Improving Einstein-Podolsky-Rosen Steering Inequalities with State Information

We discuss the relationship between entropic Einstein-Podolsky-Rosen (EPR)-steering inequalities and their underlying uncertainty relations, along with the hypothesis that improved uncertainty relations lead to tighter EPR-steering inequalities. In particular, we discuss how the intrinsic uncertainty in a mixed quantum state is used to improve existing uncertainty relations and how this information affects one's ability to witness EPR-steering. As an example, we consider the recent improvement (using a quantum memory) to the entropic uncertainty relation between pairs of discrete observables (Nat. Phys. 6, 659 (2010)) and show that a trivial substitution of the tighter bound in the steering inequality leads to contradictions, due in part to the fact that the improved bound depends explicitly on the state being measured. By considering the assumptions that enter into the development of a steering inequality, we derive correct steering inequalities from these improved uncertainty relations and find that they are identical to ones already developed (Phys. Rev. A, 87, 062103 (2013)). In addition, we consider how one can use the information about the quantum state to improve our ability to witness EPR-steering, and develop a new symmetric EPR-steering inequality as a result.Comment: 6 page

Uncertainty Relation for Mutual Information

We postulate the existence of a universal uncertainty relation between the quantum and classical mutual informations between pairs of quantum systems. Specifically, we propose that the sum of the classical mutual information, determined by two mutually unbiased pairs of observables, never exceeds the quantum mutual information. We call this the complementary-quantum correlation (CQC) relation and prove its validity for pure states, for states with one maximally mixed subsystem, and for all states when one measurement is minimally disturbing. We provide results of a Monte Carlo simulation suggesting the CQC relation is generally valid. Importantly, we also show that the CQC relation represents an improvement to an entropic uncertainty principle in the presence of a quantum memory, and that it can be used to verify an achievable secret key rate in the quantum one-time pad cryptographic protocol.Comment: 6 pages, 2 figure

Reserve Bank Operations in the Foreign Exchange Market: Effectiveness and Profitability

Since the float of the Australian dollar in December 1983, the Reserve Bank has intervened in the foreign exchange market in order to exert a stabilising influence. Whether this intervention has been stabilising cannot be directly observed since the behaviour of the exchange rate in its absence cannot be known. However, there are a number of ways of assessing it indirectly. The best known is the Friedman “profits test”. Friedman (1953) argued that a central bank which was stabilising the exchange rate would tend to buy foreign exchange when its price was low, and sell when its price is high, and hence its operations would be profitable. This paper applies the profits test to the Bank’s foreign exchange operations since the exchange rate was floated. The main conclusion is that over this period the Bank’s foreign exchange operations have produced total profits of around $A3.4 billion, suggesting that intervention has tended to be stabilising. Other statistical tests developed by Wonnacott (1982) and Mayer and Taguchi (1983), also presented in this paper, support this conclusion.

EPR Steering Inequalities from Entropic Uncertainty Relations

We use entropic uncertainty relations to formulate inequalities that witness Einstein-Podolsky-Rosen (EPR) steering correlations in diverse quantum systems. We then use these inequalities to formulate symmetric EPR-steering inequalities using the mutual information. We explore the differing natures of the correlations captured by one-way and symmetric steering inequalities, and examine the possibility of exclusive one-way steerability in two-qubit states. Furthermore, we show that steering inequalities can be extended to generalized positive operator valued measures (POVMs), and we also derive hybrid-steering inequalities between alternate degrees of freedom.Comment: 10 pages, 2 figure

Annual Survey of Virginia Law: Corporate and Business Law

Virginia corporate and business law changes in the last year continue to challenge the practitioner to stay abreast of such developments in order to provide accurate advice to clients. This article summarizes the developments in the law in Virginia occurring from June 1999 through May 2000, with the legislative changes described based on Virginia General Assembly action in the 2000 session. Part II examines those legislative changes in corporate and business law (excluding public service corporation/public utility law issues). While many of the legislative changes are not significant, three new uniform laws (revised Article 9 of the Uniform Commercial Code ( UCC ), dealing with secured transactions, the Uniform Electronic Transactions Act, and the Uniform Computer Information Transactions Act) are likely to have a major impact on significant areas of business law practice and business conduct. Part III reviews judicial decisions on commercial law and business entity issues during the year, including a controversial decision on the duty of directors

The Implementation of Monetary Policy in Australia

In January 1990, the Reserve Bank of Australia (RBA) began announcing and explaining changes in the target cash rate. This has increased public understanding of monetary policy and, by increasing the attention given to changes in interest rates, has affected the way in which changes in policy are transmitted to the economy. In addition, the discipline of having to announce and explain changes in the target cash rate to the public has led to a clearer focus on the objectives of monetary policy within the RBA and improved the accountability of the Bank. It has also led to a substantial decline in the volatility of short-term interest rates and more rapid pass-through of changes in the target cash rate into deposit and lending rates. In Australia, as in many other countries, interest rates have tended to be adjusted in a series of steps in the same direction. In part, this can be explained in terms of the uncertainty that policy-makers face, and the costs involved in frequently reversing the direction of interest-rate changes.

Improving Einstein–Podolsky–Rosen Steering Inequalities with State Information

We discuss the relationship between entropic Einstein–Podolsky–Rosen (EPR)-steering inequalities and their underlying uncertainty relations along with the hypothesis that improved uncertainty relations lead to tighter EPR-steering inequalities. In particular, we discuss how using information about the state of a quantum system affects oneʼs ability to witness EPR-steering. As an example, we consider the recent improvement to the entropic uncertainty relation between pairs of discrete observables (Berta et al., 2010 [10]). By considering the assumptions that enter into the development of a steering inequality, we derive correct steering inequalities from these improved uncertainty relations and find that they are identical to ones already developed (Schneeloch et al., 2013 [9]). In addition, we consider how one can use state information to improve our ability to witness EPR-steering, and develop a new continuous variable symmetric EPR-steering inequality as a result