Generalization of entanglement to convex operational theories: Entanglement relative to a subspace of observables

We define what it means for a state in a convex cone of states on a space of observables to be generalized-entangled relative to a subspace of the observables, in a general ordered linear spaces framework for operational theories. This extends the notion of ordinary entanglement in quantum information theory to a much more general framework. Some important special cases are described, in which the distinguished observables are subspaces of the observables of a quantum system, leading to results like the identification of generalized unentangled states with Lie-group-theoretic coherent states when the special observables form an irreducibly represented Lie algebra. Some open problems, including that of generalizing the semigroup of local operations with classical communication to the convex cones setting, are discussed.Comment: 19 pages, to appear in proceedings of Quantum Structures VII, Int. J. Theor. Phy

A generalized no-broadcasting theorem

We prove a generalized version of the no-broadcasting theorem, applicable to essentially \emph{any} nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with ``super-quantum'' correlations. A strengthened version of the quantum no-broadcasting theorem follows, and its proof is significantly simpler than existing proofs of the no-broadcasting theorem.Comment: 4 page

A violation of the uncertainty principle implies a violation of the second law of thermodynamics

Uncertainty relations state that there exist certain incompatible measurements, to which the outcomes cannot be simultaneously predicted. While the exact incompatibility of quantum measurements dictated by such uncertainty relations can be inferred from the mathematical formalism of quantum theory, the question remains whether there is any more fundamental reason for the uncertainty relations to have this exact form. What, if any, would be the operational consequences if we were able to go beyond any of these uncertainty relations? We give a strong argument that justifies uncertainty relations in quantum theory by showing that violating them implies that it is also possible to violate the second law of thermodynamics. More precisely, we show that violating the uncertainty relations in quantum mechanics leads to a thermodynamic cycle with positive net work gain, which is very unlikely to exist in nature.Comment: 8 pages, revte

Experimentally realizable quantum comparison of coherent states and its applications

When comparing quantum states to each other, it is possible to obtain an unambiguous answer, indicating that the states are definitely different, already after a single measurement. In this paper we investigate comparison of coherent states, which is the simplest example of quantum state comparison for continuous variables. The method we present has a high success probability, and is experimentally feasible to realize as the only required components are beam splitters and photon detectors. An easily realizable method for quantum state comparison could be important for real applications. As examples of such applications we present a "lock and key" scheme and a simple scheme for quantum public key distribution.Comment: 14 pages, 5 figures, version one submitted to PRA. Version two is the final accepted versio

Introduction to Quantum Information Processing

As a result of the capabilities of quantum information, the science of quantum information processing is now a prospering, interdisciplinary field focused on better understanding the possibilities and limitations of the underlying theory, on developing new applications of quantum information and on physically realizing controllable quantum devices. The purpose of this primer is to provide an elementary introduction to quantum information processing, and then to briefly explain how we hope to exploit the advantages of quantum information. These two sections can be read independently. For reference, we have included a glossary of the main terms of quantum information.Comment: 48 pages, to appear in LA Science. Hyperlinked PDF at http://www.c3.lanl.gov/~knill/qip/prhtml/prpdf.pdf, HTML at http://www.c3.lanl.gov/~knill/qip/prhtm

Crime in Context: Utilizing Risk Terrain Modeling and Conjunctive Analysis of Case Configurations to Explore the Dynamics of Criminogenic Behavior Settings.

Risk terrain modeling (RTM) is a geospatial crime analysis tool designed to diagnose environmental risk factors for crime and identify the places where their spatial influence is collocated to produce vulnerability for illegal behavior. However, the collocation of certain risk factors’ spatial influences may result in more crimes than the collocation of a different set of risk factors’ spatial influences. Absent from existing RTM outputs and methods is a straightforward method to compare these relative interactions and their effects on crime. However, as a multivariate method for the analysis of discrete categorical data, conjunctive analysis of case configurations (CACC) can enable exploration of the interrelationships between risk factors’ spatial influences and their varying effects on crime occurrence. In this study, we incorporate RTM outputs into a CACC to explore the dynamics among certain risk factors’ spatial influences and how they create unique environmental contexts, or behavior settings, for crime at microlevel places. We find that most crime takes place within a few unique behavior settings that cover a small geographic area and, further, that some behavior settings were more influential on crime than others. Moreover, we identified particular environmental risk factors that aggravate the influence of other risk factors. We suggest that by focusing on these microlevel environmental crime contexts, police can more efficiently target their resources and further enhance place-based approaches to policing that fundamentally address environmental features that produce ideal opportunities for crime

Distinguishing multi-partite states by local measurements

We analyze the distinguishability norm on the states of a multi-partite system, defined by local measurements. Concretely, we show that the norm associated to a tensor product of sufficiently symmetric measurements is essentially equivalent to a multi-partite generalisation of the non-commutative 2-norm (aka Hilbert-Schmidt norm): in comparing the two, the constants of domination depend only on the number of parties but not on the Hilbert spaces dimensions. We discuss implications of this result on the corresponding norms for the class of all measurements implementable by local operations and classical communication (LOCC), and in particular on the leading order optimality of multi-party data hiding schemes.Comment: 18 pages, 6 figures, 1 unreferenced referenc

Improving Detectors Using Entangling Quantum Copiers

We present a detection scheme which using imperfect detectors, and imperfect quantum copying machines (which entangle the copies), allows one to extract more information from an incoming signal, than with the imperfect detectors alone.Comment: 4 pages, 2 figures, REVTeX, to be published in Phys. Rev.

Quantum communication using a bounded-size quantum reference frame

Typical quantum communication schemes are such that to achieve perfect decoding the receiver must share a reference frame with the sender. Indeed, if the receiver only possesses a bounded-size quantum token of the sender's reference frame, then the decoding is imperfect, and we can describe this effect as a noisy quantum channel. We seek here to characterize the performance of such schemes, or equivalently, to determine the effective decoherence induced by having a bounded-size reference frame. We assume that the token is prepared in a special state that has particularly nice group-theoretic properties and that is near-optimal for transmitting information about the sender's frame. We present a decoding operation, which can be proven to be near-optimal in this case, and we demonstrate that there are two distinct ways of implementing it (corresponding to two distinct Kraus decompositions). In one, the receiver measures the orientation of the reference frame token and reorients the system appropriately. In the other, the receiver extracts the encoded information from the virtual subsystems that describe the relational degrees of freedom of the system and token. Finally, we provide explicit characterizations of these decoding schemes when the system is a single qubit and for three standard kinds of reference frame: a phase reference, a Cartesian frame (representing an orthogonal triad of spatial directions), and a reference direction (representing a single spatial direction).Comment: 17 pages, 1 figure, comments welcome; v2 published versio

Three-dimensionality of space and the quantum bit: an information-theoretic approach

It is sometimes pointed out as a curiosity that the state space of quantum two-level systems, i.e. the qubit, and actual physical space are both three-dimensional and Euclidean. In this paper, we suggest an information-theoretic analysis of this relationship, by proving a particular mathematical result: suppose that physics takes place in d spatial dimensions, and that some events happen probabilistically (not assuming quantum theory in any way). Furthermore, suppose there are systems that carry "minimal amounts of direction information", interacting via some continuous reversible time evolution. We prove that this uniquely determines spatial dimension d=3 and quantum theory on two qubits (including entanglement and unitary time evolution), and that it allows observers to infer local spatial geometry from probability measurements.Comment: 13 + 22 pages, 9 figures. v4: some clarifications, in particular in Section V / Appendix C (added Example 39