Spectral decomposition of Bell's operators for qubits

The spectral decomposition is given for the N-qubit Bell operators with two observables per qubit. It is found that the eigenstates (when non-degenerate) are N-qubit GHZ states even for those operators that do not allow the maximal violation of the corresponding inequality. We present two applications of this analysis. In particular, we discuss the existence of pure entangled states that do not violate any Mermin-Klyshko inequality for $N\geq 3$.Comment: 12 pages, 1 figure

The Quantum Frontier

The success of the abstract model of computation, in terms of bits, logical operations, programming language constructs, and the like, makes it easy to forget that computation is a physical process. Our cherished notions of computation and information are grounded in classical mechanics, but the physics underlying our world is quantum. In the early 80s researchers began to ask how computation would change if we adopted a quantum mechanical, instead of a classical mechanical, view of computation. Slowly, a new picture of computation arose, one that gave rise to a variety of faster algorithms, novel cryptographic mechanisms, and alternative methods of communication. Small quantum information processing devices have been built, and efforts are underway to build larger ones. Even apart from the existence of these devices, the quantum view on information processing has provided significant insight into the nature of computation and information, and a deeper understanding of the physics of our universe and its connections with computation. We start by describing aspects of quantum mechanics that are at the heart of a quantum view of information processing. We give our own idiosyncratic view of a number of these topics in the hopes of correcting common misconceptions and highlighting aspects that are often overlooked. A number of the phenomena described were initially viewed as oddities of quantum mechanics. It was quantum information processing, first quantum cryptography and then, more dramatically, quantum computing, that turned the tables and showed that these oddities could be put to practical effect. It is these application we describe next. We conclude with a section describing some of the many questions left for future work, especially the mysteries surrounding where the power of quantum information ultimately comes from.Comment: Invited book chapter for Computation for Humanity - Information Technology to Advance Society to be published by CRC Press. Concepts clarified and style made more uniform in version 2. Many thanks to the referees for their suggestions for improvement

de Finetti reductions for correlations

When analysing quantum information processing protocols one has to deal with large entangled systems, each consisting of many subsystems. To make this analysis feasible, it is often necessary to identify some additional structure. de Finetti theorems provide such a structure for the case where certain symmetries hold. More precisely, they relate states that are invariant under permutations of subsystems to states in which the subsystems are independent of each other. This relation plays an important role in various areas, e.g., in quantum cryptography or state tomography, where permutation invariant systems are ubiquitous. The known de Finetti theorems usually refer to the internal quantum state of a system and depend on its dimension. Here we prove a different de Finetti theorem where systems are modelled in terms of their statistics under measurements. This is necessary for a large class of applications widely considered today, such as device independent protocols, where the underlying systems and the dimensions are unknown and the entire analysis is based on the observed correlations.Comment: 5+13 pages; second version closer to the published one; new titl

Violation of Bell's inequalities implies distillability for N qubits

We consider quantum systems composed of $N$ qubits, and the family of all Bell's correlation inequalities for two two-valued measurements per site. We show that if a $N$-qubit state $\rho$ violates any of these inequalities, then it is at least bipartite distillable. Indeed there exists a link between the amount of Bell's inequality violation and the degree of distillability. Thus, we strengthen the interpretation of Bell's inequalities as detectors of useful entanglement.Comment: 6 pages, 3 figures, REVTEX. List of authors extended. Partially rewritten, a rather qualitative explanation of the results. Conclusions unchange

Unforgeable Noise-Tolerant Quantum Tokens

The realization of devices which harness the laws of quantum mechanics represents an exciting challenge at the interface of modern technology and fundamental science. An exemplary paragon of the power of such quantum primitives is the concept of "quantum money". A dishonest holder of a quantum bank-note will invariably fail in any forging attempts; indeed, under assumptions of ideal measurements and decoherence-free memories such security is guaranteed by the no-cloning theorem. In any practical situation, however, noise, decoherence and operational imperfections abound. Thus, the development of secure "quantum money"-type primitives capable of tolerating realistic infidelities is of both practical and fundamental importance. Here, we propose a novel class of such protocols and demonstrate their tolerance to noise; moreover, we prove their rigorous security by determining tight fidelity thresholds. Our proposed protocols require only the ability to prepare, store and measure single qubit quantum memories, making their experimental realization accessible with current technologies.Comment: 18 pages, 5 figure

Maxwell's Demon walks into Wall Street: Stochastic Thermodynamics meets Expected Utility Theory

The interplay between thermodynamics and information theory has a long history, but its quantitative manifestations are still being explored. We import tools from expected utility theory from economics into stochastic thermodynamics. We prove that, in a process obeying Crooks' fluctuation relations, every $\alpha$ R\'enyi divergence between the forward process and its reverse has the operational meaning of the ``certainty equivalent'' of dissipated work (or, more generally, of entropy production) for a player with risk aversion $r=\alpha-1$. The two known cases $\alpha=1$ and $\alpha=\infty$ are recovered and receive the new interpretation of being associated to a risk-neutral and an extreme risk-averse player respectively. Among the new results, the condition for $\alpha=0$ describes the behavior of a risk-seeking player willing to bet on the transient violations of the second law. Our approach further leads to a generalized Jarzynski equality, and generalizes to a broader class of statistical divergences.Comment: 5 pages, 1 figur

Bell inequalities and distillability in N-quantum-bit systems

The relation between Bell inequalities with two two-outcome measurements per site and distillability is analyzed in systems of an arbitrary number of quantum bits. We observe that the violation of any of these inequalities by a quantum state implies that pure-state entanglement can be distilled from it. The corresponding distillation protocol may require that some of the parties join into several groups. We show that there exists a link between the amount of the Bell inequality violation and the size of the groups they have to form for distillation. Thus, a strong violation is always sufficient for full N-partite distillability. This result also allows for a security proof of multi-partite quantum key distribution (QKD) protocols.Comment: REVTEX, 12 pages, two figure

Quantum correlations in Newtonian space and time: arbitrarily fast communication or nonlocality

We investigate possible explanations of quantum correlations that satisfy the principle of continuity, which states that everything propagates gradually and continuously through space and time. In particular, following [J.D. Bancal et al, Nature Physics 2012], we show that any combination of local common causes and direct causes satisfying this principle, i.e. propagating at any finite speed, leads to signalling. This is true even if the common and direct causes are allowed to propagate at a supraluminal-but-finite speed defined in a Newtonian-like privileged universal reference frame. Consequently, either there is supraluminal communication or the conclusion that Nature is nonlocal (i.e. discontinuous) is unavoidable.Comment: It is an honor to dedicate this article to Yakir Aharonov, the master of quantum paradoxes. Version 2 contains some more references and a clarified conclusio

Do all pure entangled states violate Bell's inequalities for correlation functions?

Any pure entangled state of two particles violates a Bell inequality for two-particle correlation functions (Gisin's theorem). We show that there exist pure entangled N>2 qubit states that do not violate any Bell inequality for N particle correlation functions for experiments involving two dichotomic observables per local measuring station. We also find that Mermin-Ardehali-Belinskii-Klyshko inequalities may not always be optimal for refutation of local realistic description.Comment: 4 pages, journal versio