**The laws of physics do not prohibit counterfactual communication**

(2022, npj Quantum Information – 10.1038/s41534-022-00564-w)

It has been conjectured that counterfactual communication is impossible, even for post-selected quantum particles. We strongly challenge this by proposing exactly such a counterfactual scheme where—unambiguously—none of Alice’s photons that contribute information to her about Bob’s message have been to Bob. We demonstrate counterfactuality experimentally by means of weak measurements, and conceptually using consistent histories—thus simultaneously satisfying both criteria. Importantly, the fidelity of Alice learning Bob’s bit can be made arbitrarily close to unity.

**Could wavefunctions simultaneously represent knowledge and reality?** (2022, Quantum Studies: Mathematics and Foundations – 10.1007/s40509-022-00271-3)

Harrigan and Spekkens give formal definitions for the wavefunction in quantum mechanics to be ψ-ontic or ψ-epistemic, such that the wavefunction can only be one or the other. We argue that nothing about the informal ideas of epistemic and ontic interpretations rules out wavefunctions representing both reality and knowledge. The implications of the Pusey-Barrett-Rudolph theorem and many other issues need to be rethought in the light of our analysis.

**Is the dynamical quantum Cheshire cat detectable?** (2022, arXiv – 2204.03374)

We explore how one might detect the dynamical quantum Cheshire cat proposed by Aharonov et al. We show that, in practice, we need to bias the initial state by adding/subtracting a small probability amplitude (`field’) of the orthogonal state, which travels with the disembodied property, to make the effect detectable (i.e. if our initial state is |↑z⟩, we need to bias this with some small amount δ of state |↓z⟩). This biasing, which can be done either directly or via weakly entangling the state with a pointer, effectively provides a phase reference with which we can measure the evolution of the state. The outcome can then be measured as a small probability difference in detections in a mutually unbiased basis, proportional to this biasing δ. We show this is different from counterfactual communication, which provably does not require any probe field to travel between sender Bob and receiver Alice for communication. We further suggest an optical polarisation experiment where these phenomena might be demonstrated in a laboratory.

**Comment on “Why interference phenomena do not capture the essence of quantum theory” by Catani et al **(2022, arXiv – 2204.01768)

It was recently argued by Catani et al that it is possible to reproduce the phenomenology of the double-slit experiment with a deterministic, local, and classical model (arXiv:2111.13727). The stated aim of their argument is to falsify the claim made by Feynman (in his third book of Lectures on Physics) that the double-slit experiment is “impossible, absolutely impossible, to explain in any classical way” and that it “contains the only mystery” of quantum mechanics. We here want to point out some problems with their argument, and defend Feynman’s position.

**Reply to arXiv:2111.13357 (“The Quantum Eraser Non-Paradox”)** (2021, arXiv – 2112.00436)

In a recent criticism (arXiv:2111.13357) of our paper arXiv:2111.09347, Drezet argues that we have forgotten to consider superpositions of detector eigenstates. However, such superpositions do not occur in the models our paper is concerned with. We also note that no one has ever observed such detector superpositions.

**The Quantum Eraser Paradox** (2021, arXiv – 2111.09347)

The Delayed-Choice Quantum Eraser experiment is commonly interpreted as implying that in quantum mechanics a choice made at one time can influence an earlier event. We here suggest an extension of the experiment that results in a paradox when interpreted using a local realist interpretation combined with backward causation (“retrocausality”). We argue that resolving the paradox requires giving up the idea that, in quantum mechanics, a choice can influence the past, and that it instead requires a violation of Statistical Independence without retrocausality. We speculate what the outcome of the experiment would be.

**Does the weak trace show the past of a quantum particle?** (2021, arXiv – 2109.14060)

We investigate the weak trace method for determining the path of a quantum particle. Specifically, looking at nested interferometer experiments, when internal interferometers are tuned to destructive interference, we show that the weak trace method gives misleading results. Obtaining the weak value of the position operator necessarily perturbs the system away from destructive interference, showing weak coupling and no coupling are not equivalent. Furthermore, there is no reason to associate the weak value of the spatial projection operator with the classical idea of `particle presence’, not least because it can have features contrary to the classical idea of a particle being present (for example, a particle having a single, continuous path).

**The wavefunction as a true ensemble** (2021, arXiv – 2109.02676)

In quantum mechanics, the wave-function only predicts probabilities of measurement outcomes, not individual outcomes. This suggests that it describes an ensemble of states with different values of a hidden variable. Here, we analyse this idea with reference to currently known theorems and experiments. We argue that the ψ-ontic/epistemic distinction fails to properly identify ensemble interpretations and propose a more useful definition. We then show that all ψ-ensemble interpretations which reproduce quantum mechanics violate Statistical Independence. Finally, we explain how this interpretation helps make sense of some otherwise puzzling phenomena in quantum mechanics, such as the delayed choice experiment, the Elitzur-Vaidman bomb detector, and the Extended Wigner’s Friends Scenario.

**Supermeasured: Violating Statistical Independence without violating statistical independence** (2021, arXiv – 2108.07292)

Bell’s theorem is often said to imply that quantum mechanics violates local causality, and that local causality cannot be restored with a hidden-variables theory. This however is only correct if the hidden-variables theory fulfils an assumption called Statistical Independence. Violations of Statistical Independence are commonly interpreted as correlations between the measurement settings and the hidden variables (which determine the measurement outcomes). Such correlations have been discarded as “finetuning” or a “conspiracy”. We here point out that the common interpretation is at best physically ambiguous and at worst incorrect. The problem with the common interpretation is that Statistical Independence might be violated because of a non-trivial measure in state space, a possibility we propose to call “supermeasured”. We use Invariant Set Theory as an example of a supermeasured theory that violates the Statistical Independence assumption in Bell’s theorem without requiring correlations between hidden variables and measurement settings.

**Properties of Invariant Set Theory** (2021, arXiv – 2108.08144)

In a recent paper (arXiv:2107.04761), Sen critiques a superdeterministic model of quantum physics, Invariant Set Theory, proposed by one of the authors. He concludes that superdeterminism is `unlikely to solve the puzzle posed by the Bell correlations’. He also claims that the model is neither local nor ψ-epistemic. We here detail multiple problems with Sen’s argument.

**Comment on “Scheme of the arrangement for attack on the protocol BB84”** (2021, Optik – 10.1016/j.ijleo.2021.167451)

In a recent paper (Khokhlov, 2016), a protocol was proposed for using weak measurement to attack BB84. This claimed the four basis states typically used could be perfectly discriminated, and so an interceptor could obtain all information carried. We show this attack fails when considered using standard quantum mechanics, as expected — such “single-shot” quantum state discrimination is impossible, even using weak measurement.

**Counterfactual Ghost Imaging ** (2021, npj Quantum Information – s41534-021-00411-4)

We give a protocol for ghost imaging in a way that is always counterfactual – while imaging an object, no light interacts with that object. This extends the idea of counterfactuality beyond communication, showing how this interesting phenomenon can be leveraged for metrology. Given, in the infinite limit, no photons ever go to the imaged object, it presents a method of imaging even the most light-sensitive of objects without damaging them. Even when not in the infinite limit, it still provides a many-fold improvement in visibility and signal-to-noise ratio over previous protocols, with over an order of magnitude reduction in absorbed intensity.

**Backscatter and spontaneous four-wave mixing in micro-ring resonators** (2021, Journal of Physics: Photonics – 10.1088/2515-7647/abf236)

We model backscatter for electric fields propagating through optical micro-ring resonators, as occurring both in-ring and in-coupler. These provide useful tools for modelling transmission and in-ring fields in these optical devices. We then discuss spontaneous four-wave mixing and use the models to obtain heralding efficiencies and rates. We observe a trade-off between these, which becomes more extreme as the rings become more strongly backscattered.

**Experimental Tests of Invariant Set Theory** (2021, arXiv – 2102.07795)

We identify points of difference between Invariant Set Theory and standard quantum theory, and evaluate if these would lead to noticeable differences in predictions between the two theories. From this evaluation, we design a number of experiments, which, if undertaken, would allow us to investigate whether standard quantum theory or invariant set theory best describes reality.

** How Quantum is Quantum Counterfactual Communication?** (2021, Foundations of Physics – 10.1007/s10701-021-00412-5)

Quantum Counterfactual Communication is the recently-proposed idea of using quantum physics to send messages between two parties, without any matter/energy transfer associated with the bits sent. While this has excited massive interest, both for potential ‘unhackable’ communication, and insight into the foundations of quantum mechanics, it has been asked whether this process is essentially quantum, or could be performed classically. We examine counterfactual communication, both classical and quantum, and show that the protocols proposed so far for sending signals that don’t involve matter/energy transfer associated with the bits sent must be quantum, insofar as they require wave-particle duality.

**Exchange-free computation on an unknown qubit at a distance** (2021, New Journal of Physics – 10.1088/1367-2630/abd3c4)

We present a way of directly manipulating an arbitrary qubit, without exchange of particles. This includes as an application the preparation of an arbitrary state at Alice by Bob, exchange-free. Hence, we are able to propose an exchange-free protocol that allows one party to directly enact, by means of a suitable program, any computation on a remote second party’s unknown qubit. We go on to show how to realise this in the exchange-free control of a universal two-qubit gate, thus opening the possibility of directly enacting any desired algorithm on a remote programmable quantum circuit.

**Deterministic Teleportation and Universal Computation Without Particle Exchange ** (2020, arXiv – 2009.05564)

Teleportation is a cornerstone of quantum technologies, and has played a key role in the development of quantum information theory. Pushing the limits of teleportation is therefore of particular importance. Here, we apply a different aspect of quantum weirdness to teleportation—namely exchange-free computation at a distance. The controlled-phase universal gate we propose, where no particles are exchanged between control and target, allows complete Bell detection among two remote parties, and is experimentally feasible. Our teleportation-with-a-twist, which we extend to telecloning, then requires no pre-shared entanglement between sender and receiver, nor classical communication, with the teleported state gradually appearing at its destination.

**Counterfactuality, Definiteness and Bell’s Theorem**

(2019, arXiv – 1909.06608)

We show counterfactual definiteness separates classical from quantum physics, by analysing Bell’s Theorem. By comparing what it prohibited by various interpretations, we show most interpretations just require counterfactual semi-definiteness (the definiteness of possible options available after a measurement event), rather than full counterfactual indefiniteness. While less definite than classical counterfactual definiteness, it allows us a far more sophisticated tool to consider the physical interpretation of multi-valued variables in a way not yet done. Working from this, we further consider its relation to how counterfactual possibilities interact.