Atom lasers, coherent states, and coherence II. Maximally robust ensembles of pure states

As discussed in the preceding paper [Wiseman and Vaccaro, preceding paper, Phys. Rev. A 65, 043605 (2002)], the stationary state of an optical or atom laser far above threshold is a mixture of coherent field states with random phase, or, equivalently, a Poissonian mixture of number states. We are interested in which, if either, of these descriptions of rho(ss) as a stationary ensemble of pure states, is more natural. In the preceding paper we concentrated upon the question of whether descriptions such as these are physically realizable (PR). In this paper we investigate another relevant aspect of these ensembles, their robustness. A robust ensemble is one for which the pure states that comprise it survive relatively unchanged for a long time under the system evolution. We determine numerically the most robust ensembles as a function of the parameters in the laser model: the self-energy chi of the bosons in the laser mode, and the excess phase noise nu. We find that these most robust ensembles are PR ensembles, or similar to PR ensembles, for all values of these parameters. In the ideal laser limit (nu=chi=0), the most robust states are coherent states. As the phase noise or phase dispersion is increased through nu or the self-interaction of the bosons chi, respectively, the most robust states become more and more amplitude squeezed. We find scaling laws for these states, and give analytical derivations for them. As the phase diffusion or dispersion becomes so large that the laser output is no longer quantum coherent, the most robust states become so squeezed that they cease to have a well-defined coherent amplitude. That is, the quantum coherence of the laser output is manifest in the most robust PR ensemble being an ensemble of states with a well-defined coherent amplitude. This lends support to our approach of regarding robust PR ensembles as the most natural description of the state of the laser mode. It also has interesting implications for atom lasers in particular, for which phase dispersion due to self-interactions is expected to be large.

Atom lasers, coherent states, and coherence. I. Physically realizable ensembles of pure states

A laser, be it an optical laser or an atom laser, is an open quantum system that produces a coherent beam of bosons (photons or atoms, respectively). Far above threshold, the stationary state rho(ss) of the laser mode is a mixture of coherent-field states with random phase, or, equivalently, a Poissonian mixture of number states. This paper answers the question: can descriptions such as these, of rho(ss) as a stationary ensemble of pure states, be physically realized? Here physical realization is as defined previously by us [H. M. Wiseman and J. A. Vaccaro, Phys. Lett. A 250, 241 (1998)]: an ensemble of pure states for a particular system can be physically realized if, without changing the dynamics of the system, an experimenter can (in principle) know at any time that the system is in one of the pure-state members of the ensemble. Such knowledge can be obtained by monitoring the baths to which the system is coupled, provided that coupling is describable by a Markovian master equation. Using a family of master equations for the (atom) laser, we solve for the physically realizable (PR) ensembles. We find that for any finite self-energy chi of the bosons in the laser mode, the coherent-state ensemble is not PR; the closest one can come to it is an ensemble of squeezed states. This is particularly relevant for atom lasers, where the self-energy arising from elastic collisions is expected to be large. By contrast, the number-state ensemble is always PR. As the self-energy chi increases, the states in the PR ensemble closest to the coherent-state ensemble become increasingly squeezed. Nevertheless, there are values of chi for which states with well-defined coherent amplitudes are PR, even though the atom laser is not coherent (in the sense of having a Bose-degenerate output). We discuss the physical significance of this anomaly in terms of conditional coherence (and hence conditional Bose degeneracy).

Universal state inversion and concurrence in arbitrary dimensions

Wootters [Phys. Rev. Lett. 80, 2245 (1998)] has given an explicit formula for the entanglement of formation of two qubits in terms of what he calls the concurrence of the joint density operator. Wootters's concurrence is defined with the help of the superoperator that flips the spin of a qubit. We generalize the spin-flip superoperator to a universal inverter, which acts on quantum systems of arbitrary dimension, and we introduce the corresponding generalized concurrence for joint pure states of D-1 X D-2 bipartite quantum systems. We call this generalized concurrence the I concurrence to emphasize its relation to the universal inverter. The universal inverter, which is a positive, but not completely positive superoperator, is closely related to the completely positive universal-NOT superoperator, the quantum analogue of a classical NOT gate. We present a physical realization of the universal-NOT Superoperator.

Entanglement under restricted operations: Analogy to mixed-state entanglement

We show that the classification of bipartite pure entangled states when local quantum operations are restricted yields a structure that is analogous in many respects to that of mixed-state entanglement. Specifically, we develop this analogy by restricting operations through local superselection rules, and show that such exotic phenomena as bound entanglement and activation arise using pure states in this setting. This analogy aids in resolving several conceptual puzzles in the study of entanglement under restricted operations. In particular, we demonstrate that several types of quantum optical states that possess confusing entanglement properties are analogous to bound entangled states. Also, the classification of pure-state entanglement under restricted operations can be much simpler than for mixed-state entanglement. For instance, in the case of local Abelian superselection rules all questions concerning distillability can be resolved.

Better Bell-inequality violation by collective measurements

The standard Bell-inequality experiments test for violation of local realism by repeatedly making local measurements on individual copies of an entangled quantum state. Here we investigate the possibility of increasing the violation of a Bell inequality by making collective measurements. We show that the nonlocality of bipartite pure entangled states, quantified by their maximal violation of the Bell-Clauser-Horne inequality, can always be enhanced by collective measurements, even without communication between the parties. For mixed states we also show that collective measurements can increase the violation of Bell inequalities, although numerical evidence suggests that the phenomenon is not common as it is for pure states.

Equivalence between two-mode spin squeezed states and pure entangled states with equal spin

We prove that a pure entangled state of two subsystems with equal spin is equivalent to a two-mode spin-squeezed state under local operations except for a set of bipartite states with measure zero, and provide a counterexample to the generalization of this result to two subsystems of unequal spin.

Quantum and classical fidelities for Gaussian states

We examine the physical significance of fidelity as a measure of similarity for Gaussian states by drawing a comparison with its classical counterpart. We find that the relationship between these classical and quantum fidelities is not straightforward, and in general does not seem to provide insight into the physical significance of quantum fidelity. To avoid this ambiguity we propose that the efficacy of quantum information protocols be characterized by determining their transfer function and then calculating the fidelity achievable for a hypothetical pure reference input state. (c) 2007 Optical Society of America.

Mixed-state entanglement in the light of pure-state entanglement constrained by superselection rules

We show that the classification of bi-partite pure entangled states when local quantum operations are restricted, e.g., constrained by local superselection rules, yields a structure that is analogous in many respects to that of mixed-state entanglement, including such exotic phenomena as bound entanglement and activation. This analogy aids in resolving several conceptual puzzles in the study of entanglement under restricted operations. Specifically, we demonstrate that several types of quantum optical states that possess confusing entanglement properties are analogous to bound entangled states. Also, the classification of pure-state entanglement under restricted operations can be much simpler than for mixed state entanglement. For instance, in the case of local Abelian superselection rules all questions concerning distillability can be resolved.

Distortion product otoacoustic emissions in children at school entry: A comparison with pure tone screening and tympanometry results

This study examined the test performance of distortion product otoacoustic emissions (DPOAEs) when used as a screening tool in the school setting. A total of 1003 children (mean age 6.2 years, SD = 0.4) were tested with pure-tone screening, tympanometry, and DPOAE assessment. Optimal DPOAE test performance was determined in comparison with pure-tone screening results using clinical decision analysis. The results showed hit rates of 0.86, 0.89, and 0.90, and false alarm rates of 0.52, 0.19, and 0.22 for criterion signal-to-noise ratio (SNR) values of 4, 5, and 11 dB at 1.1, 1.9, and 3.8 kHz respectively. DPOAE test performance was compromised at 1.1 kHz. In view of the different test performance characteristics across the frequencies, the use of a fixed SNR as a pass criterion for all frequencies in DPOAE assessments is not recommended. When compared to pure tone plus tympanometry results, the DPOAEs showed deterioration in test performance, suggesting that the use of DPOAEs alone might miss children with subtle middle ear dysfunction. However, when the results of a test protocol, which incorporates both DPOAEs and tympanometry, were used in comparison with the gold standard of pure-tone screening plus tympanometry, test performance was enhanced. In view of its high performance, the use of a protocol that includes both DPOAEs and tympanometry holds promise as a useful tool in the hearing screening of schoolchildren, including difficult-to-test children.

Entangled States and Collective Nonclassical Effects in Two-Atom Systems

We propose a review of recent developments on entanglement and nonclassical effects in collective two-atom systems and present a uniform physical picture of the many predicted phenomena. The collective effects have brought into sharp focus some of the most basic features of quantum theory, such as nonclassical states of light and entangled states of multiatom systems. The entangled states are linear superpositions of the internal states of the system which cannot be separated into product states of the individual atoms. This property is recognized as entirely quantum-mechanical effect and have played a crucial role in many discussions of the nature of quantum measurements and, in particular, in the developments of quantum communications. Much of the fundamental interest in entangled states is connected with its practical application ranging from quantum computation, information processing, cryptography, and interferometry to atomic spectroscopy.

Fault-tolerant quantum computation with cluster states

The one-way quantum computing model introduced by Raussendorf and Briegel [Phys. Rev. Lett. 86, 5188 (2001)] shows that it is possible to quantum compute using only a fixed entangled resource known as a cluster state, and adaptive single-qubit measurements. This model is the basis for several practical proposals for quantum computation, including a promising proposal for optical quantum computation based on cluster states [M. A. Nielsen, Phys. Rev. Lett. (to be published), quant-ph/0402005]. A significant open question is whether such proposals are scalable in the presence of physically realistic noise. In this paper we prove two threshold theorems which show that scalable fault-tolerant quantum computation may be achieved in implementations based on cluster states, provided the noise in the implementations is below some constant threshold value. Our first threshold theorem applies to a class of implementations in which entangling gates are applied deterministically, but with a small amount of noise. We expect this threshold to be applicable in a wide variety of physical systems. Our second threshold theorem is specifically adapted to proposals such as the optical cluster-state proposal, in which nondeterministic entangling gates are used. A critical technical component of our proofs is two powerful theorems which relate the properties of noisy unitary operations restricted to act on a subspace of state space to extensions of those operations acting on the entire state space. We expect these theorems to have a variety of applications in other areas of quantum-information science.

Substrate-inhibited kinetics with catalyst deactivation in an isothermal CSTR. II. Multiple pseudosteady states and reactor failure

Analytical expressions are derived for the time and magnitude of failure of an isothermal CSTR with substrate-inhibited kinetics, caused by slow catalyst deactivation under three types of parallel and series mechanisms. Reactors operating at high space velocity are found to be most susceptible to early failure and poisoning by product is more dangerous than by reactant. The magnitude of the jump across steady states depends solely on the Langmuir-Hinshelwood kinetic parameters and a detailed analysis of reactor behavior during the jump itself is given.

Adopting turtle excluder devices in Australia and the United States: What are the differences in technology transfer, promotion, and acceptance?

Turtle excluder devices (TEDs) are being trialed on a voluntary basis in many Australian prawn (shrimp) trawl fisheries to reduce sea turtle captures. Analysis of TED introductions into shrimp trawl fisheries of the United States provided major insights into why conflicts occurred between shrimpers, conservationists, and government agencies. A conflict over the introduction and subsequent regulation of TEDs occurred because the problem and the solution were perceived differently by the various stakeholders. Attempts to negotiate and mediate the conflict broke down, resulting in litigation against the U.S. government by conservationists and shrimpers. Litigation was not an efficient resolution to the sea turtle-TED-trawl conflict but it appears that litigation was the only remaining path of resolution once the issue became polarized. We review two major Australian trawl fisheries to identify any significant differences in circumstances that may affect TED acceptance. Australian trawl fisheries are structured differently and good communication occurs between industry and researchers. TEDs are being introduced as mature technology. Furthermore, bycatch issues are of increasing concern to all stakeholders. These factors, combined with insights derived from previous conflicts concerning TEDs in the United Stares, increase the possibilities that TEDs will be introduced to Australian fishers with better acceptance.