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Quantum Communication with Redundancy-free Error Correction

Sándor Imre

The limits of classical information theory are stretched at several points by the consideration of quantum mechanics. Entanglement in itself is a unique phenomenon, and its application has enabled solutions such as super-dense compression, teleportation or super-activation of quantum channels. Noisy classical channels can only be made error-free by adding redundancy, and even this can only be done for certain channels. However, in this article, we examine an equally unique possibility, namely, what properties can make the quantum channels error-free without adding redundancy just by using appropriate quantum transformations. We will show the quantum coding required for this and illustrate its efficiency through examples.The limits of classical information theory are stretched at several points by the consideration of quantum mechanics. Entanglement in itself is a unique phenomenon, and its application has enabled solutions such as super-dense compression, teleportation or super-activation of quantum channels. Noisy classical channels can only be made error-free by adding redundancy, and even this can only be done for certain channels. However, in this article, we examine an equally unique possibility, namely, what properties can make the quantum channels error-free without adding redundancy just by using appropriate quantum transformations. We will show the quantum coding required for this and illustrate its efficiency through examples.

Aug 12, 20250 citations

Steady state entanglement beyond the thermodynamic limit

Francesco Tacchino, Alexia Auffèves, Marcelo França Santos +1 more

Oct 3, 20170 citations

Thermodynamics of Entanglement

Shinji Mukohyama A

Jan 1, 19980 citations

Free ride for quantum theory

David Gevaux

Nature PhysicsApr 1, 20130 citations

Grassmannization of the 3D Ising Model

Enrico Martello, G. G. N. Angilella, Lode Pollet

The application of Feynman’s diagrammatic technique to classical link models with local constraints seems impossible due to (i) the absence of a free Gaussian theory on top of which the perturbative expansion can be constructed, and (ii) Dyson’s collapse argument, rendering the perturbative expansion divergent. However, we show for the classical 3D Ising model how both problems can be circumvented using a Grassmann representation. This makes it possible to obtain an expansion of the spin correlation function and the magnetic susceptibility in terms of the inverse temperature in the thermodynamic limit, through which the values for the critical temperature and critical index g are evaluated within 1.6% and 5.4% of their accepted values, respectively. Our work is a straightforward adaptation of the theory previously developed in an earlier paper.The application of Feynman’s diagrammatic technique to classical link models with local constraints seems impossible due to (i) the absence of a free Gaussian theory on top of which the perturbative expansion can be constructed, and (ii) Dyson’s collapse argument, rendering the perturbative expansion divergent. However, we show for the classical 3D Ising model how both problems can be circumvented using a Grassmann representation. This makes it possible to obtain an expansion of the spin correlation function and the magnetic susceptibility in terms of the inverse temperature in the thermodynamic limit, through which the values for the critical temperature and critical index g are evaluated within 1.6% and 5.4% of their accepted values, respectively. Our work is a straightforward adaptation of the theory previously developed in an earlier paper.

Italian Quantum Information Science Conference (IQIS)Jun 6, 20190 citations

Entanglement theory and the second law of thermodynamics

Fernando G. S. L. Brandão, Martin Bodo Plenio

arXiv:0810.2319Nature PhysicsOct 12, 2008189 citations

Entanglement renders free riding redundant in the thermodynamic limit

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