arXiv subjects

A. P. Lund

Publications and source records attributed to A. P. Lund.

At least 19 recordsLinked to original sources

arXiv2021

Reconstruction of photon number conditioned states using phase randomized homodyne measurements

We experimentally demonstrate the reconstruction of a photon number conditioned state without using a photon number discriminating detector. By using only phase randomized homodyne measurements, we reconstruct up to the three photon subtracted squeezed vacuum state. The reconstructed Wigner functions of these states show regions of pronounced negativity, signifying the non-classical nature of the reconstructed states. The techniques presented allow for complete characterization of the role of a conditional measurement on an ensemble of states, and might prove useful in systems where photon counting still proves technically challenging.

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arXiv2017

Exact Boson Sampling using Gaussian continuous variable measurements

BosonSampling is a quantum mechanical task involving Fock basis state preparation and detection and evolution using only linear interactions. A classical algorithm for producing samples from this quantum task cannot be efficient unless the polynomial hierarchy of complexity classes collapses, a situation believe to be highly implausible. We present method for constructing a device which uses Fock state preparations, linear interactions and Gaussian continuous-variable measurements for which one can show exact sampling would be hard for a classical algorithm in the same way as Boson Sampling. The detection events used from this arrangement does not allow a similar conclusion for the classical hardness of approximate sampling to be drawn. We discuss the details of this result outlining some specific properties that approximate sampling hardness requires.

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arXiv2017

Quantum Sampling Problems, BosonSampling and Quantum Supremacy

There is a large body of evidence for the potential of greater computational power using information carriers that are quantum mechanical over those governed by the laws of classical mechanics. But the question of the exact nature of the power contributed by quantum mechanics remains only partially answered. Furthermore, there exists doubt over the practicality of achieving a large enough quantum computation that definitively demonstrates quantum supremacy. Recently the study of computational problems that produce samples from probability distributions has added to both our understanding of the power of quantum algorithms and lowered the requirements for demonstration of fast quantum algorithms. The proposed quantum sampling problems do not require a quantum computer capable of universal operations and also permit physically realistic errors in their operation. This is an encouraging step towards an experimental demonstration of quantum algorithmic supremacy. In this paper, we will review sampling problems and the arguments that have been used to deduce when sampling problems are hard for classical computers to simulate. Two classes of quantum sampling problems that demonstrate the supremacy of quantum algorithms are BosonSampling and IQP Sampling. We will present the details of these classes and recent experimental progress towards demonstrating quantum supremacy in BosonSampling.

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arXiv2016

Models of reduced-noise, probabilistic linear amplifiers

We construct an amplifier that interpolates between a nondeterministic, immaculate linear amplifier and a deterministic, ideal linear amplifier and beyond to nonideal linear amplifiers. The construction involves cascading an immaculate linear amplifier that has amplitude gain $g_1$ with a (possibly) nonideal linear amplifier that has gain $g_2$. With respect to normally ordered moments, the device has output noise $μ^2(G^2-1)$ where $G=g_1 g_2$ is the overall amplitude gain and $μ^2$ is a noise parameter. When $μ^2\ge1$, our devices realize ideal ($μ^2=1$) and nonideal ($μ^2>1$) linear amplifiers. When $0\leμ^2<1$, these devices work effectively only over a restricted region of phase space and with some subunity success probability $p_{\checkmark}$. We investigate the performance of our $μ^2$-amplifiers in terms of a gain-corrected probability-fidelity product and the ratio of input to output signal-to-noise ratios corrected for success probability.

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arXiv2013

Boson Sampling from Gaussian States

We pose a generalized Boson Sampling problem. Strong evidence exists that such a problem becomes intractable on a classical computer as a function of the number of Bosons. We describe a quantum optical processor that can solve this problem efficiently based on Gaussian input states, a linear optical network and non-adaptive photon counting measurements. All the elements required to build such a processor currently exist. The demonstration of such a device would provide the first empirical evidence that quantum computers can indeed outperform classical computers and could lead to applications.

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arXiv2013

Generation of distributed entangled coherent states over a lossy environment with inefficient detectors

Entangled coherent states are useful for various applications in quantum information processing but they are are sensitive to loss. We propose a scheme to generate distributed entangled coherent states over a lossy environment in such a way that the fidelity is independent of the losses at detectors heralding the generation of the entanglement. We compare our scheme with a previous one for the same purpose [Ourjoumtsev {\em et al.}, Nat. Phys. {\bf 5} 189 (2009)] and find parameters for which our new scheme results in superior performance.

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arXiv2013

Optimal architecture for a non-deterministic noiseless linear amplifier

Non-deterministic quantum noiseless linear amplifiers are a new technology with interest in both fundamental understanding and new applications. With a noiseless linear amplifier it is possible to perform tasks such as improving the performance of quantum key distribution and purifying lossy channels. Previous designs for noiseless linear amplifiers involving linear optics and photon counting are non-optimal because they have a probability of success lower than the theoretical bound given by the theory of generalised quantum measurement. This paper develops a theoretical model which reaches this limit. We calculate the fidelity and probability of success of this new model for coherent states and Einstein-Podolsky-Rosen (EPR) entangled states.

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arXiv2011

Photon number discrimination without a photon counter and its application to reconstructing non-Gaussian states

The non-linearity of a conditional photon-counting measurement can be used to `de-Gaussify' a Gaussian state of light. Here we present and experimentally demonstrate a technique for photon number resolution using only homodyne detection. We then apply this technique to inform a conditional measurement; unambiguously reconstructing the statistics of the non-Gaussian one and two photon subtracted squeezed vacuum states. Although our photon number measurement relies on ensemble averages and cannot be used to prepare non-Gaussian states of light, its high efficiency, photon number resolving capabilities, and compatibility with the telecommunications band make it suitable for quantum information tasks relying on the outcomes of mean values.

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arXiv2011

Efficient quantum computing with weak measurements

Projective measurements with high quantum efficiency is often assumed to be required for efficient circuit based quantum computing. We argue that this is not the case and show that this fact has actually be known previously though not deeply explored. We examine this issue by giving an example of how to perform the quantum ordering finding algorithm efficiently using non-local weak measurements given that the measurements used are of bounded weakness and some fixed but arbitrary probability of success less than unity is required. We also show that it is possible to perform the same computation with only local weak measurements but this must necessarily introduce an exponential overhead.

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arXiv2010

Measuring measurement--disturbance relationships with weak values

Using formal definitions for measurement precision ε and disturbance (measurement backaction) η, Ozawa [Phys. Rev. A 67, 042105 (2003)] has shown that Heisenberg's claimed relation between these quantities is false in general. Here we show that the quantities introduced by Ozawa can be determined experimentally, using no prior knowledge of the measurement under investigation --- both quantities correspond to the root-mean-squared difference given by a weak-valued probability distribution. We propose a simple three-qubit experiment which would illustrate the failure of Heisenberg's measurement--disturbance relation, and the validity of an alternative relation proposed by Ozawa.

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arXiv2009

Noiseless Linear Amplification and Distillation of Entanglement

The idea of signal amplification is ubiquitous in the control of physical systems, and the ultimate performance limit of amplifiers is set by quantum physics. Increasing the amplitude of an unknown quantum optical field, or more generally any harmonic oscillator state, must introduce noise. This linear amplification noise prevents the perfect copying of the quantum state, enforces quantum limits on communications and metrology, and is the physical mechanism that prevents the increase of entanglement via local operations. It is known that non-deterministic versions of ideal cloning and local entanglement increase (distillation) are allowed, suggesting the possibility of non-deterministic noiseless linear amplification. Here we introduce, and experimentally demonstrate, such a noiseless linear amplifier for continuous-variables states of the optical field, and use it to demonstrate entanglement distillation of field-mode entanglement. This simple but powerful circuit can form the basis of practical devices for enhancing quantum technologies. The idea of noiseless amplification unifies approaches to cloning and distillation, and will find applications in quantum metrology and communications.

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arXiv2008

Nondeterministic Noiseless Linear Amplification of Quantum Systems

We introduce the concept of non-deterministic noiseless linear amplification. We propose a linear optical realization of this transformation that could be built with current technology. We discuss two applications; ideal probabilistic cloning of coherent states and distillation of continuous variable entanglement. For the latter example we demonstrate that highly pure entanglement can be distilled from transmission over a lossy channel.

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arXiv2007

Fault-tolerant linear optical quantum computing with small-amplitude coherent states

Quantum computing using two optical coherent states as qubit basis states has been suggested as an interesting alternative to single photon optical quantum computing with lower physical resource overheads. These proposals have been questioned as a practical way of performing quantum computing in the short term due to the requirement of generating fragile diagonal states with large coherent amplitudes. Here we show that by using a fault-tolerant error correction scheme, one need only use relatively small coherent state amplitudes ($α> 1.2$) to achieve universal quantum computing. We study the effects of small coherent state amplitude and photon loss on fault tolerance within the error correction scheme using a Monte Carlo simulation and show the quantity of resources used for the first level of encoding is orders of magnitude lower than the best known single photon scheme. %We study this reigem using a Monte Carlo simulation and incorporate %the effects of photon loss in this simulation.

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arXiv2006

Non-Gaussian, Mixed Continuous-Variable Entangled States

We study a class of mixed non-Gaussian entangled states that, whilst closely related to Gaussian entangled states, none-the-less exhibit distinct properties previously only associated with more exotic, pure non-Gaussian states.

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arXiv2005

Adaptive Phase Measurements in Linear Optical Quantum Computation

Photon counting induces an effective nonlinear optical phase shift on certain states derived by linear optics from single photons. Although this no nlinearity is nondeterministic, it is sufficient in principle to allow scalable linear optics quantum computation (LOQC). The most obvious way to encode a qubit optically is as a superposition of the vacuum and a single photon in one mode -- so-called "single-rail" logic. Until now this approach was thought to be prohibitively expensive (in resources) compared to "dual-rail" logic where a qubit is stored by a photon across two modes. Here we attack this problem with real-time feedback control, which can realize a quantum-limited phase measurement on a single mode, as has been recently demonstrated experimentally. We show that with this added measurement resource, the resource requirements for single-rail LOQC are not substantially different from those of dual-rail LOQC. In particular, with adaptive phase measurements an arbitrary qubit state $α\ket{0} + β\ket{1}$ can be prepared deterministically.

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arXiv2005

Production of superpositions of coherent states in traveling optical fields with inefficient photon detection

We develop an all-optical scheme to generate superpositions of macroscopically distinguishable coherent states in traveling optical fields. It non-deterministically distills coherent state superpositions (CSSs) with large amplitudes out of CSSs with small amplitudes using inefficient photon detection. The small CSSs required to produce CSSs with larger amplitudes are extremely well approximated by squeezed single photons. We discuss some remarkable features of this scheme: it effectively purifies mixed initial states emitted from inefficient single photon sources and boosts negativity of Wigner functions of quantum states.

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arXiv2004

Coherent state LOQC gates using simplified diagonal superposition resource states

In this paper we explore the possibility of fundamental tests for coherent state optical quantum computing gates [T. C. Ralph, et. al, Phys. Rev. A \textbf{68}, 042319 (2003)] using sophisticated but not unrealistic quantum states. The major resource required in these gates are state diagonal to the basis states. We use the recent observation that a squeezed single photon state ($\hat{S}(r) \ket{1}$) approximates well an odd superposition of coherent states ($\ketα - \ket{-α}$) to address the diagonal resource problem. The approximation only holds for relatively small $α$ and hence these gates cannot be used in a scaleable scheme. We explore the effects on fidelities and probabilities in teleportation and a rotated Hadamard gate.

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arXiv2004

Conditional Production of Superpositions of Coherent States with Inefficient Photon Detection

It is shown that a linear superposition of two macroscopically distinguishable optical coherent states can be generated using a single photon source and simple all-optical operations. Weak squeezing on a single photon, beam mixing with an auxiliary coherent state, and photon detecting with imperfect threshold detectors are enough to generate a coherent state superposition in a free propagating optical field with a large coherent amplitude ($α>2$) and high fidelity ($F>0.99$). In contrast to all previous schemes to generate such a state, our scheme does not need photon number resolving measurements nor Kerr-type nonlinear interactions. Furthermore, it is robust to detection inefficiency and exhibits some resilience to photon production inefficiency.

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