Huy Nguyen Le

State complexity and quantum computation

The complexity of a quantum state may be closely related to the usefulness of the state for quantum computation. We discuss this link using the tree size of a multiqubit state, a complexity measure that has two noticeable (and, so far, unique) features: it is in principle computable, and non-trivial lower bounds can be obtained, hence identifying truly complex states. In this paper, we first review the definition of tree size, together with known results on the most complex three and four qubits states. Moving to the multiqubit case, we revisit a mathematical theorem for proving a lower bound on tree size that scales superpolynomially in the number of qubits. Next, states with superpolynomial tree size, the Immanant states, the Deutsch-Jozsa states, the Shors states and the subgroup states, are described. We show that the universal resource state for measurement based quantum computation, the 2D-cluster state, has superpolynomial tree size. Moreover, we show how the complexity of subgroup states and the 2D cluster state can be verified efficiently. The question of how tree size is related to the speed up achieved in quantum computation is also addressed. We show that superpolynomial tree size of the resource state is essential for measurement based quantum computation. The necessary role of large tree size in the circuit model of quantum computation is still a conjecture; and we prove a weaker version of the conjecture.

Robust self-testing of the three-qubitWstate

Self-testing is a device independent method which can be used to determine the nature of a physical system or device, without knowing any detail of the inner mechanism or the physical dimension of Hilbert space of the system. The only information required are the number of measurements, number of outputs of each measurement and the statistics of each measurement. Earlier works on self testing restricted either to two parties scenario or multipartite graph states. Here, we construct a method to self-test the three-qubit

Rabi oscillation in a quantum cavity: Markovian and non-Markovian dynamics

W

Rectification of light in the quantum regime

state, and show how to extend it to other pure three-qubit states. Our bounds are robust against the inevitable experimental errors.

Two photons on an atomic beam splitter: Nonlinear scattering and induced correlations

We investigate the Rabi oscillation of an atom placed inside a quantum cavity where each mirror is formed by a chain of atoms trapped near a one-dimensional waveguide. This proposal was studied previously with the use of Markov approximation, where the delay due to the finite travel time of light between the two cavity mirrors is neglected. We show that Rabi oscillation analogous to that obtained with high-finesse classical cavities is achieved only when this travel time is much larger than the time scale that characterizes the superradiant response of the mirrors. Therefore, the delay must be taken into account and the dynamics of the problem is inherently non-Markovian. Parameters of interest such as the Rabi frequency and the cavity loss rate due to photon leakage through the mirrors are obtained.

Proposal for monitoring and heralding position states of atoms in a one-dimensional waveguide

One of the missing elements for realising an integrated optical circuit is a rectifying device playing the role of an optical diode. A proposal based on a pair of two-level atoms strongly coupled to a one-dimensional waveguide showed a promising behavior based on a semiclassical study [Fratini et al., Phys. Rev. Lett. 113, 243601 (2014)]. Our study in the full quantum regime shows that, in such a device, rectification is a purely multiphoton effect. For an input field in a coherent state, rectification reaches up to

Rabi oscillation in a quantum cavity

70%

Linear and Nonlinear Two-Photon Bunching on an Atomic Beam Splitter

for the range of power in which one of the two atoms is excited, but not both.

A new breed of Schr\"odinger's cats: super-polynomial complex states

Optical emitters strongly coupled to photons propagating in one-dimensional waveguides are a promising platform for optical quantum information processing. Here, we present a theoretical study of the scattering of two indistinguishable photons on a single two-level atom in a Hong-Ou-Mandel set-up. By computing the dynamics, we can describe the system at any time of the scattering event. This allows us to highlight the one-to-one correspondence between the saturation of the atom and the effective interaction induced between the photons. Furthermore, we discuss the integrability of the atomic beamsplitter and provide an intuitive picture for the correlations observed between the outgoing photons.

Super-polynomial complex quantum states

We study the single-photon transport in a single-mode waveguide, in which two-level atoms in spatial superpositions are embedded. We find that the transmission of the photon can be used as a non-destructive probe for coherence of the superposition. The protocol proposed is shown to be independent of the distance between the wells in which the atoms are trapped. Furthermore, we show that by looking at the transmission in a suitable regime, a maximally entangled state can be post-selected from an unknown superposition.