7 research outputs found
Trading locality for time: certifiable randomness from low-depth circuits
The generation of certifiable randomness is the most fundamental
information-theoretic task that meaningfully separates quantum devices from
their classical counterparts. We propose a protocol for exponential certified
randomness expansion using a single quantum device. The protocol calls for the
device to implement a simple quantum circuit of constant depth on a 2D lattice
of qubits. The output of the circuit can be verified classically in linear
time, and is guaranteed to contain a polynomial number of certified random bits
assuming that the device used to generate the output operated using a
(classical or quantum) circuit of sub-logarithmic depth. This assumption
contrasts with the locality assumption used for randomness certification based
on Bell inequality violation or computational assumptions. To demonstrate
randomness generation it is sufficient for a device to sample from the ideal
output distribution within constant statistical distance.
Our procedure is inspired by recent work of Bravyi et al. (Science 2018), who
introduced a relational problem that can be solved by a constant-depth quantum
circuit, but provably cannot be solved by any classical circuit of
sub-logarithmic depth. We develop the discovery of Bravyi et al. into a
framework for robust randomness expansion. Our proposal does not rest on any
complexity-theoretic conjectures, but relies on the physical assumption that
the adversarial device being tested implements a circuit of sub-logarithmic
depth. Success on our task can be easily verified in classical linear time.
Finally, our task is more noise-tolerant than most other existing proposals
that can only tolerate multiplicative error, or require additional conjectures
from complexity theory; in contrast, we are able to allow a small constant
additive error in total variation distance between the sampled and ideal
distributions.Comment: 36 pages, 2 figure
An inherently infinite-dimensional quantum correlation
Bell’s theorem, a landmark result in the foundations of physics, establishes that quantum mechanics is a non-local theory. It asserts, in particular, that two spatially separated, but entangled, quantum systems can be correlated in a way that cannot be mimicked by classical systems. A direct operational consequence of Bell’s theorem is the existence of statistical tests which can detect the presence of entanglement. Remarkably, certain correlations not only witness entanglement, but they give quantitative bounds on the minimum dimension of quantum systems attaining them. In this work, we show that there exists a correlation which is not attainable by quantum systems of any arbitrary finite dimension, but is attained exclusively by infinite-dimensional quantum systems (such as infinite-level systems arising from quantum harmonic oscillators). This answers the long-standing open question about the existence of a finite correlation witnessing infinite entanglement
An inherently infinite-dimensional quantum correlation
The existence of nonlocal correlations which cannot be attained exactly by finite-dimensional systems, but can be attained by infinite-dimensional ones, has been the subject of several theoretical efforts. Here, Coladangelo and Stark exhibit such a correlation, in a form that requires only two players