arXiv subjects

G. Gilbert

Publications and source records attributed to G. Gilbert.

8 recordsLinked to original sources

arXiv2020

Magic DIAMOND: Multi-Fascicle Diffusion Compartment Imaging with Tensor Distribution Modeling and Tensor-Valued Diffusion Encoding

Diffusion tensor imaging provides increased sensitivity to microstructural tissue changes compared to conventional anatomical imaging but also presents limited specificity. To tackle this problem, the DIAMOND model subdivides the voxel content into diffusion compartments and draws from diffusion-weighted data to estimate compartmental non-central matrix-variate Gamma distribution of diffusion tensors, thereby resolving crossing fascicles while accounting for their respective heterogeneity. Alternatively, tensor-valued diffusion encoding defines new acquisition schemes tagging specific features of the intra-voxel diffusion tensor distribution directly from the outcome of the measurement. However, the impact of such schemes on estimating brain microstructural features has only been studied in a handful of parametric single-fascicle models. In this work, we derive a general Laplace transform for the non-central matrix-variate Gamma distribution, which enables the extension of DIAMOND to tensor-valued encoded data. We then evaluate this "Magic DIAMOND" model in silico and in vivo on various combinations of tensor-valued encoded data. Assessing uncertainty on parameter estimation via stratified bootstrap, we investigate both voxel-based and fixel-based metrics by carrying out multi-peak tractography. We show that our estimated metrics can be mapped along tracks robustly across regions of fiber crossing, which opens new perspectives for tractometry and microstructure mapping along specific white-matter tracts.

physics.med-ph↗

arXiv2007

Quantum Sensor Miniaturization

The classical bound on image resolution defined by the Rayleigh limit can be beaten by exploiting the properties of quantum mechanical entanglement. If entangled photons are used as signal states, the best possible resolution is instead given by the Heisenberg limit, an improvement proportional to the number of entangled photons in the signal. In this paper we present a novel application of entanglement by showing that the resolution obtained by an imaging system utilizing separable photons can be achieved by an imaging system making use of entangled photons, but with the advantage of a smaller aperture, thus resulting in a smaller and lighter system. This can be especially valuable in satellite imaging where weight and size play a vital role.

quant-ph↗

arXiv2006

On the use of photonic N00N states for practical quantum interferometry

The performance of photonic $N00N$ states, propagating in an attenuating medium, is analyzed with respect to phase estimation. It is shown that, for $N00N$ states propagating through a lossy medium, the Heisenberg limit is never achieved. It is also shown that, for a given value of $N$, a signal comprised of an attenuated separable state of $N$ photons will actually produce a better phase estimate than will a signal comprised of an equally attenuated $N00N$ state, unless the transmittance of the medium is very high. This is a consequence of the need to utilize measurement operators appropriate to the different signal states. The result is that, for most practical applications in realistic scenarios with attenuation, the resolution of $N00N$ state-based phase estimation not only does not achieve the Heisenberg Limit, but is actually worse than the Standard Quantum Limit. It is demonstrated that this performance deficit becomes more pronounced as the number, $N$, of photons in the signal increases.

quant-ph↗

arXiv2003

Practical Quantum Cryptography: A Comprehensive Analysis (Part One)

We perform a comprehensive analysis of practical quantum cryptography (QC) systems implemented in actual physical environments via either free-space or fiber-optic cable quantum channels for ground-ground, ground-satellite, air-satellite and satellite-satellite links. (1) We obtain universal expressions for the effective secrecy capacity and rate for QC systems taking into account three important attacks on individual quantum bits, including explicit closed-form expressions for the requisite amount of privacy amplification. Our analysis also includes the explicit calculation in detail of the total cost in bits of continuous authentication, thereby obtaining new results for actual ciphers of finite length. (2) We perform for the first time a detailed, explicit analysis of all systems losses due to propagation, errors, noise, etc. as appropriate to both optical fiber cable- and satellite communications-based implementations of QC. (3) We calculate for the first time all system load costs associated to classical communication and computational constraints that are ancillary to, but essential for carrying out, the pure QC protocol itself. (4) We introduce an extended family of generalizations of the Bennett-Brassard (BB84) QC protocol that equally provide unconditional secrecy but allow for the possibility of optimizing throughput rates against specific cryptanalytic attacks. (5) We obtain universal predictions for maximal rates that can be achieved with practical system designs under realistic environmental conditions. (6) We propose a specific QC system design that includes the use of a novel method of high-speed photon detection that may be able to achieve very high throughput rates for actual implementations in realistic environments.

quant-ph↗

arXiv2002

Secrecy, Computational Loads and Rates in Practical Quantum Cryptography

A number of questions associated with practical implementations of quantum cryptography systems having to do with unconditional secrecy, computational loads and effective secrecy rates in the presence of perfect and imperfect sources are discussed. The different types of unconditional secrecy, and their relationship to general communications security, are discussed in the context of quantum cryptography. In order to actually carry out a quantum cryptography protocol it is necessary that sufficient computational resources be available to perform the various processing steps, such as sifting, error correction, privacy amplification and authentication. We display the full computer machine instruction requirements needed to support a practical quantum cryptography implementation. We carry out a numerical comparison of system performance characteristics for implementations that make use of either weak coherent sources of light or perfect single photon sources, for eavesdroppers making individual attacks on the quantum channel characterized by different levels of technological capability. We find that, while in some circumstances it is best to employ perfect single photon sources, in other situations it is preferable to utilize weak coherent sources. In either case the secrecy level of the final shared cipher is identical, with the relevant distinguishing figure-of-merit being the effective throughput rate.

quant-ph↗

arXiv2001

Privacy Amplification in Quantum Key Distribution: Pointwise Bound versus Average Bound

In order to be practically useful, quantum cryptography must not only provide a guarantee of secrecy, but it must provide this guarantee with a useful, sufficiently large throughput value. The standard result of generalized privacy amplification yields an upper bound only on the average value of the mutual information available to an eavesdropper. Unfortunately this result by itself is inadequate for cryptographic applications. A naive application of the standard result leads one to incorrectly conclude that an acceptable upper bound on the mutual information has been achieved. It is the pointwise value of the bound on the mutual information, associated with the use of some specific hash function, that corresponds to actual implementations. We provide a fully rigorous mathematical derivation that shows how to obtain a cryptographically acceptable upper bound on the actual, pointwise value of the mutual information. Unlike the bound on the average mutual information, the value of the upper bound on the pointwise mutual information and the number of bits by which the secret key is compressed are specified by two different parameters, and the actual realization of the bound in the pointwise case is necessarily associated with a specific failure probability. The constraints amongst these parameters, and the effect of their values on the system throughput, have not been previously analyzed. We show that the necessary shortening of the key dictated by the cryptographically correct, pointwise bound, can still produce viable throughput rates that will be useful in practice.

quant-ph↗

arXiv2001

Constraints on Eavesdropping on the BB84 Protocol

An undetected eavesdropping attack must produce count rate statistics that are indistinguishable from those that would arise in the absence of such an attack. In principle this constraint should force a reduction in the amount of information available to the eavesdropper. In this paper we illustrate, by considering a particular class of eavesdropping attacks, how the general analysis of this problem may proceed.

quant-ph↗

arXiv2001

The Secrecy Capacity of Practical Quantum Cryptography

Quantum cryptography has attracted much recent attention due to its potential for providing secret communications that cannot be decrypted by any amount of computational effort. This is the first analysis of the secrecy of a practical implementation of the BB84 protocol that simultaneously takes into account and presents the {\it full} set of complete analytical expressions for effects due to the presence of pulses containing multiple photons in the attenuated output of the laser, the finite length of individual blocks of key material, losses due to error correction, privacy amplification, continuous authentication, errors in polarization detection, the efficiency of the detectors, and attenuation processes in the transmission medium. The analysis addresses eavesdropping attacks on individual photons rather than collective attacks in general. Of particular importance is the first derivation of the necessary and sufficient amount of privacy amplification compression to ensure secrecy against the loss of key material which occurs when an eavesdropper makes optimized individual attacks on pulses containing multiple photons. It is shown that only a fraction of the information in the multiple photon pulses is actually lost to the eavesdropper.

quant-ph↗