The Strong Law of Demand

We show that a demand function is derived from maximizing a quasilinear utility function subject to a budget constraint if and only if the demand function is cyclically monotone. On finite data sets consisting of pairs of market prices and consumption vectors, this result is equivalent to a solution of the Afriat inequalities where all the marginal utilities of income are equal. We explore the implications of these results for maximization of a random quasilinear utility function subject to a budget constraint and for representative agent general equilibrium models. The duality theory for cyclically monotone demand is developed using the Legendre-Fenchel transform. In this setting, a consumer's surplus is measured by the conjugate of her utility function.Permanent income hypothesis, Afriat's theorem, Law of demand, Consumer's surplus, Testable restrictions

The role of auxiliary states in state discrimination with linear optical evices

The role of auxiliary photons in the problem of identifying a state secretly chosen from a given set of L-photon states is analyzed. It is shown that auxiliary photons do not increase the ability to discriminate such states by means of a global measurement using only optical linear elements, conditional transformation and auxiliary photons.Comment: 5 pages. 1 figure. RevTex documen

Rationalizing and Curve-Fitting Demand Data with Quasilinear Utilities

In the empirical and theoretical literature a consumer's utility function is often assumed to be quasilinear. In this paper we provide necessary and sufficient conditions for testing if the consumer acts as if she is maximizing a quasilinear utility function over her budget set. If the consumer's choices are inconsistent with maximizing a quasilinear utility function over her budget set, then we compute the "best" quasilinear rationalization of her choices.Quasilinear utilities, Afriat inequalities, Curve-fitting

Multipartite secure state distribution

We introduce the distribution of a secret multipartite entangled state in a real-world scenario as a quantum primitive. We show that in the presence of noisy quantum channels (and noisy control operations) any state chosen from the set of two-colorable graph states (CSS codewords) can be created with high fidelity while it remains unknown to all parties. This is accomplished by either blind multipartite entanglement purification, which we introduce in this paper, or by multipartite entanglement purification of enlarged states, which offers advantages over an alternative scheme based on standard channel purification and teleportation. The parties are thus provided with a secret resource of their choice for distributed secure applications.Comment: V2: Replaced with published version: title changed, 2 figures added, presentation improve

Loss-resistant state teleportation and entanglement swapping using a quantum-dot spin in an optical microcavity

We present a scheme for efficient state teleportation and entanglement swapping using a single quantum-dot spin in an optical microcavity based on giant circular birefringence. State teleportation or entanglement swapping is heralded by the sequential detection of two photons, and is finished after the spin measurement. The spin-cavity unit works as a complete Bell-state analyzer with a built-in spin memory allowing loss-resistant repeater operation. This device can work in both the weak coupling and the strong coupling regime, but high efficiencies and high fidelities are only achievable when the side leakage and cavity loss is low. We assess the feasibility of this device, and show it can be implemented with current technology. We also propose a spin manipulation method using single photons, which could be used to preserve the spin coherence via spin echo techniques.Comment: The manuscript is extended, including BSA fidelity, efficiency, and a compatible scheme for spin manipulations and spin echoes to prolong the spin coherenc