Testing randomness with photons

Abstract

Generating and characterising randomness is fundamentally important in both classical and quantum information science. Here we report the experimental demonstration of ensembles of pseudorandom optical processes comprising what are known as t-designs. We show that in practical scenarios, certain finite ensembles of two-mode transformations---1- and 2-designs---are indistinguishable from truly random operations for 1- and 2-photon quantum interference, but they fail to mimic randomness for 2- and 3-photon cases, respectively. This provides a novel optical test of pseudo randomness. We make use of the fact that t-photon behaviour is governed by degree-2t polynomials in the parameters of the optical process to experimentally verify the ensembles' behaviour for complete bases of polynomials. This ensures that outputs will be uniform for arbitrary configurations, satisfying the strict definition of pseudorandomness implicit in the mathematical definition.

10 pages, 12 figures (including appendix)

References in corpus (7)

• Randomized Benchmarking of Quantum Gates
• Evenly distributed unitaries: on the structure of unitary designs
• Randomizing quantum states: Constructions and applications
• Symmetrised Characterisation of Noisy Quantum Processes
• The mother of all protocols: Restructuring quantum information's family tree
• Randomized benchmarking and process tomography for gate errors in a solid-state qubit
• Investigating the limits of randomized benchmarking protocols

Cited by in corpus (7)

• Growth of genuine multipartite entanglement in random unitary circuits
• Derandomizing quantum circuits with measurement based unitary designs
• Experimental Implementation of Efficient Quantum Pseudorandomness on a 12-spin System
• Fault-tolerant quantum speedup from constant depth quantum circuits
• Unitary $t$-designs from $relaxed$ seeds
• Implementation of single-qubit measurement-based t-designs using IBM processors
• Investigating the effect of noise channels on the quality of unitary t-designs