Quantum Information

Quantum systems typically reach thermal equilibrium rather quickly when coupled to an external thermal environment. The usual way of bounding the speed of this process is by estimating the spectral gap of the dissipative generator. However, the gap, by itself, does not always yield a reasonable estimate for the thermalization time in many-body systems: without further structure, a uniform lower bound on it only constraints the thermalization time to be polynomially growing with system size. In this talk, we will discuss that for all 2-local models with commuting Hamiltonians, the thermalization time that one can estimate from the gap is in fact much smaller than direct estimates suggest: at most logarithmic in the system size. This yields the so-called rapid mixing of dissipative dynamics. We will show this result by proving that a finite gap directly implies a lower bound on the modified logarithmic Sobolev inequality (MLSI) for the class of models we consider. The result is particularly relevant for 1D systems, for which we can prove rapid thermalization with a constant decay rate, giving a qualitative improvement over all previous results. It also applies to hypercubic lattices, graphs with exponential growth rate, and trees with sufficiently fast decaying correlations in the Gibbs state. This has consequences for the rate of thermalization towards Gibbs states, and also for their relevant Wasserstein distances and transportation cost inequalities.

---

Zoom link https://pitp.zoom.us/j/91315419731?pwd=TGpFTjlHWEJZVWZkdTh6bDFKMjhQZz09

The Bekenstein bound posits a maximum entropy for matter with finite energy confined to a spacetime region. It is often interpreted as a fundamental limit on the information that can be stored by physical objects. In this work, we test this interpretation by asking whether the Bekenstein bound imposes constraints on a channel's communication capacity, a context in which information can be given a mathematically rigorous and operationally meaningful definition. We first derive a bound on the accessible information and demonstrate that the Bekenstein bound constrains the decoding instead of the encoding. Then we study specifically the Unruh channel that describes a stationary Alice exciting different species of free scalar fields to send information to an accelerating Bob, who is therefore confined to a Rindler wedge and exposed to the noise of Unruh radiation. We show that the classical and quantum capacities of the Unruh channel obey the Bekenstein bound. In contrast, the entanglement-assisted capacity is as large as the input size even at arbitrarily high Unruh temperatures. This reflects that the Bekenstein bound can be violated if we do not properly constrain the decoding operation in accordance with the bound. We further find that the Unruh channel can transmit a significant number of zero-bits, which are communication resources that can be used as minimal substitutes for the classical/quantum bits needed for many primitive information processing protocols, such as dense coding and teleportation. We show that the Unruh channel has a large zero-bit capacity even at high temperatures, which underpins the capacity boost with entanglement assistance and allows Alice and Bob to perform quantum identification. Therefore, unlike classical bits and qubits, zero-bits and their associated information processing capability are not constrained by the Bekenstein bound. (This talk is based on the recent work (https://arxiv.org/abs/2309.07436) with Patrick Hayden.)

---

Zoom link: https://pitp.zoom.us/j/98778081764?pwd=WktjNU84R3NWRXNyVmt1eDVMK2JnUT09