The Quantum Formalization Drive

We show that there exist bipartite quantum states which contain large hidden classical correlation that can be unlocked by a disproportionately small amount of classical communication. In particular, there are $(2n+1)$-qubit states for which a one bit message doubles the optimal classical mutual information between measurement results on the subsystems, from …

We study quantum channels with respect to their image, i.e., the image of the set of density operators under the action of the channel. We first characterize the set of quantum channels having polytopic images and show that additivity of the minimal output entropy can be violated in this class. We then provide a complete characterization of quantum channels …

We present a spectral sequence connecting the continuous and 'locally continuous' group cohomologies for topological groups. As an application it is shown that for contractible topological groups these cohomology concepts coincide. Similar results for k-groups and smooth cochains on Lie groups are also obtained.

In this paper, we prove that the cyclotomic BMW algebras B2p+1,n are cellular in the sense of [16]. We also classify the irreducible B2p+1,nmodules over a field.

A decomposition theorem for self-adjoint operators proved by Riesz and Lorch is extended to normal operators. This extension gives a new proof of the spectral theorem for unbounded normal operators.

We show that, in any open set of distillable states, all asymptotic entanglement measures $E(ρ)$ are continuous as a function of (a single copy of) $ρ$, even though they quantify the entanglement properties of $ρ^{\otimes N}$ is the large $N$ limit.

In this paper, we introduce the concept of dual universality of hash functions and present its applications to quantum cryptography. We begin by establishing the one-to-one correspondence between a linear function family {\cal F} and a code family {\cal C}, and thereby defining \varepsilon-almost dual universal_2 hash functions, as a generalization of the…

Notions of a Gaussian state and a Gaussian linear map are generalized to the case of anticommuting (Grassmann) variables. Conditions under which a Gaussian map is trace preserving and (or) completely positive are formulated. For any Gaussian map an explicit formula relating correlation matrices of input and output states is presented. This formalism allows…

We prove the security of the Bennett-Brassard (BB84) quantum key distribution protocol in the case where the source and detector are under the limited control of an adversary. Our proof applies when both the source and the detector have small basis-dependent flaws, as is typical in practical implementations of the protocol. We derive a general lower bound…

We present a polynomiality property of the Littlewood-Richardson coefficients c_{λμ}^ν. The coefficients are shown to be given by polynomials in λ, μand νon the cones of the chamber complex of a vector partition function. We give bounds on the degree of the polynomials depending on the maximum allowed number of parts of the partitions λ, μand ν. We first…

We study non-equilibrium statistical mechanics of a Gaussian dynamical system and compute in closed form the large deviation functionals describing the fluctuations of the entropy production observable with respect to the reference state and the non-equilibrium steady state. The entropy production observable of this model is an unbounded function on the…

Bundle gerbes are a higher version of line bundles, we present nonabelian bundle gerbes as a higher version of principal bundles. Connection, curving, curvature and gauge transformations are studied both in a global coordinate independent formalism and in local coordinates. These are the gauge fields needed for the construction of Yang-Mills theories with…

Parallel transport of a connection in a smooth fibre bundle yields a functor from the path groupoid of the base manifold into a category that describes the fibres of the bundle. We characterize functors obtained like this by two notions we introduce: local trivializations and smooth descent data. This provides a way to substitute categories of functors for…

We study the Fluctuation Theorem (FT) for entropy production in chaotic discrete-time dynamical systems on compact metric spaces, and extend it to empirical measures, all continuous potentials, and all weak Gibbs states. In particular, we establish the FT in the phase transition regime. These results hold under minimal chaoticity assumptions (expansiveness…

Quantum circuits with gates (local unitaries) respecting a global symmetry have broad applications in quantum information science and related fields, such as condensed matter theory and quantum thermodynamics. However, despite their widespread use, fundamental properties of such circuits are not well-understood. Recently, it was found that generic unitaries…

An inseparability criterion based on the total variance of a pair of Einstein-Podolsky-Rosen type operators is proposed for continuous variable systems. The criterion provides a sufficient condition for entanglement of any two-party continuous variable states. Furthermore, for all the Gaussian states, this criterion turns out to be a necessary and…

Optical communication channels are ultimately quantum-mechanical in nature, and we must therefore look beyond classical information theory to determine their communication capacity as well as to find efficient encoding and decoding schemes of the highest rates. Thermal channels, which arise from linear coupling of the field to a thermal environment, are of…

Quantum systems carry information. Quantum theory supports at least two distinct kinds of information (classical and quantum), and a variety of different ways to encode and preserve information in physical systems. A system's ability to carry information is constrained and defined by the noise in its dynamics. This paper introduces an operational framework,…

In this paper, we give a necessary and sufficient condition for a cyclotomic Brauer algebra being semisimple. This generalizes previous result for a Brauer algebra.

We introduce a new notion of a sufficient subalgebra for quantum states: a subalgebra is 2- sufficient for a pair of states $\{ρ_0,ρ_1\}$ if it contains all Bayes optimal tests of $ρ_0$ against $ρ_1$. In classical statistics, this corresponds to the usual definition of sufficiency. We show this correspondence in the quantum setting for some special cases.…

We introduce new teleportation protocols which are generalizations of the original teleportation protocols that use the Pauli group [Bennett, et al. Physical Review Letters, 70(13) 1895-1899] and the port-based teleportation protocols, introduced by Hiroshima and Ishizaka [Physical Review Letters, 101(24) 240501], that use the symmetric permutation group.…

We exhibit infinitely many new, constrained inequalities for the von Neumann entropy, and show that they are independent of each other and the known inequalities obeyed by the von Neumann entropy (basically strong subadditivity). The new inequalities were proved originally by Makarychev et al. [Commun. Inf. Syst., 2(2):147-166, 2002] for the Shannon…

The cyclotomic Birman-Murakami-Wenzl (or BMW) algebras B_n^k, introduced by R. Haring-Oldenburg, are extensions of the cyclotomic Hecke algebras of Ariki-Koike, in the same way as the BMW algebras are extensions of the Hecke algebras of type A. In this paper we focus on the case n=2, producing a basis of B_2^k and constructing its left regular…

A representation $π$ of a locally compact group $G$ is called \e{trace class}, if for every test function $f$ the induced operator $π(f)$ is a trace class operator. The group $G$ is called \e{trace class}, if every $π\in G$ is trace class. We show that trace class groups are type I and give a criterion for semi-direct products to be trace class and show that a…