Entanglement-free Heisenberg-limited phase estimation

Measurement underpins all quantitative science. A key example is the measurement of optical phase, used in length metrology and many other applications. Advances in precision measurement have consistently led to important scientific discoveries. At the fundamental level, measurement precision is limited by the number N of quantum resources (such as photons) that are used. Standard measurement schemes, using each resource independently, lead to a phase uncertainty that scales as 1/sqrt(N) - known as the standard quantum limit. However, it has long been conjectured that it should be possible to achieve a precision limited only by the Heisenberg uncertainty principle, dramatically improving the scaling to 1/N. It is commonly thought that achieving this improvement requires the use of exotic quantum entangled states, such as the NOON state. These states are extremely difficult to generate. Measurement schemes with counted photons or ions have been performed with N <= 6, but few have surpassed the standard quantum limit and none have shown Heisenberg-limited scaling. Here we demonstrate experimentally a Heisenberg-limited phase estimation procedure. We replace entangled input states with multiple applications of the phase shift on unentangled single-photon states. We generalize Kitaev's phase estimation algorithm using adaptive measurement theory to achieve a standard deviation scaling at the Heisenberg limit. For the largest number of resources used (N = 378), we estimate an unknown phase with a variance more than 10 dB below the standard quantum limit; achieving this variance would require more than 4,000 resources using standard interferometry. Our results represent a drastic reduction in the complexity of achieving quantum-enhanced measurement precision.Comment: Published in Nature. This is the final versio

Interaction-based quantum metrology showing scaling beyond the Heisenberg limit

Quantum metrology studies the use of entanglement and other quantum resources to improve precision measurement. An interferometer using N independent particles to measure a parameter X can achieve at best the "standard quantum limit" (SQL) of sensitivity {\delta}X \propto N^{-1/2}. The same interferometer using N entangled particles can achieve in principle the "Heisenberg limit" {\delta}X \propto N^{-1}, using exotic states. Recent theoretical work argues that interactions among particles may be a valuable resource for quantum metrology, allowing scaling beyond the Heisenberg limit. Specifically, a k-particle interaction will produce sensitivity {\delta}X \propto N^{-k} with appropriate entangled states and {\delta}X \propto N^{-(k-1/2)} even without entanglement. Here we demonstrate this "super-Heisenberg" scaling in a nonlinear, non-destructive measurement of the magnetisation of an atomic ensemble. We use fast optical nonlinearities to generate a pairwise photon-photon interaction (k = 2) while preserving quantum-noise-limited performance, to produce {\delta}X \propto N^{-3/2}. We observe super-Heisenberg scaling over two orders of magnitude in N, limited at large N by higher-order nonlinear effects, in good agreement with theory. For a measurement of limited duration, super-Heisenberg scaling allows the nonlinear measurement to overtake in sensitivity a comparable linear measurement with the same number of photons. In other scenarios, however, higher-order nonlinearities prevent this crossover from occurring, reflecting the subtle relationship of scaling to sensitivity in nonlinear systems. This work shows that inter-particle interactions can improve sensitivity in a quantum-limited measurement, and introduces a fundamentally new resource for quantum metrology

Entanglement-enhanced probing of a delicate material system

Quantum metrology uses entanglement and other quantum effects to improve the sensitivity of demanding measurements. Probing of delicate systems demands high sensitivity from limited probe energy and has motivated the field's key benchmark-the standard quantum limit. Here we report the first entanglement-enhanced measurement of a delicate material system. We non-destructively probe an atomic spin ensemble by means of near-resonant Faraday rotation, a measurement that is limited by probe-induced scattering in quantum-memory and spin-squeezing applications. We use narrowband, atom-resonant NOON states to beat the standard quantum limit of sensitivity by more than five standard deviations, both on a per-photon and per-damage basis. This demonstrates quantum enhancement with fully realistic loss and noise, including variable-loss effects. The experiment opens the way to ultra-gentle probing of single atoms, single molecules, quantum gases and living cells.Comment: 7 pages, 8 figures; Nature Photonics, advance online publication, 16 December 201

Super-resolving phase measurements with a multi-photon entangled state

Using a linear optical elements and post-selection, we construct an entangled polarization state of three photons in the same spatial mode. This state is analogous to a ``photon-number path entangled state'' and can be used for super-resolving interferometry. Measuring a birefringent phase shift, we demonstrate two- and three-fold improvements in phase resolution.Comment: 4 pages, 3 figure

Quantum-inspired interferometry with chirped laser pulses

We introduce and implement an interferometric technique based on chirped femtosecond laser pulses and nonlinear optics. The interference manifests as a high-visibility (> 85%) phase-insensitive dip in the intensity of an optical beam when the two interferometer arms are equal to within the coherence length of the light. This signature is unique in classical interferometry, but is a direct analogue to Hong-Ou-Mandel quantum interference. Our technique exhibits all the metrological advantages of the quantum interferometer, but with signals at least 10^7 times greater. In particular we demonstrate enhanced resolution, robustness against loss, and automatic dispersion cancellation. Our interferometer offers significant advantages over previous technologies, both quantum and classical, in precision time delay measurements and biomedical imaging.Comment: 6 pages, 4 figure

Coordinated optimization of visual cortical maps (II) Numerical studies

It is an attractive hypothesis that the spatial structure of visual cortical architecture can be explained by the coordinated optimization of multiple visual cortical maps representing orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we defined a class of analytically tractable coordinated optimization models and solved representative examples in which a spatially complex organization of the orientation preference map is induced by inter-map interactions. We found that attractor solutions near symmetry breaking threshold predict a highly ordered map layout and require a substantial OD bias for OP pinwheel stabilization. Here we examine in numerical simulations whether such models exhibit biologically more realistic spatially irregular solutions at a finite distance from threshold and when transients towards attractor states are considered. We also examine whether model behavior qualitatively changes when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. Our numerical results support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the spatially irregular architecture of the visual cortex. We discuss several alternative scenarios and additional factors that may improve the agreement between model solutions and biological observations.Comment: 55 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:1102.335

Reading faces: differential lateral gaze bias in processing canine and human facial expressions in dogs and 4-year-old children

Sensitivity to the emotions of others provides clear biological advantages. However, in the case of heterospecific relationships, such as that existing between dogs and humans, there are additional challenges since some elements of the expression of emotions are species-specific. Given that faces provide important visual cues for communicating emotional state in both humans and dogs, and that processing of emotions is subject to brain lateralisation, we investigated lateral gaze bias in adult dogs when presented with pictures of expressive human and dog faces. Our analysis revealed clear differences in laterality of eye movements in dogs towards conspecific faces according to the emotional valence of the expressions. Differences were also found towards human faces, but to a lesser extent. For comparative purpose, a similar experiment was also run with 4-year-old children and it was observed that they showed differential processing of facial expressions compared to dogs, suggesting a species-dependent engagement of the right or left hemisphere in processing emotions

Can a falling tree make a noise in two forests at the same time?

It is a commonplace to claim that quantum mechanics supports the old idea that a tree falling in a forest makes no sound unless there is a listener present. In fact, this conclusion is far from obvious. Furthermore, if a tunnelling particle is observed in the barrier region, it collapses to a state in which it is no longer tunnelling. Does this imply that while tunnelling, the particle can not have any physical effects? I argue that this is not the case, and moreover, speculate that it may be possible for a particle to have effects on two spacelike separate apparatuses simultaneously. I discuss the measurable consequences of such a feat, and speculate about possible statistical tests which could distinguish this view of quantum mechanics from a ``corpuscular'' one. Brief remarks are made about an experiment underway at Toronto to investigate these issues.Comment: 9 pp, Latex, 3 figs, to appear in Proc. Obsc. Unr. Conf.; Fig 2 postscript repaired on 26.10.9

Acquisition of pneumococci specific effector and regulatory Cd4+ T cells localising within human upper respiratory-tract mucosal lymphoid tissue

The upper respiratory tract mucosa is the location for commensal Streptococcus (S.) pneumoniae colonization and therefore represents a major site of contact between host and bacteria. The CD4(+) T cell response to pneumococcus is increasingly recognised as an important mediator of immunity that protects against invasive disease, with data suggesting a critical role for Th17 cells in mucosal clearance. By assessing CD4 T cell proliferative responses we demonstrate age-related sequestration of Th1 and Th17 CD4(+) T cells reactive to pneumococcal protein antigens within mucosal lymphoid tissue. CD25(hi) T cell depletion and utilisation of pneumococcal specific MHCII tetramers revealed the presence of antigen specific Tregs that utilised CTLA-4 and PDL-1 surface molecules to suppress these responses. The balance between mucosal effector and regulatory CD4(+) T cell immunity is likely to be critical to pneumococcal commensalism and the prevention of unwanted pathology associated with carriage. However, if dysregulated, such responses may render the host more susceptible to invasive pneumococcal infection and adversely affect the successful implementation of both polysaccharide-conjugate and novel protein-based pneumococcal vaccines

Operational approach to open dynamics and quantifying initial correlations

A central aim of physics is to describe the dynamics of physical systems. Schrodinger's equation does this for isolated quantum systems. Describing the time evolution of a quantum system that interacts with its environment, in its most general form, has proved to be difficult because the dynamics is dependent on the state of the environment and the correlations with it. For discrete processes, such as quantum gates or chemical reactions, quantum process tomography provides the complete description of the dynamics, provided that the initial states of the system and the environment are independent of each other. However, many physical systems are correlated with the environment at the beginning of the experiment. Here, we give a prescription of quantum process tomography that yields the complete description of the dynamics of the system even when the initial correlations are present. Surprisingly, our method also gives quantitative expressions for the initial correlation.Comment: Completely re-written for clarity of presentation. 15 pages and 2 figure