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We introduce a quantification of genuine three-party pure-state coherence for wave fields, classical and quantum, by borrowing concepts from classical optics. The tensor structure of a classical paraxial light beam composed of three principle degrees of freedom is shown to be equivalent to that of a three-qubit quantum state. The traditional basis-independent optical coherence quantity called degree of polarization is then determined to be the desired quantitative two-party coherence measure. When appropriately generalized, a set of fundamental constraint relations is derived among three two-party coherences. The constraint relations can be geometrically interpreted and visualized as tetrahedra nested within a coherence cube. A measure of three-party coherence is defined based on the constraints. We are reporting completed experimental tests and confirmations of the constraints as well as measurement of three-party coherence in the optical context. Our approach based on classical optics also opens an alternative way to analyze quantum coherence., Comment: 9 pages, 3 figures, 1 table

We provide the first experimental confirmation of a three-way quantum coherence identity possessed by single pure-state photons. Our experimental results demonstrate that traditional wave-particle duality is specifically limited by this identity. As a new consequence, we show that quantum duality itself can be amplified, attenuated, or turned completely off. In the Young double-slit context this quantum coherence identity is found to be directly relevant, and it supplies a rare quantitative backup for one of Bohr's philosophical pronouncements., Comment: 5 pages, 5 figures

Ninety years ago in 1927, at an international congress in Como, Italy, Niels Bohr gave an address which is recognized as the first instance in which the term "complementarity", as a physical concept, was spoken publicly [1], revealing Bohr's own thinking about Louis de Broglie's "duality". Bohr had very slowly accepted duality as a principle of physics: close observation of any quantum object will reveal either wave-like or particle-like behavior, one or the other of two fundamental and complementary features. Little disagreement exists today about complementarity's importance and broad applicability in quantum science. Book-length scholarly examinations even provide speculations about the relevance of complementarity in fields as different from physics as biology, psychology and social anthropology, connections which were apparently of interest to Bohr himself (see Jammer [2], Murdoch [3] and Whitaker [4]). Confusion evident in Como following his talk was not eliminated by Bohr's article [1], and complementarity has been subjected to nine decades of repeated examination ever since with no agreed resolution. Semi-popular treatments [5] as well as expert examinations [6-9] show that the topic cannot be avoided, and complementarity retains its central place in the interpretation of quantum mechanics. However, recent approaches by our group [10-13] and others [14-20] to the underlying notion of coherence now allow us to present a universal formulation of complementarity that may signal the end to the confusion. We demonstrate a new relationship that constrains the behavior of an electromagnetic field (quantum or classical) in the fundamental context of two-slit experiments. We show that entanglement is the ingredient needed to complete Bohr's formulation of complementarity, debated for decades because of its incompleteness., Comment: 8 pages, 4 figures

Visibility $V$ and distinguishability $D$ quantify wave-ray duality: $V^2 + D^2 \le 1$. We join them to polarization $P$ via the Polarization Coherence Theorem, a tight equality: $P^2 = V^2 + D^2$., Comment: Optica Memorandum, 2 pages

The growing recognition that entanglement is not exclusively a quantum property, and does not even originate with Schr\"odinger's famous remark about it [Proc. Camb. Phil. Soc. 31, 555 (1935)], prompts examination of its role in marking the quantum-classical boundary. We have done this by subjecting correlations of classical optical fields to new Bell-analysis experiments, and report here values of the Bell parameter greater than ${\cal B} = 2.54$. This is many standard deviations outside the limit ${\cal B} = 2$ established by the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality [Phys. Rev. Lett. 23, 880 (1969)], in agreement with our theoretical classical prediction, and not far from the Tsirelson limit ${\cal B} = 2.828...$. These results cast a new light on the standard quantum-classical boundary description, and suggest a reinterpretation of it., Comment: Comments and Remarks are warmly welcome! arXiv admin note: text overlap with arXiv:1406.3338

For many decades the word "entanglement" has been firmly attached to the world of quantum mechanics, as is the phrase "Bell violation". Here we introduce Shimony-Wolf fields, entirely classical non-deterministic states, as a basis for entanglement and Bell analyses. Such fields are well known in coherence optics and are open to test. We present experimental results showing that Shimony-Wolf states exhibit strong classical Bell violation, in effect opening a way of examining a new sector of the boundary between quantum and classical physics., Comment: 15 pages

For many decades the word "entanglement" has been firmly attached to the world of quantum mechanics. So is the phrase "Bell violation". Here we show, without contradicting quantum mechanics, that classical non-deterministic fields also provide a natural basis for entanglement and Bell analyses. Surprisingly, such fields are not eliminated by the Clauser-Horne-Shimony-Holt Bell violation test as viable alternatives to quantum theory. An experimental setup for verification is proposed., Comment: 5 pages

We formulate the classical polarization theory for light by using entanglement analysis. We demonstrate a route to a systematic and consistent measure of ordinary light polarization that extends automatically to a new understanding of the degree of polarization at a point, when a distinct beam direction is absent. We have drawn on recent work [Qian and Eberly, arXiv 1009.5622] dealing with the conservation of quantum information.

We use classical electron ensembles and the aligned-electron approximation to examine the effect of laser pulse duration on the dynamics of strong-field double ionization. We cover the range of intensities $10^{14}-10^{16} W/cm^2$ for the laser wavelength 780 nm. The classical scenario suggests that the highest rate of recollision occurs early in the pulse and promotes double ionization production in few-cycle pulses. In addition, the purely classical ensemble calculation predicts an exponentially decreasing recollision rate with each subsequent half cycle. We confirm the exponential behavior by trajectory back-analysis.

We report the discovery of a "dark area theorem," a new quantum optical relation for propagation of unmatched pulses in thick three-level $\Lambda$-type media. We define dark area and derive the dark area theorem for a coherently prepared and inhomogeneously broadened lambda medium. We also obtain the first equation for the spatial evolution of the dark state amplitude prior to pulse-matching., Comment: 8 pages, 4 figures