Michael Hamrick

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.

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.

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.

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.

The normalized Bushmitch-Fikus-Hamrick (NBFH) metric

Most assessments of network performance make use of metrics that are defined directly in terms of concepts relevant to the transport, network, link and physical layers. These measures of performance provide engineering data useful in characterizing those layers of the architecture, but they do not directly address the operational impact of network behavior. Measures of effectiveness do address operational impacts from an end user perspective, but generally require simulation and analysis of both system and operational architectures. In this paper, we present a framework for assessing the operational impact of network performance using metrics derived from an examination of the network traffic alone, without explicit reference to an operational model but utilizing operationally driven criteria. We apply the framework to an evaluation of different Courses of Action (COAs) for allocating levels of service platforms to the end users of the networked system. We examine the sensitivity of the metric to variations in its parameters with special attention to the operational weighting factors. We conclude that this framework provides a well-behaved objective function that adequately characterizes the degree to which a networked system satisfies its operational requirements. This allows for the evaluation of a range of network and operational alternatives using existing network transport analysis tools without the need for coupled operational simulation.

On the practicality of quantum interferometry using photonic N00N states

We show that attenuated N00N states lead to a worse phase estimate than an equally attenuated N separable state unless the transmittance of the medium is very high.

Realistic Constraints on Photonic Quantum Interferometry

We analyze the phase estimation ability of photonic N00N states propagating in a lossy medium. In such a medium a N00N state of N enangled photons cannot achieve the maximum 1/N phase estimation resolution. In fact, unless the transmittance of the medium is extremely high, a signal comprised of an attenuated separable state of N photons will produce a better phase estimate than a comparable signal of an equally attenuated N00N state. Thus, for most practical applications the resolution provided photonic N00N states is actually worse than the 1/√N Standard Quantum Limit. This performance deficit becomes more pronounced as the number of photons in the signal increases.

Operator Quantum Fault Tolerance

We introduce a universal operator theoretic framework for quantum fault tolerance that incorporates a top-down approach based on specification of the full system dynamics. This approach leads to more accurate error thresholds.