arXiv subjects

Nathan Walk

Publications and source records attributed to Nathan Walk.

30 records · Page 2Linked to original sources

arXiv2019

Finite-size effects in continuous-variable QKD with Gaussian post-selection

In a continuous-variable quantum key distribution (CV-QKD) protocol, which is based on heterodyne detection at the receiver, the application of a noiseless linear amplifier (NLA) on the received signal before the detection can be emulated by the post-selection of the detection outcome. Such a post-selection, which is also called a measurement-based NLA, requires a cut-off to produce a normalisable filter function. Increasing the cut-off with respect to the received signals results in a more faithful emulation of the NLA and nearly Gaussian output statistics at the cost of discarding more data. While recent works have shown the benefits of post-selection via an asymptotic security analysis, we undertake the first investigation of such a post-selection utilising a composable security proof in the realistic finite-size regime, where this trade-off is extremely relevant. We show that this form of post-selection can improve the secure range of a CV-QKD over lossy thermal channels if the finite block size is sufficiently large and that the optimal value for the filter cut-off is typically in the non-Gaussian regime. The relatively modest improvement in the finite-size regime as compared to the asymptotic case highlights the need for new tools to prove the security of non-Gaussian cryptographic protocols. These results also represent a quantitative assessment of a measurement-based NLA with an entangled-state input in both the Gaussian and non-Gaussian regime.

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arXiv2019

Harnessing symmetry-protected topological order for quantum memories

Spin chains with symmetry-protected edge modes are promising candidates to realize intrinsically robust physical qubits that can be used for the storage and processing of quantum information. In any experimental realization of such physical systems, weak perturbations in the form of induced interactions and disorder are unavoidable and can be detrimental to the stored information. At the same time, the latter may in fact be beneficial; for instance by deliberately inducing disorder which causes the system to localize. In this work, we explore the potential of using an $XZX$ cluster Hamiltonian to encode quantum information into the local edge modes and comprehensively investigate the influence of both many-body interactions and disorder on their stability over time, adding substance to the narrative that many-body localization may stabilize quantum information. We recover the edge state at each time step, allowing us to reconstruct the quantum channel that captures the locally constrained out of equilibrium time evolution. With this representation in hand, we analyze how well classical and quantum information are preserved over time as a function of disorder and interactions. We find that the performance of the edge qubits varies dramatically between disorder realizations. Whereas some show a smooth decoherence over time, a sizeable fraction are rapidly rendered unusable as memories. We also find that the stability of the classical information -- a precursor for the usefulness of the chain as a quantum memory -- depends strongly on the direction in which the bit is encoded. When employing the chain as a genuine quantum memory, encoded qubits are most faithfully recovered for low interaction and high disorder.

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arXiv2018

Optimal realistic attacks in continuous-variable quantum key distribution

Quantum cryptographic protocols are typically analysed by assuming that potential opponents can carry out all physical operations, an assumption which grants capabilities far in excess of present technology. Adjusting this assumption to reflect more realistic capabilities is an attractive prospect, but one that can only be justified with a rigorous, quantitative framework that relates adversarial restrictions to the protocols security and performance. We investigate the effect of limitations on the eavesdropper's (Eve's) ability to make a coherent attack on the security of continuous-variable quantum key distribution (CV-QKD). We consider a realistic attack, in which the total decoherence induced during the attack is modelled by a Gaussian channel. Based on our decoherence model we propose an optimal hybrid attack, which allows Eve to perform a combination of both coherent and individual attacks simultaneously. We evaluate the asymptotic and composable finite-size security of a heterodyne CV-QKD protocol against such hybrid attacks in terms of Eve's decoherence. We show that when the decoherence is greater than a threshold value, Eve's most effective strategy is reduced to the individual attack. Thus, if we are willing to assume that the decoherence caused by the memory and the collective measurement is large enough, it is sufficient to analyse the security of the protocol only against individual attacks, which significantly improves the CV-QKD performance in terms of both the key rate and the maximum secure transmission distance.

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arXiv2016

Composably secure time-frequency quantum key distribution

We present a composable security proof, valid against arbitrary attacks and including finite-size effects, for a high dimensional time-frequency quantum key distribution (TFQKD) protocol based upon spectrally entangled photons. Previous works have focused on TFQKD schemes as it combines the impressive loss tolerance of single-photon QKD with the large alphabets of continuous variable (CV) schemes, which enables the potential for more than one bit of secret key per transmission. However, the finite-size security of such schemes has only been proven under the assumption of collective Gaussian attacks. Here, by combining recent advances in entropic uncertainty relations for CVQKD with decoy state analysis, we derive a composable security proof that predicts key rates on the order of Mbits/s over metropolitan distances (40km or less) and maximum transmission distances of up to 140km.

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arXiv2016

Experimental demonstration of Gaussian protocols for one-sided device-independent quantum key distribution

Nonlocal correlations, a longstanding foundational topic in quantum information, have recently found application as a resource for cryptographic tasks where not all devices are trusted, for example in settings with a highly secure central hub, such as a bank or government department, and less secure satellite stations which are inherently more vulnerable to hardware "hacking" attacks. The asymmetric phenomena of Einstein-Podolsky-Rosen steering plays a key role in one-sided device-independent quantum key distribution (1sDI-QKD) protocols. In the context of continuous-variable (CV) QKD schemes utilizing Gaussian states and measurements, we identify all protocols that can be 1sDI and their maximum loss tolerance. Surprisingly, this includes a protocol that uses only coherent states. We also establish a direct link between the relevant EPR steering inequality and the secret key rate, further strengthening the relationship between these asymmetric notions of nonlocality and device independence. We experimentally implement both entanglement-based and coherent-state protocols, and measure the correlations necessary for 1sDI key distribution up to an applied loss equivalent to 7.5 km and 3.5 km of optical fiber transmission respectively. We also engage in detailed modelling to understand the limits of our current experiment and the potential for further improvements. The new protocols we uncover apply the cheap and efficient hardware of CVQKD systems in a significantly more secure setting.

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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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arXiv2015

Observation of genuine one-way Einstein-Podolsky-Rosen steering

Within the hierarchy of inseparable quantum correlations, Einstein-Podolsky-Rosen steering is distinguished from both entanglement and Bell nonlocality by its asymmetry -- there exist conditions where the steering phenomenon changes from being observable to not observable, simply by exchanging the role of the two measuring parties. Whilst this one-way steering feature has been previously demonstrated for the restricted class of Gaussian measurements, for the general case of positive-operator-valued measures even its theoretical existence has only recently been settled. Here, we prove, and then experimentally observe, the one-way steerability of an experimentally practical class of entangled states in this general setting. As well as its foundational significance, the demonstration of fundamentally asymmetric nonlocality also has practical implications for the distribution of the trust in quantum communication networks.

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arXiv2014

Measurement-Based Noiseless Linear Amplification for Quantum Communication

Entanglement distillation is an indispensable ingredient in extended quantum communication networks. Distillation protocols are necessarily non-deterministic and require advanced experimental techniques such as noiseless amplification. Recently it was shown that the benefits of noiseless amplification could be extracted by performing a post-selective filtering of the measurement record to improve the performance of quantum key distribution. We apply this protocol to entanglement degraded by transmission loss of up to the equivalent of 100km of optical fibre. We measure an effective entangled resource stronger than that achievable by even a maximally entangled resource passively transmitted through the same channel. We also provide a proof-of-principle demonstration of secret key extraction from an otherwise insecure regime. The measurement-based noiseless linear amplifier offers two advantages over its physical counterpart: ease of implementation and near optimal probability of success. It should provide an effective and versatile tool for a broad class of entanglement-based quantum communication protocols.

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arXiv2014

Channel purification via continuous-variable quantum teleportation with Gaussian post-selection

We present a protocol based on continuous-variable quantum teleportation and Gaussian post- selection that can be used to correct errors introduced by a lossy channel. We first show that the global transformation enacted by the protocol is equivalent to an effective system composed of a noiseless amplification (or attenuation), and an effective quantum channel, which can in theory have no loss and an amount of thermal noise arbitrarily small, hence tending to an identity channel. An application of our protocol is the probabilistic purification of quantum non-Gaussian states using only Gaussian operations.

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arXiv2012

Non-deterministic noiseless amplification via non-symplectic phase space transformations

We analyse the action of an ideal noiseless linear amplifier operator, $g^\hat{n}$, using the Wigner function phase space representation. In this setting we are able to clarify the gain $g$ for which a physical output is produced when this operator is acted upon inputs other than coherent states. We derive compact closed form expressions for the action of $N$ local amplifiers, with potentially different gains, on arbitrary $N$-mode Gaussian states and provide several examples of the utility of this formalism for determining important quantities including amplification and the strength and purity of the distilled entanglement, and for optimising the use of the amplification in quantum information protocols.

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arXiv2012

Gaussian Post-selection for Continuous Variable Quantum Cryptography

We extend the security proof for continuous variable quantum key distribution protocols using post selection to account for arbitrary eavesdropping attacks by employing the concept of an equivalent protocol where the post-selection is implemented as a series of quantum operations including a virtual distillation. We introduce a particular `Gaussian' post selection and demonstrate that the security can be calculated using only experimentally accessible quantities. Finally we explicitly evaluate the performance for the case of a noisy Gaussian channel in the limit of unbounded key length and find improvements over all pre-existing continuous variable protocols in realistic regimes.

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arXiv2011

Security of Post-selection based Continuous Variable Quantum Key Distribution against Arbitrary Attacks

We extend the security proof for continuous variable quantum key distribution protocols using post selection to account for arbitrary eavesdropping attacks by employing the concept of an equiv- alent protocol where the post-selection is implemented as a projective quantum measurement. We demonstrate that the security can be calculated using only experimentally accessible quantities and finally explicitly evaluate the performance for the case of a noisy Gaussian channel in the limit of unbounded key length.

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