Entanglement Swapping Chains for General Pure States

We consider entanglement swapping schemes with general (rather than maximally) entangled bipartite states of arbitary dimension shared pairwise between three or more parties in a chain. The intermediate parties perform generalised Bell measurements with the result that the two end parties end up sharing a entangled state which can be converted into maximally entangled states. We obtain an expression for the average amount of maximal entanglement concentrated in such a scheme and show that in a certain reasonably broad class of cases this scheme is provably optimal and that, in these cases, the amount of entanglement concentrated between the two ends is equal to that which could be concentrated from the weakest link in the chain.Comment: 18 pages, 5 figure

Remote State Preparation

Quantum teleportation uses prior entanglement and forward classical communication to transmit one instance of an unknown quantum state. Remote state preparation (RSP) has the same goal, but the sender knows classically what state is to be transmitted. We show that the asymptotic classical communication cost of RSP is one bit per qubit - half that of teleportation - and becomes even less when transmitting part of a known entangled state. We explore the tradeoff between entanglement and classical communication required for RSP, and discuss RSP capacities of general quantum channels.Comment: 4 pages including 1 epsf figure; v3 has an additional author and discusses relation to work of Devetak and Berger (quant-ph/0102123); v4 improves low-entanglement protocols without back communication to perform as well as low-entanglement protocols with back communication; v5 (journal version) has a few small change

Quantum privacy amplification and the security of quantum cryptography over noisy channels

Existing quantum cryptographic schemes are not, as they stand, operable in the presence of noise on the quantum communication channel. Although they become operable if they are supplemented by classical privacy-amplification techniques, the resulting schemes are difficult to analyse and have not been proved secure. We introduce the concept of quantum privacy amplification and a cryptographic scheme incorporating it which is provably secure over a noisy channel. The scheme uses an `entanglement purification' procedure which, because it requires only a few quantum Controlled-Not and single-qubit operations, could be implemented using technology that is currently being developed. The scheme allows an arbitrarily small bound to be placed on the information that any eavesdropper may extract from the encrypted message.Comment: 13 pages, Latex including 2 postcript files included using psfig macro

Changing Farming Systems – Financial Implications for Farming Businesses

Future prosperity of farming businesses depends not only on immediate prospects, but also on the capability to adapt to changing circumstances. In looking to the future, farm managers need to assess where the current farming system is taking them, and whether changing to an alternative farming system might be more profitable. There are various techniques for assessing the profitability of alternative farming systems, but frequently the cost of transition is overlooked. The financial consequences of transition to a new farming system are assessed for two case study farms using a spreadsheet tool (STEP), developed by the authors. The tool assists farm managers in assessing the risk of transition strategies as well as comparing rotations.Farm Management,

Information Flow in Entangled Quantum Systems

All information in quantum systems is, notwithstanding Bell's theorem, localised. Measuring or otherwise interacting with a quantum system S has no effect on distant systems from which S is dynamically isolated, even if they are entangled with S. Using the Heisenberg picture to analyse quantum information processing makes this locality explicit, and reveals that under some circumstances (in particular, in Einstein-Podolski-Rosen experiments and in quantum teleportation) quantum information is transmitted through 'classical' (i.e. decoherent) information channels.Comment: PostScript version now available: http://www.qubit.org/people/patrickh/Papers/InformationFlow.p

Mixed State Entanglement and Quantum Error Correction

Entanglement purification protocols (EPP) and quantum error-correcting codes (QECC) provide two ways of protecting quantum states from interaction with the environment. In an EPP, perfectly entangled pure states are extracted, with some yield D, from a mixed state M shared by two parties; with a QECC, an arbi- trary quantum state $|\xi\rangle$ can be transmitted at some rate Q through a noisy channel $\chi$ without degradation. We prove that an EPP involving one- way classical communication and acting on mixed state $\hat{M}(\chi)$ (obtained by sharing halves of EPR pairs through a channel $\chi$) yields a QECC on $\chi$ with rate $Q=D$, and vice versa. We compare the amount of entanglement E(M) required to prepare a mixed state M by local actions with the amounts $D_1(M)$ and $D_2(M)$ that can be locally distilled from it by EPPs using one- and two-way classical communication respectively, and give an exact expression for $E(M)$ when $M$ is Bell-diagonal. While EPPs require classical communica- tion, QECCs do not, and we prove Q is not increased by adding one-way classical communication. However, both D and Q can be increased by adding two-way com- munication. We show that certain noisy quantum channels, for example a 50% depolarizing channel, can be used for reliable transmission of quantum states if two-way communication is available, but cannot be used if only one-way com- munication is available. We exhibit a family of codes based on universal hash- ing able toachieve an asymptotic $Q$ (or $D$) of 1-S for simple noise models, where S is the error entropy. We also obtain a specific, simple 5-bit single- error-correcting quantum block code. We prove that {\em iff} a QECC results in high fidelity for the case of no error the QECC can be recast into a form where the encoder is the matrix inverse of the decoder.Comment: Resubmission with various corrections and expansions. See also http://vesta.physics.ucla.edu/~smolin/ for related papers and information. 82 pages latex including 19 postscript figures included using psfig macro

Transaction attributes and buyer-supplier relationships in AMT acquisition and implementation : the case of Malaysia.

This paper explores how transaction attributes of technology affect differences in the relationship between technology buyers and suppliers. It also examines the impact on performance of different patterns of relationship between technology buyers and suppliers. Data obtained from 147 manufacturing firms in Malaysia are used to test several hypotheses, which were derived from a review of the literature on technology, transaction cost theory and buyer–supplier relationships (BSR). The research results indicate that the higher the level of technological complexity, specificity and uncertainty, the more firms are likely to engage in a closer relationship with technology suppliers. Even though the majority of firms reported improvements in their performance, results indicate that firms demonstrating a closer relationship with technology suppliers are more likely to achieve higher levels of performance than those that do not. It is also shown that with high levels of transaction attribute, implementation performance suffers more when firms have weak relationships with technology suppliers than with moderate and low levels of transaction attribute