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.
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.
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 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 give a causal inference scheme using quantum observations alone for a case with both temporal and spatial correlations: a bipartite quantum system with measurements at two times. The protocol determines compatibility with five causal structures distinguished by the direction of causal influence and whether there are initial correlations. We derive and exploit a closed-form expression for the spacetime pseudo-density matrix (PDM) for many times and qubits. This PDM can be determined by light-touch coarse-grained measurements alone. We prove that if there is no signalling between two subsystems, the reduced state of the PDM cannot have negativity, regardless of initial spatial correlations. In addition, the protocol exploits the time asymmetry of the PDM to determine the temporal order. The protocol succeeds for a state with coherence undergoing a fully decohering channel. Thus coherence in the channel is not necessary for the quantum advantage of causal inference from observations alone.
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.
In recent years, the investigation of causal relations in quantum theory has attracted a lot of interest. In particular, it has been found that it is possible to conceive of scenarios where some parties perform operations that are compatible with quantum theory locally, but that cannot be embedded into a global background causal structure. Such indefinite causal structures are of interest from a fundamental point of view, but also from the perspective of quantum information processing, since they do not fit into the usual paradigm of quantum circuits, which assumes a definite causal order. The main aim of this thesis is to study indefinite quantum causal relations involving more than two parties. Compared to the bipartite case, there are many new aspects and complications that arise in multipartite situations, which need to be clarified in order to fundamentally understand quantum causal structures, and to shed light on their implications and potential usefulness for quantum information processing.A suitable mathematical framework for the investigation of quantum causal relations is the process matrix formalism. In this framework, the notion of causal nonseparability was introduced in order to qualify scenarios that are incompatible with a definite causal order. In Chapter 2, we study how to generalise this concept to the multipartite case, how to characterise multipartite causally (non)separable quantum processes, and how to certify multipartite causal nonseparability. Another important topic is to determine which quantum scenarios with indefinite causal order are physically implementable, and how they can be realised concretely. In Chapter 3, we introduce two new classes of physically realisable multipartite quantum processes, and characterise them in terms of their process matrix descriptions. In particular, we define the class of quantum circuits with quantum control of causal order. The simplest example of such a circuit is the quantum switch, a protocol in which the order between two operations is controlled by a qubit in a superposition state, and which defines a causally nonseparable process. The class we introduce also contains more general examples of causally nonseparable processes with new features. We then show how the process matrix characterisation of this class allows us to search for new quantum information processing applications of causal nonseparability. In Chapter 4, we investigate a particular quantum communication effect in a scenario involving coherent control between two quantum channels. This leads us to a more general analysis of the notion of a coherently controlled channel, which involves certain subtilities. In Chapter 5, we turn to another problem that arises in multipartite scenarios, namely whether a given phenomenon is genuinely multipartite or not. More particularly, we study genuinely multipartite (non)causal correlations. In Chapter 6, we show that anomalous weak values are possible without post-selection. In Chapter 7, we show that certain tripartite process matrices, namely those that are unitarily extensible, have a realisation on so-called time-delocalised subsystems, i.e., quantum subsystems that are not associated with a definite time. The class of unitarily extensible tripartite process matrices is larger than the class of quantum circuits with quantum control, and in particular contains processes that violate so-called causal inequalities.
The joint expectation values of quantum observables measured by two parties typically depend on the causal structure of the measurement protocol. The two causal structures we investigate here are the direct-cause scenario, in which a single quantum state is measured twice in series with a general quantum channel between measurements, and the common-cause scenario, in which a shared bipartite quantum state is measured in parallel. Through a variety of examples of qubit channels with tunable parameters, we identify the full set of input states where the direct-cause joint expectation values of Pauli observables coincide with those obtained from a common cause, a situation that we call causal confusion. More generally, for arbitrary finite-dimensional quantum systems and light-touch observables, we prove that a channel exhibits causal confusion for some input state if and only if it is a positive-partial-transpose (PPT) channel, thereby endowing PPT channels with a new operational meaning in terms of causal confusion. Using this result, we characterize the set of qubit channels for which there exists an input state leading to causal confusion as the set of entanglement-breaking channels.