New work : Observational entropy

Hi new venture "Observational entropy in many-body theory" ---

Observational entropic study of Anderson localization

The notion of the thermodynamic entropy in the context of quantum mechanics is a controversial topic. While there were proposals to refer von Neumann entropy as the thermodynamic entropy, but it has it's own limitations. In the past few years, the observational entropy has been developed as a generalization of Boltzmann entropy to quantum mechanics, and it is presently one of the most promising candidates to provide a clear and well-defined understanding of the thermodynamic entropy in quantum mechanics. In this work, we study the behaviour of the observational entropy in the context of localization-delocalization transition for one-dimensional Aubrey-Andre (AA) model. We find that for the typical mid-spectrum states, in the delocalized phase the observation entropy grows rapidly with coarse-grain size and saturates to the maximal value, while in the localized phase the growth is logarithmic. Moreover, for a given coarse-graining, it increases logarithmically with system size in the delocalized phase, and obeys area law in the localized phase. We also find the increase of the observational entropy followed by the quantum quench, is logarithmic in time in the delocalized phase as well as at the transition point, while in the localized phase it oscillates.

Comments:8 pages, 3 figuresSubjects:Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech)Cite as:arXiv:2209.10273 [quant-ph]

Quantum Combinatorial designs

We posted our recent work in arxiv --- https://arxiv.org/abs/2205.08842

Here is the abstract and I will try to explain in detail later ---

While quantum circuits built from two-particle dual-unitary (maximally entangled) operators serve as minimal models of typically nonintegrable many-body systems, the construction and characterization of dual-unitary operators themselves are only partially understood. A nonlinear map on the space of unitary operators was proposed in PRL. 125, 070501 (2020) that results in operators being arbitrarily close to dual unitaries. Here we study the map analytically for the two-qubit case describing the basins of attraction, fixed points, and rates of approach to dual unitaries. A subset of dual-unitary operators having maximum entangling power are 2-unitary operators or perfect tensors, and are equivalent to four-party absolutely maximally entangled states. It is known that they only exist if the local dimension is larger than d=2. We use the nonlinear map, and introduce stochastic variants of it, to construct explicit examples of new dual and 2-unitary operators. A necessary criterion for their local unitary equivalence to distinguish classes is also introduced and used to display various concrete results and some conjectures. It is known that orthogonal Latin squares provide a "classical combinatorial design" for constructing permutations that are 2-unitary. We extend the underlying design from classical to genuine quantum ones for general dual-unitary operators and give an example of what might be the smallest sized genuinely quantum design of a 2-unitary in d=4.