A quantum production model

Christian Aspalter

Géraldine Haack, Alain Joye

We analyze the entropy production of Quantum Reset Models (QRMs) corresponding to quantum dynamical semigroups driven by Lindbladians motivated by a probabilistic description of dissipation in an external environment. We investigate the strict positivity of entropy production for Lindbladians given as sums of QRMs, when the Hamiltonian of the total Lindbladian is split as an affine combination of Hamiltonians of the individual QRMs. In this setup, we derive conditions on the coefficients of the combination and on the reset states ensuring either positive or zero entropy production. Second, we deal with a tri-partite system subject at its ends to two independent QRMs and a weak coupling Hamiltonian. The latter is split as an affine combination of individual Hamiltonians, and we provide necessary and sufficient conditions ensuring strict positivity of the entropy production to leading order, with the possible exception of one affine combination. We apply these results to a physically motivated model and exhibit explicit expressions for the leading orders steady-state solution, entropy production and entropy fluxes. Moreover, these approximations are numerically shown to hold beyond the expected regimes.

Yi Tan, Brenden Roberts, Nathanan Tantivasadakarn +2 more

We explore a deep connection between fracton order and product codes. In particular, we propose and analyze conditions on classical seed codes which lead to fracton order in the resulting quantum product codes. Depending on the properties of the input codes, product codes can realize either Type-I or Type-II fracton models, in both nonlocal and local constructions. For the nonlocal case, we show that a recently proposed model of lineons on nonlocal graphs can be obtained as a hypergraph product code. Interestingly, constrained mobility in this model arises only from energy barriers associated with the graph. For the local case, we introduce a novel type of classical LDPC code defined on a planar aperiodic tiling. By considering the specific example of the pinwheel tiling, we demonstrate the systematic construction of local Type-I and Type-II fracton models as product codes. Our work establishes product codes as a natural setting for exploring fracton order.

Y. S. Kim, L. M. Tomilchik, И. Д. Феранчук +1 more

Tomasz I. Tylec, Marek Kuś

Abstract In the quantum logic framework we show that the no-signaling box model is a particular type of tensor product with single box logics. Such notion of a tensor product is too strong to apply in the category of logics of quantum mechanical systems. In the light of the obtained results, the statement that no-signaling box models are generalizations of quantum models is questionable.