Gerald Gilbert

Use of maximally entangled N-photon states for practical quantum interferometry

The phase estimation performance of photonic N00N states propagating in an attenuating medium is analyzed. It is shown that the Heisenberg limit is never achieved and that an attenuated separable state of N photons will actually produce a better phase estimate than an equally attenuated N00N state unless the transmittance of the medium is sufficiently high. Thus, for most practical applications with realistic attenuation, N00N-state-based phase estimation actually performs worse than the standard quantum limit. This performance deficit becomes more pronounced as the number of photons in the signal increases.

Efficient construction of photonic quantum-computational clusters

We demonstrate a method of creating photonic two-dimensional cluster states that is considerably more efficient than previously proposed approaches. Our method uses only local unitaries and type-I fusion operations. The increased efficiency of our method compared to previously proposed constructions is obtained by identifying and exploiting local equivalence properties inherent in cluster states.

Superoperator analysis of entanglement in a four-qubit cluster state

In this paper we utilize superoperator formalism to explore the entanglement evolution of four-qubit cluster states in a number of decohering environments. A four-qubit cluster state is a resource for the performance of an arbitrary single logical qubit rotation via measurement based cluster state quantum computation. We are specifically interested in the relationship between entanglement evolution and the fidelity with which the arbitrary single logical qubit rotation can be implemented in the presence of decoherence as this will have important experimental ramifications. We also note the exhibition of entanglement sudden death (ESD) and ask how severely its onset affects the utilization of the cluster state as a means of implementing an arbitrary single logical qubit rotation.

Practical quantum interferometry using photonic N00N states

We study the phase estimation abilites of photonic N00N states, propagating in an attenuating medium, is analyzed. It is shown that N00N states of a given number of enangled photons N, never achieve the 1/N Heisenberg limit if the propagation occurs through lossy medium. It is also shown that a signal comprised of an attenuated separable state of N photons will actually produce a better phase estimate than a signal comprised of an equally attenuated N00N state unless the transmittance of the medium is very high. Thus, 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 1/(square root of)N Standard Quantum Limit. This performance deficit becomes more pronounced as the number, N, of photons in the signal increases.

Volume thresholds for quantum fault tolerance

We introduce finite-level concatenation threshold regions for quantum fault tolerance. These volume thresholds are regions in an error probability manifold that allow for the implemented system dynamics to satisfy a prescribed implementation inaccuracy bound at a given level of quantum error correction concatenation. Satisfying this condition constitutes our fundamental definition of fault tolerance. The prescribed bound provides a halting condition identifying the attainment of fault tolerance that allows for the determination of the optimum choice of quantum error correction code(s) and number of concatenation levels. Our method is constructed to apply to finite levels of concatenation, does not require that error proabilities consistently decrease from one concatenation level to the next, and allows for analysis, without approximations, of physical systems characterized by non-equiprobable distributions of qubit error probabilities. We demonstrate the utility of this method via a general error model.

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.

A Universal Operator Theoretic Framework for Quantum Fault Tolerance

We extend standard fault tolerance theory and Kitaev’s model for quantum computation so as to enable quantitative determination of design parameters for quantum computers that ensure that the overall computation yields a correct final result with some prescribed probability, as opposed to merely ensuring that the desired final quantum state is obtained. Our extension allows us to explicitly calculate the number of levels of error correction concatenation needed to achieve a correct final result with some prescribed success probability and demonstrate a clear connection between error correction and fault tolerance.

End-to-end fault tolerance

In this review we survey both standard fault tolerance theory and Kitaev’s model for quantum computation, and demonstrate how they can be combined to yield quantitative results that reveal the interplay between the two. This analysis establishes a methodology allowing one to quantitatively determine design parameters for quantum computers, the values of which ensure that an overall computation yields a correct final result with some prescribed probability of success, as opposed to merely ensuring that the desired final quantum state is obtained. As an example, we explicitly calculate the number of levels of error correction concatenation needed to achieve a correct final result with some prescribed success probability. This methodology allows one to determine parameters required in order to achieve the correct final result for the quantum computation, as opposed to merely ensuring that the desired final quantum state is produced.

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 full set of 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, and 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.

Storing small photonic cluster states in a dephasing environment

We consider the effects of decoherence on the entanglement of photonic cluster states. Large photonic cluster states can be constructed via so-called fusion operations from smaller photonic cluster states. Due to this construction process, it is necessary to store these primitive cluster states in some way so as to have them available for attempted fusion operations. While in storage the photonic cluster states may undergo dephasing. The effects of dephasing on primitive cluster states is explored here with the aim of determining how to locally rotate the qubits of the cluster state in the hopes of losing the least amount of entanglement due to the dephasing process.