protocol is based on the entanglement purification presented by Shor and Preskill [Phys. Rev. Lett. 85, 441 (2000)] and the quantum teleportation via an isotropic state. We show that a nearly perfect purification implies a nearly perfect sharing of multipartite entanglement between two parties so that the protocol can assure a faithful sharing of multipartite entanglement with Shor and Preskill's proof on the entanglement purification.

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arXiv2003

Entanglement swapping secures multiparty quantum communication

Extending the eavesdropping strategy devised by Zhang, Li and Guo [Phys. Rev. A 63, 036301 (2001)], we show that the multiparty quantum communication protocol based on entanglement swapping, which was proposed by Cabello [quant-ph/0009025], is not secure. We modify the protocol so that entanglement swapping can secure multiparty quantum communication, such as multiparty quantum key distribution and quantum secret sharing of classical information, and show that the modified protocol is secure against the Zhang-Li-Guo's strategy for eavesdropping as well as the basic intercept-resend attack.

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arXiv2003

Convex-roof extended negativity as an entanglement measure for bipartite quantum systems

We extend the concept of the negativity, a good measure of entanglement for bipartite pure states, to mixed states by means of the convex-roof extension. We show that the measure does not increase under local quantum operations and classical communication, and derive explicit formulae for the entanglement measure of isotropic states and Werner states, applying the formalism presented by Vollbrecht and Werner [Phys. Rev. A {\bf 64}, 062307 (2001)].

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arXiv2003

Entanglement for a two-parameter class of states in $2\otimes n$ quantum system

We exhibit a two-parameter class of states $ρ_{(α,γ)}$, in $2\otimes n$ quantum system for $n\ge 3$, which can be obtained from an arbitrary state by means of local quantum operations and classical communication, and which are invariant under all bilateral %unitary operations %of the form $U\otimes U$ on $2\otimes n$ quantum system. We calculate the negativity of $ρ_{(α,γ)}$, and a lower bound and a tight upper bound on its entanglement of formation. It follows from this calculation that the entanglement of formation of $ρ_{(α,γ)}$ cannot exceed its negativity.

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arXiv2000

Function-dependent Phase Transform in Quantum Computing

We construct a quantum algorithm that performs function-dependent phase transform and requires no initialization of an ancillary register. The algorithm recovers the initial state of an ancillary register regardless of whether its state is pure or mixed. Thus we can use any qubits as an ancillary register even though they are entangled with others and are occupied by other computational process. We also show that our algorithm is optimal in the sense of the number of function evaluations.

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arXiv2000

Quantum Algorithm for Generalized Deutsch-Jozsa Problem

We generalize the Deutsch-Jozsa problem and present a quantum algorithm that can solve the generalized Deutsch-Jozsa problem by a single evaluation of a given function. We discuss the initialization of an auxiliary register and present a generalized Deutsch-Jozsa algorithm that requires no initialization of an auxiliary register.

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arXiv2000

The f-conditioned Phase Transform

We present a quantum algorithm for the f-conditioned phase transform which does not require any initialization of ancillary register. We also develop a quantum algorithm that can solve the generalized Deutsch-Jozsa problem by a single evaluation of a function.

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