Entanglement conditions for two-mode states

We provide a class of inequalities whose violation shows the presence of entanglement in two-mode systems. We initially consider observables that are quadratic in the mode creation and annihilation operators and find conditions under which a two-mode state is entangled. Further examination allows us to formulate additional conditions for detecting entanglement. We conclude by showing how the methods used here can be extended to find entanglement in systems of more than two modes.Comment: 4 pages, replaced with published versio

Quantum theory of dispersive electromagnetic modes

A quantum theory of dispersion for an inhomogeneous solid is obtained, from a starting point of multipolar coupled atoms interacting with an electromagnetic field. The dispersion relations obtained are equivalent to the standard classical Sellmeir equations obtained from the Drude-Lorentz model. In the homogeneous (plane-wave) case, we obtain the detailed quantum mode structure of the coupled polariton fields, and show that the mode expansion in all branches of the dispersion relation is completely defined by the refractive index and the group-velocity for the polaritons. We demonstrate a straightforward procedure for exactly diagonalizing the Hamiltonian in one, two or three-dimensional environments, even in the presence of longitudinal phonon-exciton dispersion, and an arbitrary number of resonant transitions with different frequencies. This is essential, since it is necessary to include at least one phonon (I.R.) and one exciton (U.V.) mode, in order to accurately represent dispersion in transparent solid media. Our method of diagonalization does not require an explicit solution of the dispersion relation, but relies instead on the analytic properties of Cauchy contour integrals over all possible mode frequencies. When there is longitudinal phonon dispersion, the relevant group-velocity term is modified so that it only includes the purely electromagnetic part of the group velocity

Quadratic squeezing: An overview

The amplitude of the electric field of a mode of the electromagnetic field is not a fixed quantity: there are always quantum mechanical fluctuations. The amplitude, having both a magnitude and a phase, is a complex number and is described by the mode annihilation operator a. It is also possible to characterize the amplitude by its real and imaginary parts which correspond to the Hermitian and anti-Hermitian parts of a, X sub 1 = 1/2(a(sup +) + a) and X sub 2 = i/2(a(sup +) - a), respectively. These operators do not commute and, as a result, obey the uncertainty relation (h = 1) delta X sub 1(delta X sub 2) greater than or = 1/4. From this relation we see that the amplitude fluctuates within an 'error box' in the complex plane whose area is at least 1/4. Coherent states, among them the vacuum state, are minimum uncertainty states with delta X sub 1 = delta X sub 2 = 1/2. A squeezed state, squeezed in the X sub 1 direction, has the property that delta X sub 1 is less than 1/2. A squeezed state need not be a minimum uncertainty state, but those that are can be obtained by applying the squeeze operator

Post-harvest Treatment Effects on Physicochemical Quality Attributes of North Atlantic Squid Doryteuthis pealeii and Illex illecebrosus

Doryteuthis pealeii (longfin inshore squid) and Illex illecebrosus (Northern shortfin squid) are the two most commercially important species of squid harvested in the United States. They are also the only two species of squid in the world certified sustainable by the Marine Stewardship Council. Despite their pivotal role in the U.S. seafood industry, very little research has been performed on their quality in decades. Two common methods of freezing and secondary processing applied to squid in the U.S. industry are blast-freezing either at sea or on land; and leaving the squid whole, or fully cleaning and then brining them. To date, the effects that these different post-harvest treatments have on these species’ physicochemical qualities have not been reported. The specific objectives of this research included: (1) exploring the effects of freezing and processing treatments on various physicochemical qualities of the mantles and tentacles of D. pealeii and I. illecebrosus; (2) quantifying the yield of edible material from each species; (3) examining differences in the color of the mantle skin and meat; and (4) identifying relationships between the squid meat color and (a) the condition of its internal organs and (b) its skin color. The first study explored a wide variety of physicochemical characteristics, including instrumental color and texture, crude protein, moisture, and ash contents, water-holding capacity, salt-soluble protein, and in-vitro protein digestibility, as well as the size and weight of squid and their individual parts. Land-frozen squid were found to be significantly softer, with more soluble protein, and higher in extractible peptides than sea-frozen squid, and processed samples had significantly lower water-holding capacity and protein content than whole samples, signifying greater damage to muscle proteins. Based on these results, freezing at sea and leaving the squid whole appeared to better preserve their quality. The wings, disposed as waste in the industry despite their edibility, were found to comprise ~10% of the whole squid mass for both species; as a currently unutilized part of the squid, the wings present many opportunities for novel development of value-added products. The second study evaluated the instrumental color of squids’ external and internal mantle meat, exploring relationships between meat color and the color of the skin and the condition of select viscera. Meat color is critical in quality assurance for distribution to different markets, and discoloration leads to substantial revenue and product loss. Significant correlations were discovered between the redness (a* values) and yellowness (b* values) of the skin and the mantle underneath, as well as between the condition of the organs (from “good” to “poor”) and the meat color, where worse-quality organs were associated with increased meat redness and yellowness. The results from these studies suggest that sea-freezing should be prioritized over land- freezing, especially for I. illecebrosus, and that eviscerating and skinning squid may preserve the quality of their meat

Representation of entanglement by negative quasi-probabilities

Any bipartite quantum state has quasi-probability representations in terms of separable states. For entangled states these quasi-probabilities necessarily exhibit negativities. Based on the general structure of composite quantum states, one may reconstruct such quasi-propabilities from experimental data. Because of ambiguity, the quasi-probabilities obtained by the bare reconstruction are insufficient to identify entanglement. An optimization procedure is introduced to derive quasi-probabilities with a minimal amount of negativity. Negativities of optimized quasi-probabilities unambiguously prove entanglement, their positivity proves separability.Comment: 9 pages, 2 figures; An optimization procedure for the quasi-probabilities has been adde