395 research outputs found

    State convertibility in the von Neumann algebra framework

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    We establish a generalisation of the fundamental state convertibility theorem in quantum information to the context of bipartite quantum systems modelled by commuting semi-finite von Neumann algebras. Namely, we establish a generalisation to this setting of Nielsen's theorem on the convertibility of quantum states under local operations and classical communication (LOCC) schemes. Along the way, we introduce an appropriate generalisation of LOCC operations and connect the resulting notion of approximate convertibility to the theory of singular numbers and majorisation in von Neumann algebras. As an application of our result in the setting of II1II_1-factors, we show that the entropy of the singular value distribution relative to the unique tracial state is an entanglement monotone in the sense of Vidal, thus yielding a new way to quantify entanglement in that context. Building on previous work in the infinite-dimensional setting, we show that trace vectors play the role of maximally entangled states for general II1II_1-factors. Examples are drawn from infinite spin chains, quasi-free representations of the CAR, and discretised versions of the CCR.Comment: 36 pages, v2: journal version, 38 page

    A method to find quantum noiseless subsystems

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    We develop a structure theory for decoherence-free subspaces and noiseless subsystems that applies to arbitrary (not necessarily unital) quantum operations. The theory can be alternatively phrased in terms of the superoperator perspective, or the algebraic noise commutant formalism. As an application, we propose a method for finding all such subspaces and subsystems for arbitrary quantum operations. We suggest that this work brings the fundamental passive technique for error correction in quantum computing an important step closer to practical realization.Comment: 5 pages, to appear in Physical Review Letter

    Black hole evaporation with separated fermions

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    In models with a low quantum gravity scale, a well-motivated reason to expect quark and lepton fields are localized but physically separated is to avoid proton decay. This could happen in a ``fat-brane'' or in an additional, orthogonal 1/TeV sized dimension in which the gauge and Higgs fields live throughout. Black holes with masses of order the quantum gravity scale are therefore expected to evaporate non-universally, preferentially radiating directly into quarks or leptons but not both. Should black holes be copiously produced at a future hadron collider, we find the ratio of final state jets to charged leptons to photons is 113:8:1, which differs from previous analyses that assumed all standard model fields live at the same point in the extra dimensional space.Comment: 5 pages, REVTe

    Corrections to Gravity due to a Sol Manifold Extra Dimensional Space

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    The corrections to the gravitational potential due to a Sol extra dimensional compact manifold, denoted as MA3M_A^3, are studied. The total spacetime is of the form M4×MA3M^4\times M_A^3. The range of the Sol corrections is investigated and compared to the range of the T3T^3 corrections.Comment: 13 pages, 10 figures, published versio
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