A size criterion for macroscopic superposition states

An operational measure to quantify the sizes of some ``macroscopic quantum superpositions'', realized in recent experiments, is proposed. The measure is based on the fact that a superposition presents greater sensitivity in interferometric applications than its superposed constituent states. This enhanced sensitivity, or ``interference utility'', may then be used as a size criterion among superpositions.Comment: LaTeX2e-REVTeX4, 9 pages, 3 figures. V2: introduction and discussion slightly altere

Numerical Bayesian quantum-state assignment for a three-level quantum system. II. Average-value data with a constant, a Gaussian-like, and a Slater prior

This paper offers examples of concrete numerical applications of Bayesian quantum-state assignment methods to a three-level quantum system. The statistical operator assigned on the evidence of various measurement data and kinds of prior knowledge is computed partly analytically, partly through numerical integration (in eight dimensions) on a computer. The measurement data consist in the average of outcome values of N identical von Neumann projective measurements performed on N identically prepared three-level systems. In particular the large-N limit will be considered. Three kinds of prior knowledge are used: one represented by a plausibility distribution constant in respect of the convex structure of the set of statistical operators; another one represented by a prior studied by Slater, which has been proposed as the natural measure on the set of statistical operators; the last prior is represented by a Gaussian-like distribution centred on a pure statistical operator, and thus reflecting a situation in which one has useful prior knowledge about the likely preparation of the system. The assigned statistical operators obtained with the first two kinds of priors are compared with the one obtained by Jaynes' maximum entropy method for the same measurement situation. In the companion paper the case of measurement data consisting in absolute frequencies is considered.Comment: 10 pages, 4 figures. V2: added "Post scriptum" under Conclusions, slightly changed Acknowledgements, and corrected some spelling error

Numerical Bayesian state assignment for a three-level quantum system. I. Absolute-frequency data; constant and Gaussian-like priors

This paper offers examples of concrete numerical applications of Bayesian quantum-state-assignment methods to a three-level quantum system. The statistical operator assigned on the evidence of various measurement data and kinds of prior knowledge is computed partly analytically, partly through numerical integration (in eight dimensions) on a computer. The measurement data consist in absolute frequencies of the outcomes of N identical von Neumann projective measurements performed on N identically prepared three-level systems. Various small values of N as well as the large-N limit are considered. Two kinds of prior knowledge are used: one represented by a plausibility distribution constant in respect of the convex structure of the set of statistical operators; the other represented by a Gaussian-like distribution centred on a pure statistical operator, and thus reflecting a situation in which one has useful prior knowledge about the likely preparation of the system. In a companion paper the case of measurement data consisting in average values, and an additional prior studied by Slater, are considered.Comment: 23 pages, 14 figures. V2: Added an important note concerning cylindrical algebraic decomposition and thanks to P B Slater, corrected some typos, added reference

Unpolarized light in quantum optics

We present a new derivation of the unpolarized quantum states of light, whose general form was first derived by Prakash and Chandra [Phys. Rev. A 4, 796 (1971)]. Our derivation makes use of some basic group theory, is straightforward, and offers some new insights.Comment: 3 pages, REVTeX, presented at ICQO'200

Quantum limits on phase-shift detection using multimode interferometers

Fundamental phase-shift detection properties of optical multimode interferometers are analyzed. Limits on perfectly distinguishable phase shifts are derived for general quantum states of a given average energy. In contrast to earlier work, the limits are found to be independent of the number of interfering modes. However, the reported bounds are consistent with the Heisenberg limit. A short discussion on the concept of well-defined relative phase is also included.Comment: 6 pages, 3 figures, REVTeX, uses epsf.st

Role Expectations of the District Superintendent: Implications for Deregulating Preparation and Licensing

At this juncture when policymakers are being asked to choose between deregulation and reform, problems affecting the superintendency need to be framed appropriately and policy decisions need to be based on evidence and not raw politics or emotion. Deregulating a profession clearly is a serious matter that is prudent either when the need for the state to protect the public from practitioners is no longer valid or when the underlying knowledge has been found to be fraudulent or irrelevant (Kowalski, 2004). This paper identifies role expectations and position requirements that have evolved for school district superintendents over the past 100 years. These expectations and requirements are then analyzed to determine if they remain valid to contemporary practice

Entanglement quantification through local observable correlations

We present a significantly improved scheme of entanglement detection inspired by local uncertainty relations for a system consisting of two qubits. Developing the underlying idea of local uncertainty relations, namely correlations, we demonstrate that it's possible to define a measure which is invariant under local unitary transformations and which is based only on local measurements. It is quite simple to implement experimentally and it allows entanglement quantification in a certain range for mixed states and exactly for pure states, without first obtaining full knowledge (e.g. through tomography) of the state.Comment: 5 pages, 3 figures, revised version with new proof and replaced figure

Two-photon imaging and quantum holography

It has been claimed that ``the use of entangled photons in an imaging system can exhibit effects that cannot be mimicked by any other two-photon source, whatever strength of the correlations between the two photons'' [A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. Lett. 87, 123602 (2001)]. While we believe that the cited statement is true, we show that the method proposed in that paper, with ``bucket detection'' of one of the photons, will give identical results for entangled states as for appropriately prepared classically correlated states.Comment: 4 pages, 2 figures, REVTe

Simultaneous minimum-uncertainty measurement of discrete-valued complementary observables

We have made the first experimental demonstration of the simultaneous minimum uncertainty product between two complementary observables for a two-state system (a qubit). A partially entangled two-photon state was used to perform such measurements. Each of the photons carries (partial) information of the initial state thus leaving a room for measurements of two complementary observables on every member in an ensemble.Comment: 4 pages, 4 figures, REVTeX, submitted to PR