Bounds on quantum information storage and retrieval

We present certain universal bounds on the capacity of quantum information storage and on the time scale of its retrieval for a generic quantum field theoretic system. The capacity, quantified by the microstate entropy, is bounded from above by the surface area of the object measured in units of a Goldstone decay constant. The Goldstone bosons are universally present due to the spontaneous breaking of Poincare and internal symmetries by the information-storing object. Applied to a black hole, the bound reproduces the Bekenstein–Hawking entropy. However, the relation goes beyond gravity. The minimal time-scale required for retrieving the quantum information from a system is equal to its volume measured in units of the same Goldstone scale. For a black hole, this reproduces the Page time as well as the quantum break-time. Again, the expression for the information retrieval time is very general and is shared by non-gravitational saturated states in gauge theories including QCD. All such objects exhibit universal signatures such as the emission of ultra-soft radiation. Similar bounds apply to non-relativistic many-body systems. This article is part of the theme issue ‘Quantum technologies in particle physics’.

Universal bounds on the size of a black hole

For static black holes in Einstein gravity, if matter fields satisfy a few general conditions, we conjecture that three characteristic parameters about the spatial size of black holes, namely the outermost photon sphere area $$A_{\mathrm {ph,out}}$$ A ph , out , the corresponding shadow area $$A_{\mathrm {sh,out}}$$ A sh , out and the horizon area $$A_{{\mathcal {H}}}$$ A H satisfy a series of universal inequalities $$9A_{{\mathcal {H}}}/4\le A_{\mathrm {ph,out}}\le A_{\mathrm {sh,out}}/3\le 36\pi M^2$$ 9 A H / 4 ≤ A ph , out ≤ A sh , out / 3 ≤ 36 π M 2 , where M is the ADM mass. We present a complete proof in the spherically symmetric case and some pieces of evidence to support it in general static cases. We also discuss the properties of the photon spheres in general static spacetimes and show that, similar to horizon, photon spheres are also conformal invariant structures of the spacetimes.

Quartic Horndeski, planar black holes, holographic aspects and universal bounds

In this work, we consider a specific shift-invariant quartic Horndeski model, deriving new planar black hole solutions with axionic hair. We explore these solutions in terms of their horizon structure and their thermodynamic properties. We use the gauge/gravity dictionary to derive the DC transport coefficients of the holographic dual with the aim of investigating how the new deformation affects the universality of some renown bound proposals. Although most of them are found to hold true, we nevertheless find a highly interesting parametric violation of the heat conductivity-to-temperature lower bound which acquires a dependence on both the scale and the coupling. Finally, using a perturbative approach, a more brutal violation of the viscocity-to-entropy ratio is demonstrated.

Universal bounds on transport in holographic systems with broken translations

We study the presence of universal bounds on transport in homogeneous holographic models with broken translations. We verify numerically that, in holographic systems with momentum dissipation, the viscosity to entropy bound might be violated but the shear diffusion constant remains bounded by below. This confirms the idea that \eta/sη/s loses its privileged role in non-relativistic systems and that, in order to find more universal bounds, one should rather look at diffusion constants. We strengthen this idea by showing that, in presence of spontaneously broken translations, the Goldstone diffusion constant satisfies a universal lower bound in terms of the Planckian relaxation time and the butterfly velocity. Additionally, all the diffusive processes in the model satisfy an upper bound, imposed by causality, which is given in terms of the thermalization time – the imaginary part of the first non-hydrodynamic mode in the spectrum – and the speed of longitudinal sound. Finally, we discuss the existence of a bound on the speed of sound in holographic conformal solids and we show that the conformal value acts as a lower (and not upper) bound on the speed of longitudinal phonons. Nevertheless, we show that the stiffness \partial p/\partial \epsilon∂p/∂ϵ is still bounded by above by its conformal value. This suggests that the bounds conjectured in the past have to be considered on the stiffness of the system, related to its equation of state, and not on the propagation speed of sound.

Characterizations of woven frames

In a separable Hilbert space [Formula: see text], two frames [Formula: see text] and [Formula: see text] are said to be woven if there are constants [Formula: see text] so that for every [Formula: see text], [Formula: see text] forms a frame for [Formula: see text] with the universal bounds [Formula: see text]. This paper provides methods of constructing woven frames. In particular, bounded linear operators are used to create woven frames from a given frame. Several examples are discussed to validate the results. Moreover, the notion of woven frame sequences is introduced and characterized.