Prof. Andrew G White

Limits on measurement uncertainty 

Measurement—assigning a number to a property of a physical system—is the keystone of the natural sciences. The arrival of quantum mechanics a century ago shattered our belief in perfect measurement precision, so it is surprising that even today active debate persists over the fundamental limits on measurement imposed by quantum theory. Understanding this is key, as it sets the limit in all engineered quantum systems. 

At the heart of the measurement debate is Heisenberg’s uncertainty principle, which encompasses at least three distinct statements about the limitations on preparation and measurement of physical systems:

1. A system cannot be prepared such that a pair of noncommuting observables (e.g. position and momentum) are arbitrarily well defined
2. Such a pair of observables cannot be jointly measured with arbitrary accuracy
3. Measuring one of these observables to a given accuracy disturbs the other accordingly.

Kennard accurately quantified (1) in 1927 with the famous relation xΔp ≥ ħ/2, where Δx and Δp are the standard deviations of the position and momentum distributions of the prepared quantum system, respectively. For measurement uncertainties (2) and (3), the corresponding quantities of interest are the measurement inaccuracies ε and disturbances η. Heisenberg argued that the product of εx and ηp should obey a similar bound to (1) in a measurement-disturbance scenario.

Proof of this was lacking until 2013, when a series of theoretical papers introduced various Heisenberg-like relations, incurring instant debate as to whether they held generally—it seems not—and whether they were optimal—also not the case. In a paper in the Proceedings of the National Academy of Sciences in 2013, EQuS theorist Cyril Branciard introduced a set of optimal relations, providing the tightest bound on measurement. In 2014, we experimentally tested these relations. We engineered exceptional—indeed, unprecedented—quantum state fidelities of up to 0.99998(6), allowing us to verge upon the fundamental limits of measurement uncertainty and establish, after nearly nine decades, the limits of quantum measurement. 

Simulation of closed timelike curves

Simulation. Quantum mechanics is an outstandingly successful theory of nature at the small scale. In principle, it can be used to model a wide array of systems in biology, chemistry and physics. However in practice this is impossible, as the number of equations—and the computation time—grows exponentially with the number of particles, e.g. atoms in a molecule. 

Over thirty years ago, Nobel Laureate Richard Feynman proposed a better solution: model quantum systems with technology that is itself quantum mechanical. It is now widely recognised that quantum simulation will provide a versatile and powerful tool for investigating quantum systems that are hard—or even impossible—to access in practice. Even simple quantum simulators require a level of control of quantum systems that is at—or beyond—the forefront of today’s capabilities. 

One of the most controversial features of modern physics is closed timelike curves. As legitimate solutions to Einstein’s field equations, they allow for time travel, which instinctively seems paradoxical. However, in the quantum regime these paradoxes can be resolved, leaving closed timelike curves consistent with relativity. The study of these systems therefore provides valuable insight into nonlinearities and the emergence of causal structures in quantum mechanics— essential for any formulation of a quantum theory of gravity.

In 2014, we experimentally simulated the nonlinear behaviour of the simplest nontrivial quantum system—a qubit—interacting unitarily with an older version of itself, addressing some of the fascinating effects that arise in systems traversing a closed timelike curve [3]. These include: perfect discrimination of non-orthogonal states—which would allow quantum cloning—and most intriguingly, the ability to distinguish nominally equivalent ways of preparing pure quantum states—an effect that arises due to consistency with relativity, in contrast to similar effects due to mixed quantum states. Finally, we examine the dependence of these effects on the initial qubit state, the form of the unitary interaction and the influence of decoherence, finding that they are surprisingly robust.