Kwek, Leong Chuan

We present a method of direct estimation of important properties of a shared bipartite quantum state, within the “distant laboratories” paradigm, using only local operations and classical communication. We apply this procedure to spectrum estimation of shared states, and locally implementable structural physical approximations to incompletely positive maps. This procedure can also be applied to the estimation of channel capacity and measures of entanglement.

We present a simple quantum network, based on the controlled-SWAP gate, that can extract certain properties of quantum states without recourse to quantum tomography. It can be used used as a basic building block for direct quantum estimations of both linear and non-linear functionals of any density operator. The network has many potential applications ranging from purity tests and eigenvalue estimations to direct characterization of some properties of quantum channels. Experimental realizations of the proposed network are within the reach of quantum technology that is currently being developed.

Quantum key distribution is a matured quantum science and technology. Over the last 20 years, there has been substantial research and development in this area. Recently, silicon technology has offered tremendous promise in the field for improved miniaturization of quantum key distribution through integrated photonic chips. We expect further progress in this area both in terms of protocols, photon sources, and photon detectors. This review captures some of the recent advances in this area.

We consider a generalization of Ekert's entanglement-based quantum cryptographic protocol where qubits are replaced by N - or d -dimensional systems (qudits). In order to study its robustness against optimal incoherent attacks, we derive the information gained by a potential eavesdropper during a cloning-based individual attack. In doing so, we generalize Cerf’s formalism for cloning machines and establish the form of the most general cloning machine that respects all the symmetries of the problem. We obtain an upper bound on the error rate that guarantees the confidentiality of qudit generalizations of the Ekert’s protocol for qubits.

Quantum synchronization has been a central topic in quantum nonlinear dynamics. Despite the rapid development in this field, very few have studied how to efficiently boost synchronization. Homodyne measurement emerges as one of the successful candidates for this task but preferably in the semiclassical regime. In our work, we focus on the phase synchronization of a harmonic-driven quantum Stuart–Landau oscillator and show that the enhancement induced by homodyne measurement persists into the quantum regime. Interestingly, optimal two-photon damping rates exist when the oscillator and driving are at resonance and with a small single-photon damping rate. We also report noise-induced enhancement in quantum synchronization when the single-photon damping rate is sufficiently large. Apart from these results, we discover that adding a squeezing Hamiltonian can further boost synchronization, especially in the semiclassical regime. Furthermore, the addition of squeezing causes the optimal two-photon pumping rates to shift and converge.

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.

We study the ground state properties of a 4-qubit spin glass like (SGL) chain with probes at the end of the chain and compare our results with the non-spin glass like (NSGL) case. The SGL is modeled as a spin chain with nearest-neighbor couplings, taking on normal variates with mean J and variance Δ2. The entanglement between the probes is used to detect any discontinuity in the ground state energy spectrum. For the NSGL case, it was found that the concurrence of the probes exhibits sharp transitions whenever there are abrupt changes in the energy spectrum. In particular, for the 4-qubit case, there is a sudden change in the ground state energy at an external magnetic fi eld B of around 0.66 (resulting in a drop in concurrence of the probes) and 1.7 (manifest as a spike). The latter spike persists for fi nite temperature case. For the SGL sample with sufficiently large Δ , however, the spike is absent. Thus, an absence in the spike could act as a possible signature of the presence of SGL eff ects. Moreover, the sudden drop in concurrence at B ≈ 0:66 does not disappear but gets smeared with increasing Δ. However, this drop can be accentuated with a smaller probe coupling. The finite temperature case is also briefly discussed.

The adiabatic approximation in open systems is formulated through the effective Hamiltonian approach. By introducing an ancilla, we embed the open system dynamics into a non-Hermitian quantum dynamics of a composite system, the adiabatic evolution of the open system is then defined as the adiabatic dynamics of the composite system. Validity and invalidity conditions for this approximation are established and discussed. A High-order adiabatic approximation for open systems is introduced. As an example, the adiabatic condition for an open spin- 1 2 particle in time-dependent magnetic fields is analyzed.

A repeat-until-success (RUS) measurement-based scheme for the implementation of the distributed quantum computation by using single-photon interference at a 50:50 beam splitter is proposed. It is shown that the 50:50 beam splitter can naturally project a suitably encoded matter-photon state to either a desired entangling gate-operated state of the matter qubits or to their initial state when the photon is detected. The recurrence of the initial state permits us to implement the desired entangling gate in a RUS way. To implement a distributed quantum computation we suggest an encoding method by means of the effect of dipole-induced transparency proposed recently [E. Waks and J. Vuckovic, Phys. Rev. Lett. 96, 153601 (2006)]. The effects of the unfavorable factors on our scheme are also discussed.