International Journal of Quantum Information, 2008
We show that any M ≥ 2 distant parties who independently share the complete classical knowledge o... more We show that any M ≥ 2 distant parties who independently share the complete classical knowledge of a secret qubit state can collectively prepare the state at another remote location. Two distinct schemes for such a task are proposed: one via a single (M + 1)partite GHZ-type state and the other via M EPR-type pairs. Analytical expressions of the total success probability are derived explicitly for both the schemes. Of interest is the M -dependence of both the success probability and the receiver's action. We also construct simple quantum circuits for the two-qubit operators whose execution is necessary to accomplish the schemes.
We investigate the robustness of multiparty nonlocality under local decoherence, acting independe... more We investigate the robustness of multiparty nonlocality under local decoherence, acting independently and equally on each subsystems. To be specific, we consider an N-qubit GHZ state under depolarization, dephasing, or dissipation channel, and tested the nonlocality by violation of Mermin-Klyshko inequality, which is one of Bell's inequalities for multi-qubit systems. The results show that the robustness of nonlocality increases with the number of qubits, and that the nonlocality of an N-qubit GHZ state with even N is extremely persistent against dephasing.
We give a Shor-Preskill type security-proof to the quantum key distribution without public announ... more We give a Shor-Preskill type security-proof to the quantum key distribution without public announcement of bases [W.Y. Hwang et al., Phys. Lett. A 244, 489 (1998)]. First, we modify the Lo-Chau protocol once more so that it finally reduces to the quantum key distribution without public announcement of bases. Then we show how we can estimate the error rate in the code bits based on that in the checked bits in the proposed protocol, that is the central point of the proof. We discuss the problem of imperfect sources and that of large deviation in the error rate distributions. We discuss when the bases sequence must be discarded.
A single-particle entangled state can be generated by illuminating a beam splitter with a single ... more A single-particle entangled state can be generated by illuminating a beam splitter with a single photon. Quantum teleportation utilizing such a single-particle entangled state can be successfully achieved with a simple setup consisting only of linear optical devices such as beam splitters and phase shifters. Application of the locality assumption to a single-particle entangled state leads to Bell's inequality, a violation of which signifies the nonlocal nature of a single particle.
We present an efficient scheme to generate two-mode SU(2) macroscopic quantum superposition (Schr... more We present an efficient scheme to generate two-mode SU(2) macroscopic quantum superposition (Schr\"odinger cat) states, entangled number states and entangled coherent states for the vibrational motion of an ion trapped in a two-dimensional harmonic potential well. We also show that the same scheme can be used to realize a Fredkin gate operation.
A quantum cryptography scheme based on entanglement between a single particle state and a vacuum ... more A quantum cryptography scheme based on entanglement between a single particle state and a vacuum state is proposed. The scheme utilizes linear optics devices to detect the superposition of the vacuum and single particle states. Existence of an eavesdropper can be detected by using a variant of Bell's inequality.
We consider a quantum circuit in which shift and rotation operations on qubits are performed by s... more We consider a quantum circuit in which shift and rotation operations on qubits are performed by swap gates and controlled swap gates. These operations can be useful for quantum computers performing elementary arithmetic operations such as multiplication and a bit-wise comparison of qubits.
Identifying the Bolch sphere with the Riemann sphere(the extended complex plane), we obtain relat... more Identifying the Bolch sphere with the Riemann sphere(the extended complex plane), we obtain relations between single qubit unitary operations and M\"{o}bius transformations on the extended complex plane.
Defining a computational basis of pseudo-number states, we interpret a coherent state of large am... more Defining a computational basis of pseudo-number states, we interpret a coherent state of large amplitude, |α| ≫ d 2π , as a qudit -a d-level quantum system -in a state that is an even superposition of d pseudo-number states. A pair of such coherent-state qudits can be prepared in maximally entangled state by generalized Controlled-Z operation that is based on cross-Kerr nonlinearity, which can be weak for large d. Hence, a coherent-state optical qudit cluster state can be prepared by repetitive application of the generalized Controlled-Z operation to a set of coherent states. We thus propose an optical qudit teleportation as a simple demonstration of cluster state quantum computation.
International Journal of Quantum Information, 2008
We show that any M ≥ 2 distant parties who independently share the complete classical knowledge o... more We show that any M ≥ 2 distant parties who independently share the complete classical knowledge of a secret qubit state can collectively prepare the state at another remote location. Two distinct schemes for such a task are proposed: one via a single (M + 1)partite GHZ-type state and the other via M EPR-type pairs. Analytical expressions of the total success probability are derived explicitly for both the schemes. Of interest is the M -dependence of both the success probability and the receiver's action. We also construct simple quantum circuits for the two-qubit operators whose execution is necessary to accomplish the schemes.
We investigate the robustness of multiparty nonlocality under local decoherence, acting independe... more We investigate the robustness of multiparty nonlocality under local decoherence, acting independently and equally on each subsystems. To be specific, we consider an N-qubit GHZ state under depolarization, dephasing, or dissipation channel, and tested the nonlocality by violation of Mermin-Klyshko inequality, which is one of Bell's inequalities for multi-qubit systems. The results show that the robustness of nonlocality increases with the number of qubits, and that the nonlocality of an N-qubit GHZ state with even N is extremely persistent against dephasing.
We give a Shor-Preskill type security-proof to the quantum key distribution without public announ... more We give a Shor-Preskill type security-proof to the quantum key distribution without public announcement of bases [W.Y. Hwang et al., Phys. Lett. A 244, 489 (1998)]. First, we modify the Lo-Chau protocol once more so that it finally reduces to the quantum key distribution without public announcement of bases. Then we show how we can estimate the error rate in the code bits based on that in the checked bits in the proposed protocol, that is the central point of the proof. We discuss the problem of imperfect sources and that of large deviation in the error rate distributions. We discuss when the bases sequence must be discarded.
A single-particle entangled state can be generated by illuminating a beam splitter with a single ... more A single-particle entangled state can be generated by illuminating a beam splitter with a single photon. Quantum teleportation utilizing such a single-particle entangled state can be successfully achieved with a simple setup consisting only of linear optical devices such as beam splitters and phase shifters. Application of the locality assumption to a single-particle entangled state leads to Bell's inequality, a violation of which signifies the nonlocal nature of a single particle.
We present an efficient scheme to generate two-mode SU(2) macroscopic quantum superposition (Schr... more We present an efficient scheme to generate two-mode SU(2) macroscopic quantum superposition (Schr\"odinger cat) states, entangled number states and entangled coherent states for the vibrational motion of an ion trapped in a two-dimensional harmonic potential well. We also show that the same scheme can be used to realize a Fredkin gate operation.
A quantum cryptography scheme based on entanglement between a single particle state and a vacuum ... more A quantum cryptography scheme based on entanglement between a single particle state and a vacuum state is proposed. The scheme utilizes linear optics devices to detect the superposition of the vacuum and single particle states. Existence of an eavesdropper can be detected by using a variant of Bell's inequality.
We consider a quantum circuit in which shift and rotation operations on qubits are performed by s... more We consider a quantum circuit in which shift and rotation operations on qubits are performed by swap gates and controlled swap gates. These operations can be useful for quantum computers performing elementary arithmetic operations such as multiplication and a bit-wise comparison of qubits.
Identifying the Bolch sphere with the Riemann sphere(the extended complex plane), we obtain relat... more Identifying the Bolch sphere with the Riemann sphere(the extended complex plane), we obtain relations between single qubit unitary operations and M\"{o}bius transformations on the extended complex plane.
Defining a computational basis of pseudo-number states, we interpret a coherent state of large am... more Defining a computational basis of pseudo-number states, we interpret a coherent state of large amplitude, |α| ≫ d 2π , as a qudit -a d-level quantum system -in a state that is an even superposition of d pseudo-number states. A pair of such coherent-state qudits can be prepared in maximally entangled state by generalized Controlled-Z operation that is based on cross-Kerr nonlinearity, which can be weak for large d. Hence, a coherent-state optical qudit cluster state can be prepared by repetitive application of the generalized Controlled-Z operation to a set of coherent states. We thus propose an optical qudit teleportation as a simple demonstration of cluster state quantum computation.
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Papers by Jaewan Kim