A causal relation between quantum agents, say Alice and Bob, is necessarily mediated by an interaction. Modeling the latter as a reversible quantum channel, an intervention of Alice can have causal influence on Bob's system, modifying correlations between Alice and Bob's systems. Causal influence between quantum systems necessarily allows for signaling. Here we prove a mismatch between causal influence and signaling via direct computation of the two quantities for the Cnot gate. Finally we show a continuity theorem for causal effects of unitary channels: a channel has small causal influence if it allows for small signaling. Published by the American Physical Society 2024
A causal relation between quantum agents, say Alice and Bob, is necessarily mediated by an interaction. Modeling the latter as a reversible quantum channel, an intervention of Alice can have causal influence on Bob's system, modifying correlations between Alice and Bob's systems. Causal influence between quantum systems necessarily allows for signaling. Here we prove a mismatch between causal influence and signaling via direct computation of the two quantities for the Cnot gate. Finally we show a continuity theorem for causal effects of unitary channels: a channel has small causal influence if it allows for small signaling. Published by the American Physical Society 2024
The causal effects activated by a quantum interaction are studied, modelling the last one as a bipartite unitary channel. The two parties, say Alice and Bob, can use the channel to exchange messages -- i.e. to signal. On the other hand, the most general form of causal influence includes also the possibility for Alice, via a local operation on her system, to modify Bob's correlations and viceversa. The presence or absence of these two effects are equivalent, but when they both occur, they can differ in their magnitude. We study the properties of two functions that quantify the amount of signalling and causal influence conveyed by an arbitrary unitary channel. The functions are proved to be continuous and monotonically increasing with respect to the tensor product of channels. Monotonicity is instead disproved in the case of sequential composition. Signalling and causal influence are analytically computed for the quantum SWAP and CNOT gates, in the single use scenario, in the n-parallel uses scenario, and in the asymptotic regime. A finite gap is found between signalling and causal influence for the quantum CNOT, thus proving the existence of extra causal effects that cannot be explained in terms of communication only. However, the gap disappears in the asymptotic limit of an infinite number of parallel uses, leaving room for asymptotic equivalence between signalling and causal influence.
A no-signalling channel transforming quantum systems in Alice's and Bob's local laboratories is compatible with two different causal structures: (A⪯B) Alice's output causally precedes Bob's input and (B⪯A) Bob's output causally precedes Alice's input. Here I prove that two no-signalling channels that are not perfectly distinguishable in any ordinary quantum circuit can become perfectly distinguishable through the quantum superposition of circuits with different causal structures.
We study the relation of causal influence between input systems of a reversible evolution and its output systems, in the context of operational probabilistic theories. We analyse two different definitions that are borrowed from the literature on quantum theory—where they are equivalent. One is the notion based on signalling, and the other one is the notion used to define the neighbourhood of a cell in a quantum cellular automaton. The latter definition, that we adopt in the general scenario, turns out to be strictly weaker than the former: it is possible for a system to have causal influence on another one without signalling to it. Remarkably, the counterexample comes from classical theory, where the proposed notion of causal influence determines a redefinition of the neighbourhood of a cell in cellular automata. We stress that, according to our definition, it is impossible anyway to have causal influence in the absence of an interaction, e.g. in a Bell-like scenario. We study various conditions for causal influence, and introduce the feature that we call no interaction without disturbance , under which we prove that signalling and causal influence coincide. The proposed definition has interesting consequences on the analysis of causal networks, and leads to a revision of the notion of neighbourhood for classical cellular automata, clarifying a puzzle regarding their quantisation that apparently makes the neighbourhood larger than the original one.
We consider devices with two inputs and two outputs, Alice and Bob each having access to one input and one output. To such a device we associate time-reverses by exchanging the roles of the inputs and the outputs. We find that there are devices which admit a local hidden variable representation, but for which time-reverses enable perfect signaling between Alice and Bob. That is, a `perfect channel in one time direction' becomes a `non-channel in the other direction'. Also, for PR boxes time-reverses enable signaling between Alice and Bob, but never as a perfect channel. These results undermine the representation of causal structures as partial orders or similar `time-symmetric structures', as is often assumed in search of a theory of quantum gravity. They also provide new insights into the structure of the polytope of generalized probabilistic correlations, and contribute to the growing area of research into quantum information processing in relativistic spacetimes.
Recent years have seen great interest in extending causal inference concepts developed in the context of classical statistical models to quantum theory. So far, this program has only barely addressed causal identification, a type of causal inference problem concerned with recovering from observational data and qualitative assumptions the causal relationships generating the data, and hence the effects of hypothetical interventions. A major obstacle to a theory of causal identification in the quantum setting is the question of what should play the role of “observational data,” as any means of extracting data at a locus will almost certainly disturb the system. One might think that quantum measurements are already too much like interventions, so that the problem of causal identification is trivialized. This is not the case: when we fix a limited class of quantum measurement instruments (namely, the class of all projective measurements) to play the role of “observations,” there exist scenarios for which causal identification is impossible. In this paper, we present a framework, based on process theories (also known as strict symmetric monoidal categories), for studying quantum causal identification scenarios on the same footing as their classical counterparts. Within this framework, we present sufficient conditions for quantum causal identification in networks with unobserved confounding systems, including quantum analogs of the well-known “back-door” and “front-door” criteria. These results arise from a type of causal model designed to facilitate the transfer of inference techniques from the classical to the quantum setting. Published by the American Physical Society 2024
Causal influences are at the core of any empirical science, the reason why its quantification is of paramount relevance for the mathematical theory of causality and applications. Quantum correlations, however, challenge our notion of cause and effect, implying that tools and concepts developed over the years having in mind a classical world have to be reevaluated in the presence of quantum effects. Here, we propose the quantum version of the most common causality quantifier, the average causal effect, measuring how much a target quantum system is changed by interventions on its presumed cause. Not only does it offer an innate manner to quantify causation in two-qubit gates but also in alternative quantum computation models such as the measurement-based version, suggesting that causality can be used as a proxy for optimizing quantum algorithms. Considering quantum teleportation, we show that any pure entangled state offers an advantage in terms of causal effects as compared to separable states. This broadness of different uses showcases that, just as in the classical case, the quantification of causal influence has foundational and applied consequences and can lead to a yet totally unexplored tool for quantum information science.