arXiv subjects
Publications and source records attributed to Dong Pyo Chi.
Using Tsallis-q entropy, we introduce the generalized concept of global quantum discord, namely the q-global quantum discord, and provide its analytic evaluation for two classes of multi-qubit states. We also provide a sufficient condition, for which the pairwise quantum correlations in terms of q-global quantum discord is monogamous in multi-party quantum systems.
We investigate the approximate quantum state sharing protocol based on random unitary channels, which is secure against any exterior or interior attackers in principle. Although the protocol leaks small information for a security parameter $ε$, the scheme still preserves its information-theoretic secrecy, and reduces some pre-shared classical secret keys for a private quantum channel between a sender and two receivers. The approximate private quantum channels constructed via random unitary channels play a crucial role in the proposed quantum state sharing protocol.
We show that a quantum channel $\mathcal{N}$ constructed by averaging over $\mathcal{O}(\log d/ε^2)$ randomly chosen unitaries gives a local $ε$-randomizing map with non-negative probability. The idea comes from a small $ε$-net construction on the higher dimensional unit sphere or quantum pure states. By exploiting the net, we analyze the concentrative phenomenon of an output reduced density matrix of the channel, and this analysis imply that there exists a local random unitary channel, with relatively small unitaries, generically.
We study a relation between the concurrence of assistance and the Mermin inequality on three-qubit pure states. We find that if a given three-qubit pure state has the minimal concurrence of assistance greater than 1/2 then the state violates some Mermin inequality.
Quantum bit commitment has been known to be impossible by the independent proofs of Mayers, and Lo and Chau, under the assumption that the whole quantum states right before the unveiling phase are static to users. We here provide an unconditionally secure non-static quantum bit commitment protocol with a trusted third party, which is not directly involved in any communications between users and can be limited not to get any information of commitment without being detected by users. We also prove that our quantum bit commitment protocol is not secure without the help of the trusted third party. The proof is basically different from the Mayers-Lo-Chau's no-go theorem, because we do not assume the staticity of the finally shared quantum states between users.
Dür [Phys. Rev. Lett. {\bf 87}, 230402 (2001)] constructed $N$-qubit bound entangled states which violate a Bell inequality for $N\ge 8$, and his result was recently improved by showing that there exists an $N$-qubit bound entangled state violating the Bell inequality if and only if $N\ge 6$ [Phys. Rev. A {\bf 79}, 032309 (2009)]. On the other hand, it has been also shown that the states which Dür considered violate Bell inequalities different from the inequality for $N\ge 6$. In this paper, by employing different forms of Bell inequalities, in particular, a specific form of Bell inequalities with $M$ settings of the measuring apparatus for sufficiently large $M$, we prove that there exists an $N$-qubit bound entangled state violating the $M$-setting Bell inequality if and only if $N\ge 4$.
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.
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 $\mathcal{C}_{A(BC)}>\mathcal{C}_{AC}^a$.
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.
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.
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.
We regard the Newcomb's Paradox as a reduction of the Prisoner's Dilemma and search for the considerable quantum solution. The all known classical solutions to the Newcomb's problem always imply that human has freewill and is due to the unfair set-up(including strategies)of the Newcomb's Problem. In this reason, we here substitute the asymmetric payoff matrix to the general form of the payoff matrix M and consider both of them use the same quantum strategy. As a result we obtained the fair Nash equilibrium, which is better than the case using classical strategies. This means that whether the supernatural being has the precognition or not depends only on the choice of strategy.
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.
In this paper, we investigate properties of some multi-particle entangled states and, from the properties applying the secret sharing present a new type of quantum key distribution protocols as generalization of quantum key distribution between two persons. In the protocols each group can retrieve the secure key string, only if all members in each group should cooperate with one another. We also show that the protocols are secure against an external eavesdropper using the intercept/resend strategy.
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.
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.
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)].
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.