arXiv subjects
Publications and source records attributed to Adrian Kent.
Causal quantum theory assumes that measurements or collapses are well-defined physical processes, localised in space-time, and never give perfectly reliable outcomes and that the outcome of one measurement only influences the outcomes of others within its future light cone. Although the theory has unusual properties, it is not immediately evident that it is inconsistent with experiment to date. I discuss its implications and experimental tests.
Mistrustful cryptography includes important tasks like bit commitment, oblivious transfer, coin flipping, secure computations, position authentication, digital signatures and secure unforgeable tokens. Practical quantum implementations presently use photonic setups. In many such implementations, Alice sends photon pulses encoding quantum states and Bob chooses measurements on these states. In practice, Bob generally uses single photon threshold detectors, which cannot distinguish the number of photons in detected pulses. Also, losses and other imperfections require Bob to report the detected pulses. Thus, malicious Alice can send and track multiphoton pulses and thereby gain information about Bob's measurement choices, violating the protocols' security. Here, we provide a theoretical framework for analysing such multiphoton attacks, and present known and new attacks. We illustrate the power of these attacks with an experiment, and study their application to earlier experimental demonstrations of mistrustful quantum cryptography. We analyse countermeasures based on selective reporting and prove them inadequate. We also discuss side-channel attacks where Alice controls further degrees of freedom or sends other physical systems.
Theories involving localized collapse allow the possibility that classical information could be obtained about quantum states without using POVMS and without allowing superluminal signalling. We can model this by extending quantum theory to include hypothetical devices that read out information about the local quantum state at a given point, defined by considering only collapses in its past light cone. Like Popescu-Rohrlich boxes, these hypothetical devices would have practical and scientific implications if realisable. These include signalling through opaque media, probing the physics of distant or opaque systems without needing a reflected signal and giving detailed information about collapse dynamics without requiring direct observation of the collapsing system. These potential applications motivate systematic searches for possible signatures of these nonstandard extensions of quantum theory, and in particular for relevant gravitational effects, such as the validity of semi-classical gravity on small scales.
There has been an upsurge of interest lately in developing Wigner's hypothesis that conscious observation causes collapse by exploring dynamical collapse models in which some purportedly quantifiable aspect(s) of consciousness resist superposition. Kremnizer-Ranchin, Chalmers-McQueen and Okon-Sebastián have explored the idea that collapse may be associated with a numerical measure of consciousness. More recently, Chalmers-McQueen have argued that any single measure is inadequate because it will allow superpositions of distinct states of equal consciousness measure to persist. They suggest a satisfactory model needs to associate collapse with a set of measures quantifying aspects of consciousness, such as the "Q-shapes" defined by Tononi et al. in their "integrated information theory" (IIT) of consciousness. I argue here that Chalmers-McQueen's argument against associating a single measure with collapse requires a precise symmetry between brain states associated with different experiences and thus does not apply to the only case where we have strong intuitions, namely human (or other terrestrial biological) observers. In defence of Chalmers-McQueen's stance, it might be argued that idealized artificial information processing networks could display such symmetries. However, I argue that any theory (such as IIT) that postulates a map from network states to mind states should assign identical mind states to isomorphic network states (as IIT does). This suggests that, if such a map exists, no familiar components of mind states, such as viewing different colours, or experiencing pleasure or pain, are likely to be related by symmetries.
Experiments have recently been proposed testing whether quantum gravitational interactions generate entanglement between adjacent masses in position superposition states. We propose potentially less challenging experiments that test quantum gravity against theories with classical space-times defined by postulating semi-classical gravity (or classical effects of similar scale) for mesoscopic systems.
Models in which causation arises from higher level structures as well as from microdynamics may be relevant to unifying quantum theory with classical physics or general relativity. They also give a way of defining a form of panprotopsychist property dualism, in which consciousness and material physics causally affect one another. I describe toy models based on probabilistic cellular automata that illustrate possibilities and difficulties with these ideas.
I critique a recent analysis (Miles, Stedman & Heald, 2020) of COVID-19 lockdown costs and benefits, focussing on the United Kingdom (UK). Miles et al. (2020) argue that the March-June UK lockdown was more costly than the benefit of lives saved, evaluated using the NICE threshold of £30000 for a quality-adjusted life year (QALY) and that the costs of a lockdown for 13 weeks from mid-June would be vastly greater than any plausible estimate of the benefits, even if easing produced a second infection wave causing over 7000 deaths weekly by mid-September. I note here two key problems that significantly affect their estimates and cast doubt on their conclusions. Firstly, their calculations arbitrarily cut off after 13 weeks, without costing the epidemic end state. That is, they assume indifference between mid-September states of 13 or 7500 weekly deaths and corresponding infection rates. This seems indefensible unless one assumes that (a) there is little chance of any effective vaccine or improved medical or social interventions for the foreseeable future, (b) notwithstanding temporary lockdowns, COVID-19 will very likely propagate until herd immunity. Even under these assumptions it is very questionable. Secondly, they ignore the costs of serious illness, possible long-term lowering of life quality and expectancy for survivors. These are uncertain, but plausibly at least as large as the costs in deaths. In summary, policy on tackling COVID-19 cannot be rationally made without estimating probabilities of future medical interventions and long-term illness costs. More work on modelling these uncertainties is urgently needed.
We consider versions of the grasshopper problem (Goulko and Kent, 2017) on the circle and the sphere, which are relevant to Bell inequalities. For a circle of circumference $2π$, we show that for unconstrained lawns of any length and arbitrary jump lengths, the supremum of the probability for the grasshopper's jump to stay on the lawn is one. For antipodal lawns, which by definition contain precisely one of each pair of opposite points and have length $π$, we show this is true except when the jump length $ϕ$ is of the form $π\frac{p}{q}$ with $p,q$ coprime and $p$ odd. For these jump lengths we show the optimal probability is $1 - 1/q$ and construct optimal lawns. For a pair of antipodal lawns, we show that the optimal probability of jumping from one onto the other is $1 - 1/q$ for $p,q$ coprime, $p$ odd and $q$ even, and one in all other cases. For an antipodal lawn on the sphere, it is known (Kent and Pitalúa-García, 2014) that if $ϕ= π/q$, where $q \in \mathbb N$, then the optimal retention probability of $1-1/q$ for the grasshopper's jump is provided by a hemispherical lawn. We show that in all other cases where $0<ϕ< π/2$, hemispherical lawns are not optimal, disproving the hemispherical colouring maximality hypotheses (Kent and Pitalúa-García, 2014). We discuss the implications for Bell experiments and related cryptographic tests.
S-money [Proc. R. Soc. A 475, 20190170 (2019)] schemes define virtual tokens designed for networks with relativistic or other trusted signalling constraints. The tokens allow near-instant verification and guarantee unforgeability without requiring quantum state storage. We present refined two stage S-money schemes. The first stage, which may involve quantum information exchange, generates private user token data. In the second stage, which need only involve classical communications, users determine the valid presentation point, without revealing it to the issuer. This refinement allows the user to determine the presentation point anywhere in the causal past of all valid presentation points. It also allows flexible transfer of tokens among users without compromising user privacy.
Several versions of quantum theory assume some form of localized collapse. If measurement outcomes are indeed defined by localized collapses, then a loophole-free demonstration of Bell non-locality needs to ensure space-like separated collapses associated with the measurements of the entangled systems. This collapse locality loophole remains largely untested, with one significant exception probing Diosi's and Penrose's gravitationally induced collapse hypotheses. I describe here techniques that allow much stronger experimental tests. These apply to all the well known types of collapse postulate, including gravitationally induced collapse, spontaneous localization models and Wigner's consciousness-induced collapse.
Some versions of quantum theory treat wave function collapse as a fundamental physical phenomenon to be described by explicit laws. One motivation is to find a consistent unification of quantum theory and gravity, in which collapse prevents superpositions of space-times from developing. Another is to invoke collapse to explain our perception of definite measurement outcomes. Combining these motivations while avoiding two different collapse postulates seems to require that perceptibly different physical states necessarily create significantly different mass distributions in our organs of perception or brains. Bassi et al. investigated this question in the context of mass density dependent spontaneous collapse models. By analysing the mechanism of visual perception of a few photons in the human eye, they argued that collapse model parameters consistent with known experiment imply that a collapse would take place in the eye within the human perception time of ~100ms, so that a definite state of observing some or no photons would be created from an initial superposition. I reanalyse their arguments, and note a key problem: they treat the relevant processes as though they take place in vacuo, rather than in cytoplasm. This makes a significant difference, since the models imply that superpositions collapse at rates that depend on the difference between the coarse grained mass densities of their components. This increases the required collapse rate, most likely by at least an order of magnitude and plausibly by significantly more. This casts some doubt on the claim that there are collapse model parameters consistent with known experiment that imply collapse times of <~ 100ms within the human eye. A complete analysis would require a very detailed understanding of the physical chemistry and biology of rod cells at microscopic scales.
Summoning is a task between two parties, Alice and Bob, with distributed networks of agents in space-time. Bob gives Alice a random quantum state, known to him but not her, at some point. She is required to return the state at some later point, belonging to a subset defined by communications received from Bob at other points. Many results about summoning, including the impossibility of unrestricted summoning tasks and the necessary conditions for specific types of summoning tasks to be possible, follow directly from the quantum no-cloning theorem and the relativistic no-superluminal-signalling principle. The impossibility of cloning devices can be derived from the impossibility of superluminal signalling and the projection postulate, together with assumptions about the devices' location-independent functioning. In this qualified sense, known summoning results follow from the causal structure of space-time and the properties of quantum measurements. Bounds on the fidelity of approximate cloning can be similarly derived. Bit commitment protocols and other cryptographic protocols based on the no-summoning theorem can thus be proven secure against some classes of post-quantum but non-signalling adversaries.
We propose definitions and implementations of "S-money" - virtual tokens designed for high value fast transactions on networks with relativistic or other trusted signalling constraints, defined by inputs that in general are made at many network points, some or all of which may be space-like separated. We argue that one significant way of characterising types of money in space-time is via the "summoning" tasks they can solve: that is, how flexibly the money can be propagated to a desired space-time point in response to relevant information received at various space-time points. We show that S-money is more flexible than standard quantum or classical money in the sense that it can solve deterministic summoning tasks that they cannot. It requires the issuer and user to have networks of agents with classical data storage and communication, but no long term quantum state storage, and is feasible with current technology. User privacy can be incorporated by secure bit commitment and zero knowledge proof protocols. The level of privacy feasible in given scenarios depends on efficiency and composable security questions that remain to be systematically addressed.
Suppose some future technology enables the same consciously experienced human life to be repeated, identically or nearly so, N times, in series or in parallel. Is this roughly N times as valuable as enabling the same life once, because each life has value and values are additive? Or is it of roughly equal value as enabling the life once, because only one life is enabled, albeit in a physically unusual way? Does it matter whether the lives are contemporaneous or successive? We argue that these questions highlight a hitherto neglected facet of population ethics that may become relevant in the not necessarily far distant future.
We define a summoning task to require propagating an unknown quantum state to a point in space-time belonging to a set determined by classical inputs at points in space-time. We consider the classical analogue, in which a known classical state must be returned at precisely one allowed point. We show that, when the inputs are unconstrained, any summoning task that is possible in the classical case is also possible in the quantum case.
This review, intended for a popular audience, was originally published in the online magazine Aeon on 28 January 2014. It is reproduced on the arxiv with permission. The online version (without references) can be found at https://aeon.co/essays/what-really-happens-in-schrodinger-s-box.
In an influential paper, Eppley and Hannah argued that gravity must necessarily be quantized, by proposing a thought experiment involving classical gravitational waves interacting with quantum matter. They argue the interaction must either violate the uncertainty principle or allow superluminal signalling. The feasibility of implementing their experiment in our universe has been challenged by Mattingly, and other limitations of the argument have been noted by Huggett and Callender and by Albers et al.. However, these critiques do not directly refute the claim that coupling quantum theories with a Copenhagen collapse postulate to unentanglable classical gravitational degrees of freedom leads to contradiction. I note here that if the gravitational field interacts with matter via the local quantum state, the Eppley-Hannah argument evidently fails. This seems a plausibly natural feature of a hybrid theory, whereas the alternative considered by Eppley-Hannah is evidently inconsistent with relativity.