Perimeter Institute Quantum Discussions

Quantum information and quantum metrology can be used to study gravitational effects such as gravitational waves and the universality of the equivalence principle. On one hand, the possibility of carrying out experiments to probe gravity using quantum systems opens an avenue to deepen our understanding of the overlap of these theories. On the other hand, incorporating relativity in quantum technologies promises the development of a new generation of relativistic quantum applications of relevance in Earth-based and space-based setups.

A self-correcting quantum memory is a physical system whose quantum state can be preserved over a long period of time without the need for any external intervention. The most promising candidates are topological quantum systems which would protect information encoded in their degenerate groundspace while interacting with a thermal environment. Many models have been suggested but several approaches have been shown to fail due to no-go results of increasingly general scope.

We introduce an abstract model of computation corresponding to an experiment in which identical, non-interacting bosons are sent through a non-adaptive linear circuit before being measured. We show that despite the very limited nature of the model, an exact classical simulation would imply a collapse of the polynomial hierarchy. Moreover, under plausible conjectures, a "noisy" approximate simulation would do the same.

Privacy and coherence have long been considered closely related properties of a quantum state. Indeed, a coherently transmitted quantum state is inherently private. Surprisingly, coherent quantum communication is not always required for privacy: there are quantum channels that are too noisy to transmit quantum information but it can send private classical information. Here, we ask how different the private classical and the quantum capacities can be. We present a class of channels N_d with input dimension d^2, quantum capacity Q(N_d)