Synaptic Algebras as Models for Quantum Mechanics

Pulmannová, Sylvia

doi:10.1007/s10773-019-04045-3

Cited by 2 publications

(3 citation statements)

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“…In order to show that such POVMs are all jointly measurable, we only need to reinterpret the channel parameters (M, N, c) as the joint measurement G λ . Indeed, with (K, L, m) taken as postprocessing parameters, (31) becomes identical to (30), showing how (K , L , m ) is postprocessed from G λ . We stress that the nontrivial part is in the positivity requirements, which are not in general identical.…”

Section: Gaussian Casementioning

confidence: 83%

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Continuous-variable steering and incompatibility via state-channel duality

et al. 2017

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The term Einstein-Podolsky-Rosen steering refers to a quantum correlation intermediate between entanglement and Bell nonlocality, which has been connected to another fundamental quantum property: measurement incompatibility. In the finite-dimensional case, efficient computational methods to quantify steerability have been developed. In the infinite-dimensional case, however, less theoretical tools are available. Here, we approach the problem of steerability in the continuous variable case via a notion of state-channel correspondence, which generalizes the well-known Choi-Jamio?kowski correspondence. Via our approach we are able to generalize the connection between steering and incompatibility to the continuous variable case and to connect the steerability of a state with the incompatibility breaking property of a quantum channel, with applications to noisy NOON states and amplitude damping channels. Moreover, we apply our methods to the Gaussian steering setting, proving, among other things, that canonical quadratures are sufficient for steering Gaussian statesauthorsversionPeer reviewe

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Section: Gaussian Casementioning

confidence: 83%

“…where the postprocessing D(·|x, ·) = A x × Λ → [0, 1] is generally known as a weak Markov kernel [31]. An assemblage not jointly measurable is called incompatible.…”

Section: B Joint Measurabilitymentioning

confidence: 99%

Continuous-variable steering and incompatibility via state-channel duality

et al. 2017

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“…In what follows, A is a synaptic algebra with enveloping algebra R ⊇ A, [11,16,13,20,21,22,37,38] and P is the orthomodular lattice [5,33] of projections in A. A prototype example is the set A of all self-adjoint operators in the algebra B(H) of all bounded linear operators on the Hilbert space H with B(H) as enveloping algebra.…”

Section: Synaptic Algebrasmentioning

confidence: 99%

Observables on synaptic algebras

Jenčová¹,

Pulmannová²

2019

Preprint

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Synaptic algebras, introduced by D. Foulis, generalize different algebraic structures used so far as mathematical models of quantum mechanics: the traditional Hilbert space approach, order unit spaces, Jordan algebras, effect algebras, MV-algebras, orthomodular lattices. We study sharp and fuzzy observables on two special classes of synaptic algebras: on the so called generalized Hermitian algebras and on synaptic algebras which are Banach space duals. Relations between fuzzy and sharp observables on these two types of synaptic algebras are shown.

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Synaptic Algebras as Models for Quantum Mechanics

Cited by 2 publications

References 50 publications

Continuous-variable steering and incompatibility via state-channel duality

Continuous-variable steering and incompatibility via state-channel duality

Observables on synaptic algebras

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