Entanglement area law from specific heat capacity

We study the scaling of entanglement in low-energy states of quantum many-body models on lattices of arbitrary dimensions. We allow for unbounded Hamiltonians such that systems with bosonic degrees of freedom are included. We show that if at low enough temperatures the specific heat capacity of the model decays exponentially with inverse temperature, the entanglement in every low-energy state satisfies an area law (with a logarithmic correction). This behaviour of the heat capacity is typically observed in gapped systems. Assuming merely that the low-temperature specific heat decays polynomially with temperature, we find a subvolume scaling of entanglement. Our results give experimentally verifiable conditions for area laws, show that they are a generic property of low-energy states of matter, and, to the best of our knowledge, constitute the first proof of an area law for unbounded Hamiltonians beyond those that are integrable.Comment: v3 now featuring bosonic system

Equivalence of Statistical Mechanical Ensembles for Non-Critical Quantum Systems

We consider the problem of whether the canonical and microcanonical ensembles are locally equivalent for short-ranged quantum Hamiltonians of $N$ spins arranged on a $d$-dimensional lattices. For any temperature for which the system has a finite correlation length, we prove that the canonical and microcanonical state are approximately equal on regions containing up to $O(N^{1/(d+1)})$ spins. The proof rests on a variant of the Berry--Esseen theorem for quantum lattice systems and ideas from quantum information theory

Thermalization and Return to Equilibrium on Finite Quantum Lattice Systems

Thermal states are the bedrock of statistical physics. Nevertheless, when and how they actually arise in closed quantum systems is not fully understood. We consider this question for systems with local Hamiltonians on finite quantum lattices. In a first step, we show that states with exponentially decaying correlations equilibrate after a quantum quench. Then we show that the equilibrium state is locally equivalent to a thermal state, provided that the free energy of the equilibrium state is sufficiently small and the thermal state has exponentially decaying correlations. As an application, we look at a related important question: When are thermal states stable against noise? In other words, if we locally disturb a closed quantum system in a thermal state, will it return to thermal equilibrium? We rigorously show that this occurs when the correlations in the thermal state are exponentially decaying. All our results come with finite-size bounds, which are crucial for the growing field of quantum thermodynamics and other physical applications.Comment: 8 pages (5 for main text and 3 for appendices); v2 is essentially the published versio

Optimal control for Hamiltonian parameter estimation in non-commuting and bipartite quantum dynamics

The ability to characterise a Hamiltonian with high precision is crucial for the implementation of quantum technologies. In addition to the well-developed approaches utilising optimal probe states and optimal measurements, the method of optimal control can be used to identify time-dependent pulses applied to the system to achieve higher precision in the estimation of Hamiltonian parameters, especially in the presence of noise. Here, we extend optimally controlled estimation schemes for single qubits to non-commuting dynamics as well as two interacting qubits, demonstrating improvements in terms of maximal precision, time-stability, as well as robustness over uncontrolled protocols.Comment: Submission to SciPost Physics; 18 pages, 13 figure

The Influence of Infant Food Packaging Design on Perceptions of Kenyan Consumers: Conjoint Analysis Combined with Eye Tracking

Locally produced, healthy and affordable foods for children based on traditional recipes have the potential to improve the high rates of child malnutrition in Africa's drylands. Professional, informative packaging is needed for women's groups producing such foods to access the formal market. To identify suitable packaging designs, a conjoint experiment was combined with eye tracking. 16 packaging designs were created (D-efficient design), randomly displayed and rated for attractiveness by 98 participants. Overall, the results suggest that packaging designs for children's foods that include food safety symbols and detailed nutritional information could help Kenyan consumers build trust in the product being offered. Consumers gain information from images showing the product's ingredients and a logo composed of the colours of the Kenyan flag. The image of a cute cartoon animal helps consumers identify the product as a children's food

The Influence of Child Food Packaging Design on Perceptions of Kenyan Consumers: Conjoint Analysis Combined with Eye Tracking

Locally manufactured, healthy and affordable child foods based on traditional recipes have the potential to improve the high child malnutrition rates in African drylands. Professional, informative packaging is needed by women groups manufacturing such foods to access the formal market. With the aim of identifying suitable packaging designs, a conjoint experiment was combined with eye tracking. 16 packaging designs were created (D-efficient design), randomly displayed and their attractiveness rated by 98 participants. Overall, the results indicate that child food packaging designs displaying food safety marks and detailed nutritional information could help Kenyan consumers to build trust in the offered product. Consumers gain information from pictures displaying the product’s ingredients as well as a logo composed using the colours of the Kenyan flag. The picture of a cute cartoon animal helps consumers identify the product as child foo

The Impact of Forensic vs. Social-Science Evidence on Judicial Decisions to Grant a Writ of Habeas Corpus

Wrongful conviction is a serious dilemma for the criminal-justice system. A joint investigation by the Better Government Association and the Center on Wrongful Convictions tracked exonerations from 1989 through 2010 and identified 85 people who were wrongfully incarcerated.1 Not only were those 85 lives unfairly affected in serious ways due to the incarceration, but the actual perpetrators continued on crime sprees that went on to include 14 murders, 11 sexual assaults, 10 kidnappings, and at least 62 other felonies.2 The reversal of false convictions is becoming more frequent.3 However, scholars have asserted that the exonerations that do occur are probably a small fraction of actual wrongful convictions. Gross and colleagues pointed out that “[o]ur legal system places great weight on the finality of criminal convictions. Courts and prosecutors are exceedingly reluctant to reverse judgments or reconsider closed cases; when they do—and it’s rare—it’s usually because of a compelling showing of error.”4 Therefore, in order for a wrongful conviction to be overturned, these cases must undergo a lengthy appeals process