arXiv subjects

Christian Weedbrook

Publications and source records attributed to Christian Weedbrook.

At least 37 records · Page 2Linked to original sources

arXiv2017

Quantum supremacy and high-dimensional integration

We establish a connection between continuous-variable quantum computing and high-dimensional integration by showing that the outcome probabilities of continuous-variable instantaneous quantum polynomial (CV-IQP) circuits are given by integrals of oscillating functions in large dimensions. We prove two results related to the classical hardness of evaluating these integrals: (i) we show that there exist circuits such that these integrals are approximations of a weighted sum of #P-hard problems and (ii) we prove that calculating these integrals is as hard as calculating integrals of arbitrary bounded functions. We then leverage these results to show that, given a plausible conjecture about the hardness of computing the integrals, approximate sampling from CV-IQP circuits cannot be done in polynomial time on a classical computer unless the polynomial hierarchy collapses to the third level. Our results hold even in the presence of finite squeezing and limited measurement precision, without an explicit need for fault-tolerance.

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arXiv2017

Gaussian Boson Sampling for perfect matchings of arbitrary graphs

A famously hard graph problem with a broad range of applications is computing the number of perfect matchings, that is the number of unique and complete pairings of the vertices of a graph. We propose a method to estimate the number of perfect matchings of undirected graphs based on the relation between Gaussian Boson Sampling and graph theory. The probability of measuring zero or one photons in each output mode is directly related to the hafnian of the adjacency matrix, and thus to the number of perfect matchings of a graph. We present encodings of the adjacency matrix of a graph into a Gaussian state and show strategies to boost the sampling success probability. With our method, a Gaussian Boson Sampling device can be used to estimate the number of perfect matchings significantly faster and with lower energy consumption compared to a classical computer.

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arXiv2017

Continuous-variable quantum key distribution in fast fading channels

We investigate the performance of several continuous-variable quantum key distribution protocols in the presence of fading channels. These are lossy channels whose transmissivity changes according to a probability distribution. This is typical in communication scenarios where remote parties are connected by free-space links subject to atmospheric turbulence. In this work, we assume the worst-case scenario where an eavesdropper has full control of a fast fading process, so that she chooses the instantaneous transmissivity of a channel, while the remote parties can only detect the mean statistical process. In our study, we consider coherent-state protocols run in various configurations, including the one-way switching protocol in reverse reconciliation, the measurement-device-independent protocol in the symmetric configuration and a three-party measurement-device-independent network. We show that, regardless of the advantage given to the eavesdropper (full control of fading), these protocols can still achieve high rates.

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arXiv2016

Continuous-time limit of topological quantum walks

We derive the continuous-time limit of discrete quantum walks with topological phases. We show the existence of a continuous-time limit that preserves their topological phases. We consider both simple-step and split-step walks, and derive analytically equations of motion governing their behavior. We obtain simple analytical solutions showing the existence of bound states at the boundary of two phases, and solve the equations of motion numerically in the bulk.

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arXiv2016

Quantum machine learning over infinite dimensions

Machine learning is a fascinating and exciting field within computer science. Recently, this excitement has been transferred to the quantum information realm. Currently, all proposals for the quantum version of machine learning utilize the finite-dimensional substrate of discrete variables. Here we generalize quantum machine learning to the more complex, but still remarkably practical, infinite-dimensional systems. We present the critical subroutines of quantum machine learning algorithms for an all-photonic continuous-variable quantum computer that achieve an exponential speedup compared to their equivalent classical counterparts. Finally, we also map out an experimental implementation which can be used as a blueprint for future photonic demonstrations.

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arXiv2016

Absolutely covert quantum communication

We present truly ultimate limits on covert quantum communication by exploiting quantum-mechanical properties of the Minkowski vacuum in the quantum field theory framework. Our main results are the following: We show how two parties equipped with Unruh-DeWitt detectors can covertly communicate at large distances without the need of hiding in a thermal background or relying on various technological tricks. We reinstate the information-theoretic security standards for reliability of asymptotic quantum communication and show that the rate of covert communication is strictly positive. Therefore, contrary to the previous conclusions, covert and reliable quantum communication is possible.

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arXiv2016

Practical quantum computing on encrypted data

The ability to perform computations on encrypted data is a powerful tool for protecting a client's privacy, especially in today's 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 hacker's computational power. Here we theoretically investigate, and experimentally demonstrate with Gaussian displacement and squeezing operations, a quantum solution that achieves the unconditional security of a user's 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, which can ultimately allow for the potential widespread adoption of this quantum technology in future cloud-based computing networks.

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arXiv2016

The power of one qumode for quantum computation

Although quantum computers are capable of solving problems like factoring exponentially faster than the best-known classical algorithms, determining the resources responsible for their computational power remains unclear. An important class of problems where quantum computers possess an advantage is phase estimation, which includes applications like factoring. We introduce a new computational model based on a single squeezed state resource that can perform phase estimation, which we call the power of one qumode. This model is inspired by an interesting computational model known as deterministic quantum computing with one quantum bit (DQC1). Using the power of one qumode, we identify that the amount of squeezing is sufficient to quantify the resource requirements of different computational problems based on phase estimation. In particular, it establishes a quantitative relationship between the resources required for factoring and DQC1. For example, we find the squeezing required to factor has an exponential scaling whereas no squeezing (i.e., a coherent state) is already sufficient to solve the hardest problem in DQC1.

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arXiv2016

How Discord underlies the Noise Resilience of Quantum Illumination

The benefits of entanglement can outlast entanglement itself. In quantum illumination, entanglement is employed to better detect reflecting objects in environments so noisy that all entanglement is destroyed. Here, we show that quantum discord - a more resilient form of quantum correlations - explains the resilience of quantum illumination. We introduce a quantitative relation between the performance gain in quantum illumination and the amount of discord used to encode information about the presence or absence of a reflecting object. This highlights discord's role preserving the benefits of entanglement in entanglement breaking noise.

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arXiv2015

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 Schrödinger 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.

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arXiv2015

MDI-QKD: Continuous- versus discrete-variables at metropolitan distances

In a comment, Xu, Curty, Qi, Qian, and Lo claimed that discrete-variable (DV) measurement device independent (MDI) quantum key distribution (QKD) would compete with its continuous-variable (CV) counterpart at metropolitan distances. Actually, Xu et al.'s analysis supports exactly the opposite by showing that the experimental rate of our CV protocol (achieved with practical room-temperature devices) remains one order of magnitude higher than their purely-numerical and over-optimistic extrapolation for qubits, based on nearly-ideal parameters and cryogenic detectors (unsuitable solutions for a realistic metropolitan network, which is expected to run on cheap room-temperature devices, potentially even mobile). The experimental rate of our protocol (expressed as bits per relay use) is confirmed to be two-three orders of magnitude higher than the rate of any realistic simulation of practical DV-MDI-QKD over short-medium distances. Of course this does not mean that DV-MDI-QKD networks should not be investigated or built, but increasing their rate is a non-trivial practical problem clearly beyond the analysis of Xu et al. Finally, in order to clarify the facts, we also refute a series of incorrect arguments against CV-MDI-QKD and, more generally, CV-QKD, which were made by Xu et al. with the goal of supporting their thesis.

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arXiv2015

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.

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arXiv2015

Advances in Quantum Teleportation

Quantum teleportation is one of the most important protocols in quantum information. By exploiting the physical resource of entanglement, quantum teleportation serves as a key primitive in a variety of quantum information tasks and represents an important building block for quantum technologies, with a pivotal role in the continuing progress of quantum communication, quantum computing and quantum networks. Here we review the basic theoretical ideas behind quantum teleportation and its variant protocols. We focus on the main experiments, together with the technical advantages and disadvantages associated with the use of the various technologies, from photonic qubits and optical modes to atomic ensembles, trapped atoms, and solid-state systems. Analysing the current state-of-the-art, we finish by discussing open issues, challenges and potential future implementations.

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arXiv2015

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 led 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 believed to be hard using a classical computer. Building on this, we give an experimental implementation based on cluster states that is feasible with today's technology.

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arXiv2015

Quantum Illumination at the Microwave Wavelengths

Quantum illumination is a quantum-optical sensing technique in which an entangled source is exploited to improve the detection of a low-reflectivity object that is immersed in a bright thermal background. Here we describe and analyze a system for applying this technique at microwave frequencies, a more appropriate spectral region for target detection than the optical, due to the naturally-occurring bright thermal background in the microwave regime. We use an electro-optomechanical converter to entangle microwave signal and optical idler fields, with the former being sent to probe the target region and the latter being retained at the source. The microwave radiation collected from the target region is then phase conjugated and upconverted into an optical field that is combined with the retained idler in a joint-detection quantum measurement. The error probability of this microwave quantum-illumination system, or quantum radar, is shown to be superior to that of any classical microwave radar of equal transmitted energy.

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arXiv2014

Replicating the benefits of closed timelike curves without breaking causality

In general relativity, closed timelike curves can break causality with remarkable and unsettling consequences. At the classical level, they induce causal paradoxes disturbing enough to motivate conjectures that explicitly prevent their existence. At the quantum level, resolving such paradoxes induce radical benefits - from cloning unknown quantum states to solving problems intractable to quantum computers. Instinctively, one expects these benefits to vanish if causality is respected. Here we show that in harnessing entanglement, we can efficiently solve NP-complete problems and clone arbitrary quantum states - even when all time-travelling systems are completely isolated from the past. Thus, the many defining benefits of closed timelike curves can still be harnessed, even when causality is preserved. Our results unveil the subtle interplay between entanglement and general relativity, and significantly improve the potential of probing the radical effects that may exist at the interface between relativity and quantum theory.

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arXiv2014

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

In order 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. We find that our scheme offers benefits in terms of the expected time until success, although we require a primitive quantum memory.

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arXiv2014

High-rate quantum cryptography in untrusted networks

We extend the field of continuous-variable quantum cryptography to a network formulation where two honest parties connect to an untrusted relay by insecure quantum links. To generate secret correlations, they transmit coherent states to the relay where a continuous-variable Bell detection is performed and the outcome broadcast. Even though the detection could be fully corrupted and the links subject to optimal coherent attacks, the honest parties can still extract a secret key, achieving high rates when the relay is proximal to one party, as typical in public networks with access points or proxy servers. Our theory is confirmed by an experiment generating key-rates which are orders of magnitude higher than those achievable with discrete-variable protocols. Thus, using the cheapest possible quantum resources, we experimentally show the possibility of high-rate quantum key distribution in network topologies where direct links are missing between end-users and intermediate relays cannot be trusted.

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