We probe the foundations of causal structure inference experimentally. The causal structure concerns which events influence other events. We probe whether causal structure can be determined without intervention in quantum systems. Intervention is commonly used to determine causal structure in classical scenarios, but in the more fundamental quantum theory, there is evidence that measurements alone, even coarse-grained measurements, can suffice. We demonstrate the experimental discrimination between several possible causal structures for a bipartite quantum system at two times, solely via coarse-grained projective measurements. The measurements are implemented by an approach known as scattering circuits in a nuclear magnetic resonance platform. Using recent analytical methods the data thus gathered is sufficient to determine the causal structure. Coarse-grained projective measurements disturb the quantum state less than fine-grained projective measurements and much less than interventions that reset the system to a fixed state.
We probe the foundations of causal structure inference experimentally. The causal structure concerns which events influence other events. We probe whether causal structure can be determined without intervention in quantum systems. Intervention is commonly used to determine causal structure in classical scenarios, but in the more fundamental quantum theory, there is evidence that measurements alone, even coarse-grained measurements, can suffice. We demonstrate the experimental discrimination between several possible causal structures for a bipartite quantum system at two times, solely via coarse-grained projective measurements. The measurements are implemented by an approach known as scattering circuits in a nuclear magnetic resonance platform. Using recent analytical methods the data thus gathered is sufficient to determine the causal structure. Coarse-grained projective measurements disturb the quantum state less than fine-grained projective measurements and much less than interventions that reset the system to a fixed state.
The causal structure of a set of events specifies which events influence which others. Determining this structure, known as causal inference, is a fundamental task in science. Reset-style intervention is commonly used to determine causal structure in classical scenarios. However, in the more fundamental quantum theory, there is evidence that projective measurements alone can suffice in some cases. We here extend those cases to two systems at two times, more general channels, and from fine-grained to less invasive coarse-grained projective measurements. The measurements are implemented by scattering circuits in a nuclear magnetic resonance platform. The measurement data are analysed via the pseudo-density matrix (PDM) formalism for measurements on systems at several times, in order to determine compatibility with given causal structures. We thereby successfully demonstrate causal inference from coarse-grained measurements alone, in a scenario with several qubits and two times.
We report NMR scattering circuit experiments that reveal causal structure. The scattering circuit involves interacting a probe qubit with the system of interest and finally measuring the probe qubit. The scattering circuit thereby implements a coarse-grained projective measurement. Causal structure refers to which events influence others and in the quantum case corresponds to different quantum circuit structures. In classical scenarios, intervention is commonly used to infer causal structure. In this quantum scenario of a bipartite system at two times, we demonstrate via scattering circuit experiments that coarse-grained measurements alone suffice for determining the causal structure. The experiment is undertaken by manipulating the nuclear spins of four Carbon-13 atoms in crotonic acid. The data analysis determines the compatibility of the data with given causal structures via representing the data as a pseudo density matrix (PDM) and analysing properties of the PDM. We demonstrate the successful identification of the causal structure for partial swap channels and fully decohering channels.
Though the topic of causal inference is typically considered in the context of classical statistical models, recent years have seen great interest in extending causal inference techniques to quantum and generalized theories. Causal identification is a type of causal inference problem concerned with recovering from observational data and qualitative assumptions the causal mechanisms 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 certain locus will almost certainly disturb the system. Hence, one might think a priori that quantum measurements are already too much like interventions, so that the problem of causal identification trivializes. This is not the case. Fixing a limited class of quantum instruments (namely the class of all projective measurements) to play the role of "observations," we note that as in the classical setting, there exist scenarios for which causal identification is not possible. We then present sufficient conditions for quantum causal identification, starting with a quantum analogue of the well-known "front-door criterion" and finishing with a broader class of scenarios for which the effect of a single intervention is identifiable. These results emerge from generalizing the process-theoretic account of classical causal inference due to Jacobs, Kissinger, and Zanasi beyond the setting of Markov categories, and thereby treating the classical and quantum problems uniformly.
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
Since Bell's theorem, it is known that local realism fails to explain quantum phenomena. Bell inequality violations manifestly show the incompatibility of quantum theory with classical notions of cause and effect. As recently found, however, the instrumental scenario-a pivotal tool in causal inference-allows for nonclassicality signatures going beyond this paradigm. If we are not limited to observational data and can intervene in our setup, then we can witness quantum violations of classical bounds on the causal influence among the involved variables even when no Bell-like violation is possible. That is, through interventions, the quantum behavior of a system that would seem classical can be demonstrated. Using a photonic setup-faithfully implementing the instrumental causal structure and switching between observation and intervention run by run-we experimentally witness such a nonclassicality. We also test quantum bounds for the causal influence, showing that they provide a reliable tool for quantum causal modeling.
This thesis details two experimental tests that can be applied to particular quantum states to reveal important information. We begin by discussing the relevant background in quantum information. We introduce qubits and qudits as basic quantum states, and we discuss the evolution and measurement of quantum states. We then discuss quantum state tomography as a means by which to obtain complete information about a state, followed by a discussion of state discrimination as a means by which to determine the state given the promise that it is drawn from some known set. We then discuss relevant experimental techniques in quantum optics, including measurement, generation of entanglement, and generation of single photons from entanglement. \n \nThe first experiment we discuss deals with the causal structure of a system, which is the description of the origin of correlations between two or more states. The causal structure can be direct-cause, meaning that one state causes the other; common-cause, meaning that both states are caused by another; or hybrid-cause, which is a combination of the two. We perform the first implementation of a new type of tomography to determine the causal structure; this is called causal tomography and functions regardless of whether two qubits are related by a common state, a process, or some combination thereof. We implement a process on two entangled photons so that we can select the exact causal structure that results, which ranges continuously between direct-cause and common-cause structures. Using causal tomography, we recover causal structures that closely match expected results and demonstrate that quantum mechanics provides an advantage in causal inference. \n \nThe second experiment we discuss deals with the unambiguous discrimination of multiple quantum states. For the first time, we apply the principles of unambiguous state discrimination to high-dimensional systems. Given a state chosen randomly out of d possible states encoded in d dimensions, we implement a procedure for determining which state was chosen; this procedure in theory functions without error. We encode and detect the states in the orbital angular momentum degree of freedom up to dimension d=14. Although no experiment can provide perfectly error-free measurement due to inevitable imperfections, we obtain an error rate below the theoretical error rate of minimum-error state discrimination for dimensions up to d=12. At the time of submission of this thesis, this work has been accepted for publication in Physical Review Letters.