L. C. Kwek

Quantum nonlocality of four-qubit entangled states

We derive a Bell inequality for testing violation of local realism. Quantum nonlocality of several four-qubit states is investigated. These include the Greenberger-Zeilinger-Horne (GHZ) state, W state, linear cluster state, and the state |{chi}> that has recently been proposed in [Phys. Rev. Lett. 96, 060502 (2006)]. The Bell inequality is optimally violated by |{chi}> but not violated by the GHZ state. The linear cluster state also violates the Bell inequality though not optimally. The state |{chi}> can thus be discriminated from the linear cluster state by using the inequality. Different aspects of four-partite entanglement are also studied by considering the usefulness of a family of four-qubit mixed states as resources for two-qubit teleportation. Our results generalize those in [Phys. Rev. Lett. 72, 797 (1994)].

Quantum prisoner dilemma under decoherence

It has recently been established that quantum strategies are superior to classical ones for games such as the prisoners dilemma. However, quantum states are subject to decoherence. In this Letter, we investigate the effects of decoherence on a quantum game, namely the prisoner dilemma, through three prototype decoherence channels. We show that in the case of prisoner dilemma, the Nash equilibria are not changed by the effects of decoherence for maximally entangled states.

Geometric phase for entangled states of two spin-1/2 particles in rotating magnetic field

The geometric phase for states of two spin-1/2 particles in rotating magnetic field is calculated, in particular, the noncyclic and cyclic non-adiabatic phases for the general case are explicitly derived and discussed. We find that the cyclic geometric phase for the entangled state can always be written as a sum of the phases of the two particles respectively; the same cannot be said for the noncyclic phase. We also investigate the geometric phase of mixed state of one particle in a biparticle system, and we find that the geometric phase for one subsystem of an entangled system is always affected by another subsystem of the entangled system.

Quantum computation in noiseless subsystems with fast non-Abelian holonomies

Quantum-information processing requires a high degree of isolation from the detrimental effects of the environment as well as an extremely precise level of control of the way quantum dynamics unfolds in the information-processing system. In this paper we show how these two goals can be ideally achieved by hybridizing the concepts of noiseless subsystems and of holonomic quantum computation. An all-geometric universal computation scheme based on nonadiabatic and non-Abelian quantum holonomies embedded in a four-qubit noiseless subsystem for general collective decoherence is proposed. The implementation details of this synergistic scheme along with the analysis of its stability against symmetry-breaking imperfections are presented.

Non-classical effects of two-mode photon-added displaced squeezed states

Photon-added states which could be detected through the emission rather than absorption of electromagnetic radiation have recently been actively explored and investigated. In this paper, we study the non-classical effects associated with two-mode photon-added displaced squeezed states and discuss some of their intriguing non-classical behaviour.

Operator-sum representation of time-dependent density operators and its applications

We show that any arbitrary time-dependent density operator of an open system can always be described in terms of an operator-sum representation (Kraus representation) regardless of its initial condition and the path of its evolution in the state space, and we provide a general expression of Kraus operators for arbitrary time-dependent density operator of an N-dimensional system. Moreover, applications of our result are illustrated through several examples.

Kraus representation for the density operator of a qubit

We show that the time evolution of density operator of open qubit system can always be described in terms of the Kraus representation. A general scheme on how to construct the Kraus operators for an open qubit system is proposed, which can be generalized to open higher dimensional quantum systems.We show that the time evolution of the density operator of a qubit can always be described in terms of the Kraus representation. A general scheme on how to construct the Kraus operators for an open qubit system is proposed, which can be generalized to open higher dimensional quantum systems.

Entanglement purification based on photonic polarization parity measurements

We present an entanglement purification protocol for photonic mixed entangled states based on the two-mode polarization nondemolition parity detectors. Without the use of the controlled-NOT (CNOT) operations, the efficiency of our protocol can nearly approach that of the CNOT protocol. The total successful probability of our protocol can be nearly enhanced to the quantity twice as large as that of the linear-optics-based protocol. Besides, our protocol adopts common photon detectors rather than the sophisticated single-photon detectors required in the linear-optics-based protocol.

Unified approach for exactly solvable potentials in quantum mechanics using shift operators

We present a unified approach for solving and classifying exactly solvable potentials. Our unified approach encompasses many well-known exactly solvable potentials. Moreover, the new approach can be used to search systematically for a new class of solvable potentials.

Quantum cryptography: Security criteria reexamined

We find that the generally accepted security criteria are flawed for a whole class of protocols for quantum cryptography. This is so because a standard assumption of the security analysis, namely that the so-called square-root measurement is optimal for eavesdropping purposes, is not true in general. There are rather large parameter regimes in which the optimal measurement extracts substantially more information than the square-root measurement.