Do weak values show the past of a quantum particle? (2022, Physical Review Research (Accepted) – arXiv:2109.14060)
We investigate the use of weak values to determine the presence of an individual quantum particle. Specifically, we show four key issues with both Vaidman’s weak trace approach, and other approaches where a nonzero weak value of the spatial projection operator is implicitly assumed to indicate the presence of an individual quantum particle. First, even weak measurements disturb a system, so any approach relying on such a perturbation to determine the location of a quantum particle will only describe this disturbed system, not a hypothetical undisturbed state. Secondly, even assuming no disturbance, there is no reason to associate the non-zero weak value of an operator containing the spatial projection operator with the classical idea of `particle presence’. Thirdly, weak values are only measurable over ensembles, and so to infer properties of individual particles from values of them is problematic at best. Finally, weak values approaches to the path of a particle are not useful—they simply assume a connection between particle presence and weak values without contributing anything testable.
Bell’s theorem allows local theories of quantum mechanics (2022, Nature Physics (Correspondence) – 10.1038/s41567-022-01831-5
A recent Nature Physics editorial (Nat. Phys. (2022) 18, 961) falsely claims “any theory that uses hidden variables still requires non-local physics.” We correct this claim and explain why it is important to get this right.
What does it take to solve the measurement problem? (2022, Journal of Physics Communications – 10.1088/2399-6528/ac96cf)
We summarise different aspects of the measurement problem in quantum mechanics. We argue that it is a real problem which requires a solution, and identify the properties a theory needs to solve the problem. We show that no current interpretation of quantum mechanics solves the problem, and that, being interpretations rather than extensions of quantum mechanics, they cannot solve it. Finally, we speculate what a solution of the measurement problem might be good for.
Supermeasured: Violating Bell-Statistical Independence without violating physical statistical independence (2022, Foundations of Physics – 10.1007/s10701-022-00602-9)
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 “fine-tuning” 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 (physical statistical independence).
The wavefunction as a true ensemble (2022, Proceedings of the Royal Society A – 10.1098/rspa.2021.0705)
In quantum mechanics, the wave function predicts probabilities of possible measurement outcomes, but not which individual outcome is realized in each run of an experiment. 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 local ψ-ensemble interpretations which reproduce quantum mechanics violate statistical independence. Theories with this property are commonly referred to as superdeterministic or retrocausal. 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.
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.
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 – 10.1038/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.
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.