A Note on the correspondence between Qubit Quantum Operations and Special Relativity

We exploit a well-known isomorphism between complex hermitian $2\times 2$ matrices and $\mathbb{R}^4$, which yields a convenient real vector representation of qubit states. Because these do not need to be normalized we find that they map onto a Minkowskian future cone in $\mathbb{E}^{1,3}$, whose vertical cross-sections are nothing but Bloch spheres. Pure states are represented by light-like vectors, unitary operations correspond to special orthogonal transforms about the axis of the cone, positive operations correspond to pure Lorentz boosts. We formalize the equivalence between the generalized measurement formalism on qubit states and the Lorentz transformations of special relativity, or more precisely elements of the restricted Lorentz group together with future-directed null boosts. The note ends with a discussion of the equivalence and some of its possible consequences.Comment: 6 pages, revtex, v3: revised discussio

Typing Quantum Superpositions and Measurement

We propose a way to unify two approaches of non-cloning in quantum lambda-calculi. The first approach is to forbid duplicating variables, while the second is to consider all lambda-terms as algebraic-linear functions. We illustrate this idea by defining a quantum extension of first-order simply-typed lambda-calculus, where the type is linear on superposition, while allows cloning base vectors. In addition, we provide an interpretation of the calculus where superposed types are interpreted as vector spaces and non-superposed types as their basis.Fil: Díaz Caro, Alejandro. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Dowek, Gilles. Institut National de Recherche en Informatique et en Automatique; Franci

Virtually Abelian Quantum Walks

We introduce quantum walks on Cayley graphs of non-Abelian groups. We focus on the easiest case of virtually Abelian groups, and introduce a technique to reduce the quantum walk to an equivalent one on an Abelian group with coin system having larger dimension. We apply the technique in the case of two quantum walks on virtually Abelian groups with planar Cayley graphs, finding the exact solution.Comment: 10 pages, 3 figure

Linearity in the non-deterministic call-by-value setting

We consider the non-deterministic extension of the call-by-value lambda calculus, which corresponds to the additive fragment of the linear-algebraic lambda-calculus. We define a fine-grained type system, capturing the right linearity present in such formalisms. After proving the subject reduction and the strong normalisation properties, we propose a translation of this calculus into the System F with pairs, which corresponds to a non linear fragment of linear logic. The translation provides a deeper understanding of the linearity in our setting.Comment: 15 pages. To appear in WoLLIC 201

Blood Oxygen Level-Dependent Activation of the Primary Visual Cortex Predicts Size Adaptation Illusion

In natural scenes, objects rarely occur in isolation but appear within a spatiotemporal context. Here, we show that the perceived size of a stimulus is significantly affected by the context of the scene: brief previous presentation of larger or smaller adapting stimuli at the same region of space changes the perceived size of a test stimulus, with larger adapting stimuli causing the test to appear smaller than veridical and vice versa. In ahumanfMRI study, we measured the blood oxygen level-dependent activation (BOLD) responses of the primary visual cortex (V1) to the contours of large-diameter stimuli and found that activation closely matched the perceptual rather than the retinal stimulus size: the activated area of V1 increased or decreased, depending on the size of the preceding stimulus. A model based on local inhibitory V1 mechanisms simulated the inward or outward shifts of the stimulus contours and hence the perceptual effects. Our findings suggest that area V1 is actively involved in reshaping our perception to match the short-term statistics of the visual scene

Spatiotopic selectivity of adaptation-based compression of event duration

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Call-by-value non-determinism in a linear logic type discipline

We consider the call-by-value lambda-calculus extended with a may-convergent non-deterministic choice and a must-convergent parallel composition. Inspired by recent works on the relational semantics of linear logic and non-idempotent intersection types, we endow this calculus with a type system based on the so-called Girard's second translation of intuitionistic logic into linear logic. We prove that a term is typable if and only if it is converging, and that its typing tree carries enough information to give a bound on the length of its lazy call-by-value reduction. Moreover, when the typing tree is minimal, such a bound becomes the exact length of the reduction

Semantics of a Typed Algebraic Lambda-Calculus

Algebraic lambda-calculi have been studied in various ways, but their semantics remain mostly untouched. In this paper we propose a semantic analysis of a general simply-typed lambda-calculus endowed with a structure of vector space. We sketch the relation with two established vectorial lambda-calculi. Then we study the problems arising from the addition of a fixed point combinator and how to modify the equational theory to solve them. We sketch an algebraic vectorial PCF and its possible denotational interpretations

Immunolocalization of Aquaporin Water Channels in the Domestic Cat Male Genital Tract

Four different aquaporins (AQP1, 2, 5 and 9), integral membrane water channels that facilitate rapid passive movement of water, were immuno-localized in the excurrent ducts collected from sexually mature cats during orchiectomy. Aquaporins 1, 2 and 9, were immuno-localized at distinct levels, whereas AQP5 was undetectable all along the feline genital tract. No immunoreactivity was present at the level of the rete testis with any of the antibodies tested. In the efferent ducts, AQP1-immunoreactivity was strongly evidenced at the apical surface of the non-ciliated cells, and AQP9-immunoreactivity was shown at the periphery of both ciliated and nonciliated cells. Aquaporins 2 was absent in the caput epididymidis, either in the efferent ducts or in the epididymal duct. Otherwise, AQP2 was increasingly localized at the adluminal surface of principal cells from the corpus to the cauda epididymidis and more weakly in the vas deferens epithelium. The supranuclear zone of the epididymal principal cells was AQP9-immunoreactive throughout the duct, with the exclusion of the vacuolated sub-region of the caput and with higher reaction intensity in the cauda region. AQP1 was present in the blood vessels all along the genital tract. AQP1 was expressed also in the smooth muscle layer of the vas deferens. The tested AQP molecules showed a different expression pattern in comparison with laboratory mammals, primates and the dog, unique other carnivore species studied to date. The present information is possibly useful in regard to the regional morphology of the feline epididymis and correlated functions, which are still a matter of debate