Violation of the Leggett-Garg inequality with weak measurements of photons

By weakly measuring the polarization of a photon between two strong polarization measurements, we experimentally investigate the correlation between the appearance of anomalous values in quantum weak measurements, and the violation of realism and non-intrusiveness of measurements. A quantitative formulation of the latter concept is expressed in terms of a Leggett-Garg inequality for the outcomes of subsequent measurements of an individual quantum system. We experimentally violate the Leggett-Garg inequality for several measurement strengths. Furthermore, we experimentally demonstrate that there is a one-to-one correlation between achieving strange weak values and violating the Leggett-Garg inequality.Comment: 5 pages, 4 figure

The state of agricultural credit in New Zealand

In this paper the subject of agricultural credit has been subdivided into three sections covering background, borrowing, and lending. The background covers some of the changes in the New Zealand economy and government policies which have affected both borrowers and lenders in the agricultural sector, and consequently the amount and form of credit used. The section on borrowing (Section 3) examines the present credit needs of farmers, in particular the apparent trends towards increased equity and greater difficulty in servicing debt. The lending section (Section 4) examines the roles of government and private lending institutions in the field of agricultural credit and changes in the amount and form of credit available

A review of agricultural credit in New Zealand

The following discussion of the agricultural credit market encompasses agriculture in its wider sense. Because most of the available information and data on agricultural credit is concerned with traditional forms of pastoral farming (sheep, beef and dairy) the discussion relates primarily to those sectors. However, the growing importance of other sectors such as horticulture, grain cropping and deer farming is recognised and where possible their credit situation is also considered. The purpose of the paper is to update previous research by the Agricultural Economics Research Unit into the financing of the agriculture industry. In the past the agricultural credit situation has been relatively stable. Because of its large contribution to exports, agriculture (pastoral agriculture in particular) received considerable support from Government in the form of policies aimed at maintaining a steady flow of investment. Credit assistance was one of the cornerstones of these policies. In 1982 the Government began to change its stance. In the Budget of that year interest payments and certain development ceased to be tax deductible where the farm property was sold within 10 years of purchase. Although this steadied inflation in land prices, long term investors particularly pastoral farm investors still enjoyed considerable advantages over investors wishing to borrow capital for diversification into or expansion of enterprises which were capable of better returns on investment. It was not until late 1984 that a wide range of policies were introduced to remove these advantages and promote greater equity between enterprises and industries requiring capital for restructuring or expansion. As a result some of the conclusions reached in Discussion Papers on agricultural and horticultural credit published by the Unit as recently as April and October 1984 have been quickly overtaken by economic events and need updating. This paper begins with a background of trends in the New Zealand economy and then in chronological order details recent changes in Government Policy. This is followed by a discussion of the implications of these changes for the financing of agriculture. Finally the present state of the agricultural credit market is discussed and some conclusions are drawn. The discussion is based on a variety of sources including MAF, Reserve Bank, Treasury, AERU and private economic reports and data. A considerable part of the material was also obtained from personal correspondence and interviews with people directly involved in the finance industry. The views expressed are, of course those of the authors

Entanglement-enhanced measurement of a completely unknown phase

The high-precision interferometric measurement of an unknown phase is the basis for metrology in many areas of science and technology. Quantum entanglement provides an increase in sensitivity, but present techniques have only surpassed the limits of classical interferometry for the measurement of small variations about a known phase. Here we introduce a technique that combines entangled states with an adaptive algorithm to precisely estimate a completely unspecified phase, obtaining more information per photon that is possible classically. We use the technique to make the first ab initio entanglement-enhanced optical phase measurement. This approach will enable rapid, precise determination of unknown phase shifts using interferometry.Comment: 6 pages, 4 figure

Quantum gate characterization in an extended Hilbert space

We describe an approach for characterizing the process of quantum gates using quantum process tomography, by first modeling them in an extended Hilbert space, which includes non-qubit degrees of freedom. To prevent unphysical processes from being predicted, present quantum process tomography procedures incorporate mathematical constraints, which make no assumptions as to the actual physical nature of the system being described. By contrast, the procedure presented here ensures physicality by placing physical constraints on the nature of quantum processes. This allows quantum process tomography to be performed using a smaller experimental data set, and produces parameters with a direct physical interpretation. The approach is demonstrated by example of mode-matching in an all-optical controlled-NOT gate. The techniques described are non-specific and could be applied to other optical circuits or quantum computing architectures.Comment: 4 pages, 2 figures, REVTeX (published version

Adaptive Measurements in the Optical Quantum Information Laboratory

Adaptive techniques make practical many quantum measurements that would otherwise be beyond current laboratory capabilities. For example: they allow discrimination of nonorthogonal states with a probability of error equal to the Helstrom bound; they allow measurement of the phase of a quantum oscillator with accuracy approaching (or in some cases attaining) the Heisenberg limit; and they allow estimation of phase in interferometry with a variance scaling at the Heisenberg limit, using only single qubit measurement and control. Each of these examples has close links with quantum information, in particular experimental optical quantum information: the first is a basic quantum communication protocol; the second has potential application in linear optical quantum computing; the third uses an adaptive protocol inspired by the quantum phase estimation algorithm. We discuss each of these examples, and their implementation in the laboratory, but concentrate upon the last, which was published most recently [Higgins {\em et al.}, Nature vol. 450, p. 393, 2007].Comment: 12 pages, invited paper to be published in IEEE Journal of Selected Topics in Quantum Electronics: Quantum Communications and Information Scienc

Time-reversal and super-resolving phase measurements

We demonstrate phase super-resolution in the absence of entangled states. The key insight is to use the inherent time-reversal symmetry of quantum mechanics: our theory shows that it is possible to \emph{measure}, as opposed to prepare, entangled states. Our approach is robust, requiring only photons that exhibit classical interference: we experimentally demonstrate high-visibility phase super-resolution with three, four, and six photons using a standard laser and photon counters. Our six-photon experiment demonstrates the best phase super-resolution yet reported with high visibility and resolution.Comment: 4 pages, 3 figure

High-Fidelity Z-Measurement Error Correction of Optical Qubits

We demonstrate a quantum error correction scheme that protects against accidental measurement, using an encoding where the logical state of a single qubit is encoded into two physical qubits using a non-deterministic photonic CNOT gate. For the single qubit input states |0>, |1>, |0>+|1>, |0>-|1>, |0>+i|1>, and |0>-i|1> our encoder produces the appropriate 2-qubit encoded state with an average fidelity of 0.88(3) and the single qubit decoded states have an average fidelity of 0.93(5) with the original state. We are able to decode the 2-qubit state (up to a bit flip) by performing a measurement on one of the qubits in the logical basis; we find that the 64 1-qubit decoded states arising from 16 real and imaginary single qubit superposition inputs have an average fidelity of 0.96(3).Comment: 4 pages, 4 figures, comments welcom

Quantum process tomography of a controlled-NOT gate

We demonstrate complete characterization of a two-qubit entangling process - a linear optics controlled-NOT gate operating with coincident detection - by quantum process tomography. We use maximum-likelihood estimation to convert the experimental data into a physical process matrix. The process matrix allows accurate prediction of the operation of the gate for arbitrary input states, and calculation of gate performance measures such as the average gate fidelity, average purity and entangling capability of our gate, which are 0.90, 0.83 and 0.73, respectively.Comment: 4 pages, 2 figures. v2 contains new data corresponding to improved gate operation. Figure quality slightly reduced for arXi