Entanglement cost of two-qubit orthogonal measurements

The "entanglement cost" of a bipartite measurement is the amount of shared entanglement two participants need to use up in order to carry out the given measurement by means of local operations and classical communication. Here we numerically investigate the entanglement cost of generic orthogonal measurements on two qubits. Our results strongly suggest that for almost all measurements of this kind, the entanglement cost is strictly greater than the average entanglement of the eigenstates associated with the measurements, implying that the nonseparability of a two-qubit orthogonal measurement is generically distinct from the nonseparability of its eigenstates.Comment: Latex, 4 pages, minor change

A logarithmic-depth quantum carry-lookahead adder

We present an efficient addition circuit, borrowing techniques from the classical carry-lookahead arithmetic circuit. Our quantum carry-lookahead (QCLA) adder accepts two n-bit numbers and adds them in O(log n) depth using O(n) ancillary qubits. We present both in-place and out-of-place versions, as well as versions that add modulo 2^n and modulo 2^n - 1. Previously, the linear-depth ripple-carry addition circuit has been the method of choice. Our work reduces the cost of addition dramatically with only a slight increase in the number of required qubits. The QCLA adder can be used within current modular multiplication circuits to reduce substantially the run-time of Shor's algorithm.Comment: 21 pages, 4 color figure

New formats for computing with real-numbers under round-to-nearest

An edited version of this work was accepted in IEEE Transactions on computers, DOI 10.1109/TC.2015.2479623In this paper, a new family of formats to deal with real number for applications requiring round to nearest is proposed. They are based on shifting the set of exactly represented numbers which are used in conventional radix-R number systems. This technique allows performing radix complement and round to nearest without carry propagation with negligible time and hardware cost. Furthermore, the proposed formats have the same storage cost and precision as standard ones. Since conversion to conventional formats simply require appending one extra-digit to the operands, standard circuits may be used to perform arithmetic operations with operands under the new format. We also extend the features of the RN-representation system and carry out a thorough comparison between both representation systems. We conclude that the proposed representation system is generally more adequate to implement systems for computation with real number under round-to-nearest.Ministry of Education and Science of Spain under contracts TIN2013-42253-P

Simulating Noisy Channel Interaction

We show that $T$ rounds of interaction over the binary symmetric channel $BSC_{1/2-\epsilon}$ with feedback can be simulated with $O(\epsilon^2 T)$ rounds of interaction over a noiseless channel. We also introduce a more general "energy cost" model of interaction over a noisy channel. We show energy cost to be equivalent to external information complexity, which implies that our simulation results are unlikely to carry over to energy complexity. Our main technical innovation is a self-reduction from simulating a noisy channel to simulating a slightly-less-noisy channel, which may have other applications in the area of interactive compression

THE EFFICIENCY OF THE FUTURES MARKET FOR AGRICULTURAL COMMODITIES IN THE UK

This paper uses cointegration procedures to test for agricultural commodity futures market efficiency in the UK. Cointegration between spot and futures prices is a necessary condition for market efficiency where these prices are characterised by stochastic trends (Lai and Lai 1991). In addition, acceptance of the 'unbiasedness hypothesis' requires that the spot and lagged futures prices are cointegrated with the cointegrating vector (1, -1). Alternatively, Brenner and Kroner (1995) use a no-arbitrage cost-of-carry model to argue that the existence of cointegration between spot and futures prices depends on the time series properties of the cost-of-carry. According to Brenner and Kroner (1995), a tri-variate cointegrating relationship (the BK hypothesis) should exist among the spot price, the lagged futures price and the lagged interest rate (that component of cost-of-carry most likely to be non-stationary). These variables should be cointegrated with a cointegrating vector (1, -1, 1). Kellard (2002) finds that both bi-variate and tri-variate cointegrating relationships are found in a sample from the wheat futures market in the UK, and thus the so-called "cointegration paradox" emerges. As Kellard (2002) points out this paradox exists because it is theoretically impossible for two variables to be cointegrated with each other while simultaneously being cointegrated with a third variable. Using a larger sample of wheat futures market prices from LIFFE both the 'unbiasedness hypothesis' and the 'BK hypothesis' are examined. The results indicate that the 'BK hypothesis' should be rejected.Marketing,