Resilience of multi-photon entanglement under losses

We analyze the resilience under photon loss of the bi-partite entanglement present in multi-photon states produced by parametric down-conversion. The quantification of the entanglement is made possible by a symmetry of the states that persists even under polarization-independent losses. We examine the approach of the states to the set of states with a positive partial transpose as losses increase, and calculate the relative entropy of entanglement. We find that some bi-partite distillable entanglement persists for arbitrarily high losses.Comment: 5 pages, 3 figures, title changed, minor typographic errors correcte

Scaling laws for precision in quantum interferometry and bifurcation landscape of optimal state

Phase precision in optimal 2-channel quantum interferometry is studied in the limit of large photon number $N\gg 1$, for losses occurring in either one or both channels. For losses in one channel an optimal state undergoes an intriguing sequence of local bifurcations as the losses or the number of photons increase. We further show that fixing the loss paramater determines a scale for quantum metrology -- a crossover value of the photon number $N_c$ beyond which the supra-classical precision is progressively lost. For large losses the optimal state also has a different structure from those considered previously.Comment: 4 pages, 3 figures, v3 is modified in response to referee comment

Recent developments in home equity lending

The equity that has accumulated in homes is one of the largest components of U.S. household wealth. In recent years, many homeowners have borrowed large amounts against that equity, frequently to finance new consumption expenditures or pay down outstanding consumer debt. In view of the growing importance of home equity credit in household finances, the Federal Reserve has for a number of years participated in nationwide surveys of the use of home equity loans. This article presents findings from a 1997 survey and from other sources of information on home equity lending.Home equity loans

Credit cards: use and consumer attitudes, 1970-2000

From modest origins in the 1950s as a convenient way for the relatively well-to-do to settle restaurant and department store purchases without carrying cash, credit cards have become a ubiquitous financial product held by households in all economic strata. Since the late 1960s, much federal legislation has been enacted to ensure that consumers have the protections and information they need to use this widely available form of open-end credit wisely. Nevertheless, concerns persist about whether consumers fully understand the costs and implications of using credit cards and whether credit cards have encouraged widespread overindebtedness. Drawing on information from commercial banks, credit reporting agencies, and surveys of consumers, this article explores these issues as well as changes over the past three decades in consumer impressions of their card-using experiences and of conditions in the marketplace.Credit cards ; Consumer behavior

Multi-Partite Entanglement Inequalities via Spin Vector Geometry

We introduce inequalities for multi-partite entanglement, derived from the geometry of spin vectors. The criteria are constructed iteratively from cross and dot products between the spins of individual subsystems, each of which may have arbitrary dimension. For qubit ensembles the maximum violation for our inequalities is larger than that for the Mermin-Klyshko Bell inequalities, and the maximally violating states are different from Greenberger-Horne-Zeilinger states. Our inequalities are violated by certain bound entangled states for which no Bell-type violation has yet been found.Comment: 4 pages, 2 tables, 1 figure. A truncated version is published in Physical Review Letters, volume 95 issue 18, 180402 (October 2005