Parallel Repetition of Entangled Games with Exponential Decay via the Superposed Information Cost

In a two-player game, two cooperating but non communicating players, Alice and Bob, receive inputs taken from a probability distribution. Each of them produces an output and they win the game if they satisfy some predicate on their inputs/outputs. The entangled value $\omega^*(G)$ of a game $G$ is the maximum probability that Alice and Bob can win the game if they are allowed to share an entangled state prior to receiving their inputs. The $n$-fold parallel repetition $G^n$ of $G$ consists of $n$ instances of $G$ where the players receive all the inputs at the same time and produce all the outputs at the same time. They win $G^n$ if they win each instance of $G$. In this paper we show that for any game $G$ such that $\omega^*(G) = 1 - \varepsilon < 1$, $\omega^*(G^n)$ decreases exponentially in $n$. First, for any game $G$ on the uniform distribution, we show that $\omega^*(G^n) = (1 - \varepsilon^2)^{\Omega\left(\frac{n}{\log(|I||O|)} - |\log(\varepsilon)|\right)}$, where $|I|$ and $|O|$ are the sizes of the input and output sets. From this result, we show that for any entangled game $G$, $\omega^*(G^n) \le (1 - \varepsilon^2)^{\Omega(\frac{n}{Q\log(|I||O|)} - \frac{|\log(\varepsilon)|}{Q})}$ where $p$ is the input distribution of $G$ and $Q= \frac{|I|^2 \max_{xy} p_{xy}^2 }{\min_{xy} p_{xy} }$. This implies parallel repetition with exponential decay as long as $\min_{xy} \{p_{xy}\} \neq 0$ for general games. To prove this parallel repetition, we introduce the concept of \emph{Superposed Information Cost} for entangled games which is inspired from the information cost used in communication complexity.Comment: In the first version of this paper we presented a different, stronger Corollary 1 but due to an error in the proof we had to modify it in the second version. This third version is a minor update. We correct some typos and re-introduce a proof accidentally commented out in the second versio

Long-range entanglement generation via frequent measurements

A method is introduced whereby two non-interacting quantum subsystems, that each interact with a third subsystem, are entangled via repeated projective measurements of the state of the third subsystem. A variety of physical examples are presented. The method can be used to establish long range entanglement between distant parties in one parallel measurement step, thus obviating the need for entanglement swapping.Comment: 7 pages, incl. 2 figures. v2: added a few small clarifications and a referenc

Proposed experiment for the quantum "Guess my number" protocol

An experimental realization of the entanglement-assisted "Guess my number" protocol for the reduction of communication complexity, introduced by Steane and van Dam, would require producing and detecting three-qubit GHZ states with an efficiency eta > 0.70, which would require single photon detectors of efficiency sigma > 0.89. We propose a modification of the protocol which can be translated into a real experiment using present-day technology. In the proposed experiment, the quantum reduction of the multi-party communication complexity would require an efficiency eta > 0.05, achievable with detectors of sigma > 0.47, for four parties, and eta > 0.17 (sigma > 0.55) for three parties.Comment: REVTeX4, 4 pages, 1 figur

Legal Facts and Reasons for Action: Between Deflationary and Robust Conceptions of Law’s Reason-Giving Capacity

This chapter considers whether legal requirements can constitute reasons for action independently of the merits of the requirement at hand. While jurisprudential opinion on this question is far from uniform, sceptical views are becoming increasingly dominant. Such views typically contend that, while the law can be indicative of pre-existing reasons, or can trigger pre-existing reasons into operation, it cannot constitute new reasons. This chapter offers support to a somewhat less sceptical position, according to which the fact that a legal requirement has been issued can be a reason for action, yet one that is underpinned by bedrock values which law is apt to serve. Notions discussed here include a value-based conception of reasons as facts ; a distinction between complete and incomplete reasons ; and David Enoch’s idea of triggering reason-giving. Following a discussion of criticism against the view adopted here, the chapter concludes by considering some more ‘robust’ conceptions of law’s reason-giving capacity

Other‐Sacrificing Options

I argue that you can be permitted to discount the interests of your adversaries even though doing so would be impartially suboptimal. This means that, in addition to the kinds of moral options that the literature traditionally recognises, there exist what I call other-sacrificing options. I explore the idea that you cannot discount the interests of your adversaries as much as you can favour the interests of your intimates; if this is correct, then there is an asymmetry between negative partiality toward your adversaries and positive partiality toward your intimates

Intraperitoneal photodynamic therapy causes a capillary-leak syndrome.

BackgroundIn patients undergoing intraperitoneal (IP) photodynamic therapy (PDT), the combination of aggressive surgical debulking and light therapy causes an apparent systemic capillary-leak syndrome that necessitates significant intensive care unit (ICU) management after surgery.MethodsFrom May 1997 to May 2001, 65 patients underwent surgical debulking and PDT as part of an ongoing phase II trial for disseminated IP cancer. Perioperative data were reviewed retrospectively, and statistical analyses were performed to determine whether any identifiable factors were associated with the need for mechanical ventilation for longer than 1 day and with the occurrence of postoperative complications.ResultsForty-three women and 22 men (mean age, 49 years) were treated. Operative time averaged 9.8 hours, and mean estimated blood loss was 1450 mL. The mean crystalloid requirement for the first 48 hours after surgery was 29.3 L, and 49 patients required blood products. Twenty-four patients were intubated for longer than 24 hours, with a mean of 8.3 days for those intubated longer than 1 day. The median ICU stay was 4 days. Overall, 110 complications developed in 45 (69%) of the 65 patients. Significant complications included 6 patients with acute respiratory distress syndrome, 28 patients with infectious complications, and 4 patients with anastomotic complications. Statistical analyses revealed that surgery-related factors were significantly associated with these complication outcomes.ConclusionsPatients who undergo surgical debulking and IP PDT develop a significant capillary-leak syndrome after surgery that necessitates massive volume resuscitation, careful ICU monitoring, and, frequently, prolonged ventilatory support

Does Geographic Clustering Still Benefit High Tech New Ventures? The Case of the Cambridge/Boston Biotech Cluster

An empirical study of scientific communication among biotechnology companies supports the belief that geographic clustering does produce increased scientific exchange among companies. A comparison of companies within a constrained geographic area with those more dispersed shows a significantly higher level of scientific communication among the former. Scientific communication declines rapidly with plupical separation. Critical of the formation of cluster – based scientific communication networks is the presence of both universities and large firms from the same industry

Counting dependent and independent strings

The paper gives estimations for the sizes of the the following sets: (1) the set of strings that have a given dependency with a fixed string, (2) the set of strings that are pairwise \alpha independent, (3) the set of strings that are mutually \alpha independent. The relevant definitions are as follows: C(x) is the Kolmogorov complexity of the string x. A string y has \alpha -dependency with a string x if C(y) - C(y|x) \geq \alpha. A set of strings {x_1, \ldots, x_t} is pairwise \alpha-independent if for all i different from j, C(x_i) - C(x_i | x_j) \leq \alpha. A tuple of strings (x_1, \ldots, x_t) is mutually \alpha-independent if C(x_{\pi(1)} \ldots x_{\pi(t)}) \geq C(x_1) + \ldots + C(x_t) - \alpha, for every permutation \pi of [t]