My main research centres on quantum non-locality. In general the world changes through local interactions which cannot move from one place to another faster than light. However when two particles interact to form an entangled state, are separated by a large distance, and then one is measured, the wave function describing the other particle collapses seemingly instantaneously. It’s as if the act of measuring one particle affects the other faster than light. There are several different interpretations of how nature allows this, none of which have universal agreement amongst physicists. For example, one of the interpretations, many worlds, says that every outcome of the measurement happens simultaneously, and that we should view the world including ourselves as splitting into parallel universes. In this view the collapse of the state is the change of our knowledge about the other particle conditional on a particular measurement outcome.

I create thought experiments with spatially separated particles, looking at behaviours which, like the collapse above, do not exist in classical physics. Although the basic rules giving the evolution of states and the probabilities of the outcomes for any measurements are agreed, there are many surprising behaviours which follow. Bell Inequality non-locality and quantum information science including teleportation are so remarkable they won the Nobel prize in 2022. I hope that by understanding thought experiments we will get a clear understanding of how nature operates, and reconcile its implications for our view of the world. My main results fall into several groups: Conservation Laws, Teleportation, Bell Inequalities, Interaction-Free Dynamics, Entanglement, Non-Local Operations, Frames of Reference, Post-Quantum Theories, and Weak Measurements. Below I give an overview. For more details you can look at my paper posts in “News”, or read the papers themselves via the links in “Publications”.

### Conservation Laws

Conservation Laws along with their underlying symmetries underpin physics, and are familiar to anyone who ever studied conservation of energy in physics or chemistry. However in quantum mechanics, the underlying randomness of a measurement led to the laws being written in terms of *distributions* of e.g. energy being conserved. S Popescu and I argue that conservation holds in each individual measurement outcome. This result, which we proved in a simplified case, is a significant strengthening of the usual conservations laws, which we hope to extend to all physical interactions.

### Teleportation

Teleportation is the process of using pre-shared entanglement, classical communication and local operations to send a quantum state from one place to another. It’s remarkable that it’s possible at all, since the uncertainty principle prevents us from measuring all properties of a state simultaneously. I showed that one can teleport a state evolving backward in time. I used this to give a simplified instantaneous* measurement verifying that an entangled backward evolving state is an accurate combined description of two remote systems at a given time. I also worked on the theory side of quantum relay experiments in Nicolas Gisin’s group.

*The quantum part of the measurement is instantaneous.

### Bell Inequalities

John Bell showed that quantum mechanics predicts non-local correlations between measurements performed on spatially-separated systems. He created inequalities on the correlations which all classical local theories obey, and which quantum mechanics violates. N Gisin, N Linden, S Massar, S Popescu and I created a family of inequalities for arbitrarily many outcomes, which is strongly resistant to noise. With my collaborators I also created inequalities to detect true n-party non-locality, a useful inequality with three possible measurements on each party (usually there were two), and showed how to close the memory loophole.

### Interaction Free Flows

Newton’s third law states that for every action there is an equal and opposite reaction. However in quantum mechanics objects can sometimes be measured with no interaction at all, as first demonstrated by the Elitzur-Vaidman Bomb. Together with Y Aharonov and S Popescu, I showed that angular momentum, a conserved quantity, can flow across a region of space where there is a vanishingly small chance of finding any particles to carry it. This shows that the flow of conserved quantities, e.g. energy, can be completely different to the flow of any particles which may carry them. This is known as the Dynamic Cheshire Cat effect, like the cat in Alice in Wonderland which separates its grin from itself.

### Entanglement

Entangled states are the fundamental non-local states in quantum mechanics, giving correlations between experimental outcomes which cannot be reproduced classically. They can be treated as a resource for quantum information processing tasks such as teleportation or cryptography, and the amount of entanglement in each state can be quantified by using local operations and classical communication to transform one entangled state into another. Sandu Popescu and I nevertheless showed that entanglement has a close classical analogue – secret classical correlations. By comparing the two we are able to better understand entanglement, and which features of it are truly quantum.

### Non-Local Operations

Going beyond entangled states, N Linden, S Popescu and I developed a resource theory for quantum operations on spatially separated systems. These operations take quantum inputs for Alice and Bob and give them each a quantum output. We showed how one could quantify them, by relating them to the entanglement of states. Much more recently, CM Ferrera, R Simmons, J Purcell, S Popescu and I defined non-signalling operations taking classical inputs for Alice and Bob and giving quantum outputs, and contrasted them with the no-signalling PR Boxes which take classical inputs and give classical outputs.

### Frames of Reference

Some tasks require a frame of reference to be physically shared between parties. For example, two people cannot agree which is their left hand and which is their right by sending binary code to one another unless they already have shared knowledge of a left (or right) handed object*. L Diosi, N Gisin, S Massar, S Popescu and I invented Quantum Gloves, states which encode left or right handedness without encoding any directionality and using a minimum of resources. Frames of reference are also crucial for our research on the conservation laws in each individual outcome.

*Unless you perform a particle physics experiment, as the weak force has a handedness (parity-violation) built in.

### Post Quantum Non-locality

One way to understand why quantum mechanics goes beyond classical mechanics, is to go even further, to theories with non-local correlations even stronger than those in quantum mechanics, and try to see how quantum mechanics looks in comparison. Carolina Moreira Ferrera, Robin Simmons, James Purcell, Sandu Popescu and I investigated non-local boxes with classical inputs and quantum outputs, which is one particular extension beyond quantum theory. We give explicit constructions for all bi-partite pure state output boxes in this theory using standard quantum mechanics and the original post-quantum object, PR Boxes.

### Weak Measurements

Measuring a weight by putting it on the scale so briefly it barely moves the scale feels useless classically. However in Quantum Mechanics weak measurements allow us to learn something about states whilst hardly disturbing them. N Brunner, A Acin, N Gisin, V Sclarani and I showed that polarization-mode dispersion in an optical fibre can be viewed as a weak measurement. In this framework polarization-dependent losses are a post-selection. We applied the quantum formalism for weak measurements and post-selection, which was developed to probe fundamental quantum mechanics, to simplify the practical problem of optical networks in the telecom limit of weak PMD.