Toy Models of Top Down Causation.

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 probabilistic toy models based on cellular automata that illustrate possibilities and difficulties with these ideas.

Globe-hopping.

We consider versions of the grasshopper problem (Goulko & Kent 2017 Proc. R. Soc. A 473, 20170494) 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(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 & Pitalúa-García 2014 Phys. Rev. A 90, 062124) that if ϕ = π/q, where q ∈ 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 & Pitalúa-García 2014 Phys. Rev. A 90, 062124). We discuss the implications for Bell experiments and related cryptographic tests.

S-money: virtual tokens for a relativistic economy.

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 characterizing 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.

Summoning, No-Signalling and Relativistic Bit Commitments.

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.

Knowledge-Concealing Evidencing of Knowledge About a Quantum State.

Bob has a black box that emits a single pure state qudit which is, from his perspective, uniformly distributed. Alice wishes to give Bob evidence that she has knowledge about the emitted state while giving him little or no information about it. We show that zero-knowledge evidencing of such knowledge is impossible in quantum relativistic protocols, extending a previous result of Horodecki, Horodecki, and Horodecki. We also show that no such protocol can be both sound and complete. We present a new quantum relativistic protocol which we conjecture to be close to optimal in security against Alice and which reveals little knowledge to Bob, for large dimension d. We analyze its security against general attacks by Bob and restricted attacks by Alice.

Testing causal quantum theory.

Causal quantum theory assumes that measurements or collapses are well-defined physical processes, localized 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.

The grasshopper problem.

We introduce and physically motivate the following problem in geometric combinatorics, originally inspired by analysing Bell inequalities. A grasshopper lands at a random point on a planar lawn of area 1. It then jumps once, a fixed distance d, in a random direction. What shape should the lawn be to maximize the chance that the grasshopper remains on the lawn after jumping? We show that, perhaps surprisingly, a disc-shaped lawn is not optimal for any d>0. We investigate further by introducing a spin model whose ground state corresponds to the solution of a discrete version of the grasshopper problem. Simulated annealing and parallel tempering searches are consistent with the hypothesis that, for d<π-1/2, the optimal lawn resembles a cogwheel with n cogs, where the integer n is close to [Formula: see text]. We find transitions to other shapes for [Formula: see text].

Lorentzian quantum reality: postulates and toy models.

We describe postulates for a novel realist version of relativistic quantum theory or quantum field theory in Minkowski space and other background space-times, and illustrate their application with toy models.

Secure and robust transmission and verification of unknown quantum states in Minkowski space.

An important class of cryptographic applications of relativistic quantum information work as follows. B generates a random qudit and supplies it to A at point P. A is supposed to transmit it at near light speed c to to one of a number of possible pairwise spacelike separated points Q1, …, Qn. A's transmission is supposed to be secure, in the sense that B cannot tell in advance which Qj will be chosen. This poses significant practical challenges, since secure reliable long-range transmission of quantum data at speeds near to c is presently not easy. Here we propose different techniques to overcome these diffculties. We introduce protocols that allow secure long-range implementations even when both parties control only widely separated laboratories of small size. In particular we introduce a protocol in which A needs send the qudit only over a short distance, and securely transmits classical information (for instance using a one time pad) over the remaining distance. We further show that by using parallel implementations of the protocols security can be maintained in the presence of moderate amounts of losses and errors.

Memory attacks on device-independent quantum cryptography.

Device-independent quantum cryptographic schemes aim to guarantee security to users based only on the output statistics of any components used, and without the need to verify their internal functionality. Since this would protect users against untrustworthy or incompetent manufacturers, sabotage, or device degradation, this idea has excited much interest, and many device-independent schemes have been proposed. Here we identify a critical weakness of device-independent protocols that rely on public communication between secure laboratories. Untrusted devices may record their inputs and outputs and reveal information about them via publicly discussed outputs during later runs. Reusing devices thus compromises the security of a protocol and risks leaking secret data. Possible defenses include securely destroying or isolating used devices. However, these are costly and often impractical. We propose other more practical partial defenses as well as a new protocol structure for device-independent quantum key distribution that aims to achieve composable security in the case of two parties using a small number of devices to repeatedly share keys with each other (and no other party).

Unconditionally secure bit commitment by transmitting measurement outcomes.

We propose a new unconditionally secure bit commitment scheme based on Minkowski causality and the properties of quantum information. The receiving party sends a number of randomly chosen Bennett-Brassard 1984 (BB84) qubits to the committer at a given point in space-time. The committer carries out measurements in one of the two BB84 bases, depending on the committed bit value, and transmits the outcomes securely at (or near) light speed in opposite directions to remote agents. These agents unveil the bit by returning the outcomes to adjacent agents of the receiver. The protocol's security relies only on simple properties of quantum information and the impossibility of superluminal signalling.

Biological correlates of direct exposure to terrorism several years postdisaster.

BACKGROUND: It is important to understand long-term biological and psychiatric correlates of intense exposure to terrorism. METHODS: We assessed psychiatric diagnoses and biological stress measures in 50 healthy, highly exposed Oklahoma City bombing survivors recruited from a bombing registry 6 1/2 to 7 years postdisaster, comparing them with demographically matched, nonexposed community members. The Diagnostic Interview Schedule (DIS) determined Axis I psychiatric diagnoses. Participants' salivary cortisol levels were obtained at 8 am, and physiologic assessment measured participants' heart rate and blood pressure responses to a bombing-related interview. RESULTS: Eleven survivors with posttraumatic stress disorder (PTSD) had significantly higher cortisol levels than did both non-PTSD survivors and controls. Survivors with and without PTSD did not differ in any autonomic reactivity measure, whereas the total survivor group had significantly higher reactivity than controls in all measures. Positive correlations occurred between several autonomic reactivity measures, but none between cortisol and autonomic measures. CONCLUSIONS: Results differentiate the autonomic and cortisol systems relative to terrorism exposure. Findings support research associating PTSD with hypothalamic-pituitary-adrenal (HPA) axis changes, whereas autonomic reactivity appeared to be a more generalized trauma response. Correlation statistics substantiated a lack of connection between the 2 biological systems. Follow-up could elucidate the long-term course of these stress systems and eventual health status in survivors, in view of the medical morbidity noted in PTSD studies.

Physiologic reactivity despite emotional resilience several years after direct exposure to terrorism.

OBJECTIVE: Six and a half to 7 years after the 1995 terrorist bombing in Oklahoma City, the authors assessed autonomic reactivity to trauma reminders and psychiatric symptoms in adults who had some degree of direct exposure to the blast. METHOD: Sixty survivors who were listed in a state health department registry of persons exposed to the bombing and 60 age- and gender-matched members of the Oklahoma City metropolitan area community were assessed for symptoms of PTSD and depression and for axis I diagnoses. Heart rate and systolic, diastolic, and mean arterial blood pressures were measured before, during, and after bombing-related interviews. The two groups were compared on both psychometric and physiologic assessments. RESULTS: Posttraumatic stress but not depressive symptoms were significantly more prevalent in the survivor group than in the comparison group, although symptoms were below levels considered clinically relevant. Despite apparent emotional resilience or recovery, blast survivors had significantly greater autonomic reactivity to trauma reminders on all measures than comparison subjects. CONCLUSIONS: The results suggest that physiologic assessment may capture long-term effects of terrorism that are not identified by psychometric instruments. The consequences of autonomic reactivity despite emotional resilience years after experiencing trauma are unknown but theoretically could range from facilitating a protective vigilance toward future disasters to more maladaptive avoidance behaviors, somatic symptoms, or medical problems.

Maximally nonlocal and monogamous quantum correlations.

We introduce a version of the chained Bell inequality for an arbitrary number of measurement outcomes and use it to give a simple proof that the maximally entangled state of two d-dimensional quantum systems has no local component. That is, if we write its quantum correlations as a mixture of local correlations and general (not necessarily quantum) correlations, the coefficient of the local correlations must be zero. This suggests an experimental program to obtain as good an upper bound as possible on the fraction of local states and provides a lower bound on the amount of classical communication needed to simulate a maximally entangled state in dxd dimensions. We also prove that the quantum correlations violating the inequality are monogamous among nonsignaling correlations and, hence, can be used for quantum key distribution secure against postquantum (but nonsignaling) eavesdroppers.

Persistent physiological reactivity in a pilot study of partners of firefighters after a terrorist attack.

Twenty-four female partners of firefighters participating in recovery efforts associated with the 1995 terrorist bombing in Oklahoma City were assessed 43 to 44 months later. Disaster experiences, psychiatric diagnoses, posttraumatic stress symptoms, and autonomic reactivity in response to an interview about the bombing were examined. Most of the participants with postbombing disorders suffered from pre-existing conditions. The majority found the bombing a "terrible" or "shocking" experience. One participant met all DSM-III-R symptom group criteria for bombing-related posttraumatic stress disorder, and 40% met both B (intrusive re-experiencing) and D (hyperarousal) criteria. More than one half of the sample exhibited autonomic reactivity on at least one measurement. Those who met symptom group criterion D evidenced greater autonomic reactivity than those who did not, suggesting a link between self-reported posttraumatic stress disorder symptoms of arousal and biological manifestations. Thus, it may be important to assess partners of disaster recovery workers for mental health and physiological consequences related to their indirect exposure as these may persist years after the event, even in the absence of a diagnosable mental disorder.

No signaling and quantum key distribution.

Standard quantum key distribution protocols are provably secure against eavesdropping attacks, if quantum theory is correct. It is theoretically interesting to know if we need to assume the validity of quantum theory to prove the security of quantum key distribution, or whether its security can be based on other physical principles. The question would also be of practical interest if quantum mechanics were ever to fail in some regime, because a scientifically and technologically advanced eavesdropper could perhaps use postquantum physics to extract information from quantum communications without necessarily causing the quantum state disturbances on which existing security proofs rely. Here we describe a key distribution scheme provably secure against general attacks by a postquantum eavesdropper limited only by the impossibility of superluminal signaling. Its security stems from violation of a Bell inequality.

Cheat sensitive quantum bit commitment.

We define cheat sensitive cryptographic protocols between mistrustful parties as protocols which guarantee that, if either cheats, the other has some nonzero probability of detecting the cheating. We describe an unconditionally secure cheat sensitive nonrelativistic bit commitment protocol which uses quantum information to implement a task which is classically impossible; we also describe a simple relativistic protocol.

A critical look at risk assessments for global catastrophes.

Recent articles by Busza et al. (BJSW) and Dar et al. (DDH) argue that astrophysical data can be used to establish small bounds on the risk of a "killer strangelet" catastrophe scenario in the RHIC and ALICE collider experiments. The case for the safety of the experiments set out by BJSW does not rely solely on these bounds, but on theoretical arguments, which BJSW find sufficiently compelling to firmly exclude any possibility of catastrophe. Nonetheless, DDH and other commentators (initially including BJSW) suggested that these empirical bounds alone do give sufficient reassurance. This seems unsupportable when the bounds are expressed in terms of expectation value-a good measure, according to standard risk analysis arguments. For example, DDH's main bound, p(catastrophe) < 2 x 10(-8), implies only that the expectation value of the number of deaths is bounded by 120; BJSW's most conservative bound implies the expectation value of the number of deaths is bounded by 60,000. This article reappraises the DDH and BJSW risk bounds by comparing risk policy in other areas. For example, it is noted that, even if highly risk-tolerant assumptions are made and no value is placed on the lives of future generations, a catastrophe risk no higher than approximately 10(-15) per year would be required for consistency with established policy for radiation hazard risk minimization. Allowing for risk aversion and for future lives, a respectable case can be made for requiring a bound many orders of magnitude smaller. In summary, the costs of small risks of catastrophe have been significantly underestimated by BJSW (initially), by DDH, and by other commentators. Future policy on catastrophe risks would be more rational, and more deserving of public trust, if acceptable risk bounds were generally agreed upon ahead of time and if serious research on whether those bounds could indeed be guaranteed was carried out well in advance of any hypothetically risky experiment, with the relevant debates involving experts with no stake in the experiments under consideration.

Quantum bit string commitment.

A bit string commitment protocol securely commits N classical bits so that the recipient can extract only M