Kevin Marshall

Repeat-until-success cubic phase gate for universal continuous-variable quantum computation

We report that to achieve universal quantum computation using continuous variables, one needs to jump out of the set of Gaussian operations and have a non-Gaussian element, such as the cubic phase gate. However, such a gate is currently very difficult to implement in practice. Here we introduce an experimentally viable “repeat-until-success” approach to generating the cubic phase gate, which is achieved using sequential photon subtractions and Gaussian operations. Ultimately, we find that our scheme offers benefits in terms of the expected time until success, as well as the fact that we do not require any complex off-line resource state, although we require a primitive quantum memory.

Continuous-variable quantum computing on encrypted data

The ability to perform computations on encrypted data is a powerful tool for protecting a clients privacy, especially in todays era of cloud and distributed computing. In terms of privacy, the best solutions that classical techniques can achieve are unfortunately not unconditionally secure in the sense that they are dependent on a hackers computational power. Here we theoretically investigate, and experimentally demonstrate with Gaussian displacement and squeezing operations, a quantum solution that achieves the security of a users privacy using the practical technology of continuous variables. We demonstrate losses of up to 10 km both ways between the client and the server and show that security can still be achieved. Our approach offers a number of practical benefits (from a quantum perspective) that could one day allow the potential widespread adoption of this quantum technology in future cloud-based computing networks.

Device-independent quantum cryptography for continuous variables

We present the first device-independent quantum cryptography protocol for continuous variables. Our scheme is based on the Gottesman-Kitaev-Preskill encoding scheme whereby a qubit is embedded in the infinite-dimensional space of a quantum harmonic oscillator. The novel application of discrete-variable device-independent quantum key distribution to this encoding enables a continuous-variable analogue. Since the security of this protocol is based on discrete-variables we inherit by default security against collective attacks and, under certain memoryless assumptions, coherent attacks. We find that our protocol is valid over the same distances as its discrete-variable counterpart, except that we are able to take advantage of high efficiency commercially available detectors where, for the most part, only homodyne detection is required. This offers the potential of removing the difficulty in closing the loopholes associated with Bell inequalities.

Noiseless Linear Amplifiers in Entanglement-Based Continuous-Variable Quantum Key Distribution

We propose a method to improve the performance of two entanglement-based continuous-variable quantum key distribution protocols using noiseless linear amplifiers. The two entanglement-based schemes consist of an entanglement distribution protocol with an untrusted source and an entanglement swapping protocol with an untrusted relay. Simulation results show that the noiseless linear amplifiers can improve the performance of these two protocols, in terms of maximal transmission distances, when we consider small amounts of entanglement, as typical in realistic setups.

Quantum simulation of quantum field theory using continuous variables

Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has lead to the point that continuous-variable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuous-variable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonic quantum field theory, a problem that is known to be hard using a classical computer. Thus, we give an experimental implementation based on cluster states that is feasible with todays technology.

Continuous-Variable Entanglement Swapping

We present a very brief overview of entanglement swapping as it relates to continuous-variable quantum information. The technical background required is discussed and the natural link to quantum teleportation is established before discussing the nature of Gaussian entanglement swapping. The limitations of Gaussian swapping are introduced, along with the general applications of swapping in the context of to quantum communication and entanglement distribution. In light of this, we briefly summarize a collection of entanglement swapping schemes which incorporate a non-Gaussian ingredient and the benefits of such schemes are noted. Finally, we motivate the need to further study and develop such schemes by highlighting requirements of a continuous-variable repeater.

Device-independent quantum key distribution with generalized two-mode Schrödinger cat states

We show how weak non-linearities can be used in a device-independent quantum key distribution (QKD) protocol using generalized two-mode Schrodinger cat states. The QKD protocol is therefore shown to be secure against collective attacks and for some coherent attacks. We derive analytical formulas for the optimal values of the Bell parameter, the quantum bit error rate, and the device-independent secret key rate in the noiseless lossy bosonic channel. Additionally, we give the filters and measurements which achieve these optimal values. We find that over any distance in this channel the quantum bit error rate is identically zero, in principle, and the states in the protocol are always able to violate a Bell inequality. The protocol is found to be superior in some regimes to a device-independent QKD protocol based on polarization entangled states in a depolarizing channel. Finally, we propose an implementation for the optimal filters and measurements.

Verifying cross-Kerr induced number squeezing: a case study

Abstract We analyse an experimental method for creating interesting nonclassical states by processing the entanglement generated when two large coherent states interact in a cross-Kerr medium. We specifically investigate the effects of loss and noise in every mode of the experiment, as well as the effect of ‘binning’ the post-selection outcomes. Even with these imperfections, we find an optimal set of currently achievable parameters which would allow a proof-of-principle demonstration of number squeezing in states with large mean photon number. We discuss other useful states which can be generated with the same experimental tools, including a class of states which contain coherent superpositions of differing photon numbers, e.g. good approximations to the state . Finally, we suggest one possible application of this state in the field of optomechanics.

Linear mode-mixing of phonons with trapped ions

Abstract We propose a method to manipulate the normal modes in a chain of trapped ions using only two lasers. Linear chains of trapped ions have proven experimentally to be highly controllable quantum systems with a variety of refined techniques for preparation, evolution, and readout; however, typically for quantum information processing applications people have been interested in using the internal levels of the ions as the computational basis. We analyze the case where the motional degrees of freedom of the ions are the quantum system of interest, and where the internal levels are leveraged to facilitate interactions. In particular, we focus on an analysis of mode-mixing of phonons in different normal modes to mimic the quantum optical equivalent of a beam splitter.

High-fidelity teleportation of continuous-variable quantum states with discrete-variable resources

Abstract The need for high fidelity quantum teleportation arises in a variety of quantum algorithms and protocols. Unfortunately, conventional continuous variable teleportation schemes rely on EPR states that yield a fidelity that approaches unity only in the limit of an unphysical amount of squeezing. A new method, which utilizes an ensemble of single photon entangled states to teleport continuous variable states with fidelity approaching unity with finite resources was recently proposed by Andersen and Ralph [Phys. Rev. Lett. 111, 050504 (2013)]. We extend these ideas to consider the general case of using maximally entangled states of an arbitrary dimension to teleport a continuous variable state and discuss how the corresponding results are affected.The need for high-fidelity quantum teleportation arises in a variety of quantum algorithms and protocols. Unfortunately, conventional continuous-variable teleportation schemes rely on Einstein–Podolsky–Rosen states that yield a fidelity that approaches unity only in the limit of an unphysical amount of squeezing. A new method that utilizes an ensemble of single photon entangled states, qubits, to teleport continuous variable (CV) states with fidelity approaching unity with finite resources was recently proposed by Andersen and Ralph [Phys. Rev. Lett.111, 050504 (2013)]. We extend these ideas to consider the general case of using maximally entangled d-level states, qudits, to teleport a CV state and discuss how the corresponding results are affected. In particular, we find that, by using qudits with dimension greater than two, we can achieve a higher fidelity with comparable resources.