A time-dependent Tsirelson's bound from limits on the rate of information gain in quantum systems

We consider the problem of distinguishing between a set of arbitrary quantum states in a setting in which the time available to perform the measurement is limited. We provide simple upper bounds on how well we can perform state discrimination in a given time as a function of either the average energy or the range of energies available during the measurement. We exhibit a specific strategy that nearly attains this bound. Finally, we consider several applications of our result. First, we obtain a time-dependent Tsirelson's bound that limits the extent of the Bell inequality violation that can be in principle be demonstrated in a given time t. Second, we obtain a Margolus-Levitin type bound when considering the special case of distinguishing orthogonal pure states.Comment: 15 pages, revtex, 1 figur

Computability limits non-local correlations

If the no-signalling principle was the only limit to the strength of non-local correlations, we would expect that any form of no-signalling correlation can indeed be realized. That is, there exists a state and measurements that remote parties can implement to obtain any such correlation. Here, we show that in any theory in which some functions cannot be computed, there must be further limits to non-local correlations than the no-signalling principle alone. We proceed to argue that even in a theory such as quantum mechanics in which non-local correlations are already weaker, the question of computability imposes such limits.Comment: 5 pages, 1 figure, revte

Entropy in general physical theories

Information plays an important role in our understanding of the physical world. We hence propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical world, our measure reduces to the von Neumann and Shannon entropy respectively. It can even be used in a quantum or classical setting where we are only allowed to perform a limited set of operations. In a world that admits superstrong correlations in the form of non-local boxes, our measure can be used to analyze protocols such as superstrong random access encodings and the violation of `information causality'. However, we also show that in such a world no entropic measure can exhibit all properties we commonly accept in a quantum setting. For example, there exists no`reasonable' measure of conditional entropy that is subadditive. Finally, we prove a coding theorem for some theories that is analogous to the quantum and classical setting, providing us with an appealing operational interpretation.Comment: 20 pages, revtex, 7 figures, v2: Coding theorem revised, published versio

The Hilbertian Tensor Norm and Entangled Two-Prover Games

We study tensor norms over Banach spaces and their relations to quantum information theory, in particular their connection with two-prover games. We consider a version of the Hilbertian tensor norm $\gamma_2$ and its dual $\gamma_2^*$ that allow us to consider games with arbitrary output alphabet sizes. We establish direct-product theorems and prove a generalized Grothendieck inequality for these tensor norms. Furthermore, we investigate the connection between the Hilbertian tensor norm and the set of quantum probability distributions, and show two applications to quantum information theory: firstly, we give an alternative proof of the perfect parallel repetition theorem for entangled XOR games; and secondly, we prove a new upper bound on the ratio between the entangled and the classical value of two-prover games.Comment: 33 pages, some of the results have been obtained independently in arXiv:1007.3043v2, v2: an error in Theorem 4 has been corrected; Section 6 rewritten, v3: completely rewritten in order to improve readability; title changed; references added; published versio

A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations

We are interested in the problem of characterizing the correlations that arise when performing local measurements on separate quantum systems. In a previous work [Phys. Rev. Lett. 98, 010401 (2007)], we introduced an infinite hierarchy of conditions necessarily satisfied by any set of quantum correlations. Each of these conditions could be tested using semidefinite programming. We present here new results concerning this hierarchy. We prove in particular that it is complete, in the sense that any set of correlations satisfying every condition in the hierarchy has a quantum representation in terms of commuting measurements. Although our tests are conceived to rule out non-quantum correlations, and can in principle certify that a set of correlations is quantum only in the asymptotic limit where all tests are satisfied, we show that in some cases it is possible to conclude that a given set of correlations is quantum after performing only a finite number of tests. We provide a criterion to detect when such a situation arises, and we explain how to reconstruct the quantum states and measurement operators reproducing the given correlations. Finally, we present several applications of our approach. We use it in particular to bound the quantum violation of various Bell inequalities.Comment: 33 pages, 2 figure

Climate Science Special Report: Fourth National Climate Assessment (NCA4), Volume I

New observations and new research have increased our understanding of past, current, and future climate change since the Third U.S. National Climate Assessment (NCA3) was published in May 2014. This Climate Science Special Report (CSSR) is designed to capture that new information and build on the existing body of science in order to summarize the current state of knowledge and provide the scientific foundation for the Fourth National Climate Assessment (NCA4)

A framework for the study of symmetric full-correlation Bell-like inequalities

Full-correlation Bell-like inequalities represent an important subclass of Bell-like inequalities that have found applications in both a better understanding of fundamental physics and in quantum information science. Loosely speaking, these are inequalities where only measurement statistics involving all parties play a role. In this paper, we provide a framework for the study of a large family of such inequalities that are symmetrical with respect to arbitrary permutations of the parties. As an illustration of the power of our framework, we derive (i) a new family of Svetlichny inequalities for arbitrary numbers of parties, settings and outcomes, (ii) a new family of two-outcome device-independent entanglement witnesses for genuine n-partite entanglement and (iii) a new family of two-outcome Tsirelson inequalities for arbitrary numbers of parties and settings. We also discuss briefly the application of these new inequalities in the characterization of quantum correlations

Climate Science Special Report: Fourth National Climate Assessment (NCA4), Volume I

The article of record as published may be found at https://doi.org/10.7930