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In the last few years, there has been increasing interest in quantum processes with indefinite causal order. Process matrices are a convenient framework to study such processes. Ref. [1] defines higher order transformations from process…
In a conventional circuit for quantum machine learning, the quantum gates used to encode the input parameters and the variational parameters are constructed with a fixed order. The resulting output function, which can be expressed in the…
When transforming pairs of independent quantum operations according to the fundamental rules of quantum theory, an intriguing phenomenon emerges: some such higher-order operations may act on the input operations in an indefinite causal…
Our common understanding of the physical world deeply relies on the notion that events are ordered with respect to some time parameter, with past events serving as causes for future ones. Nonetheless, it was recently found that it is…
In this "map" we are going to present the concept of indefinite causal order and make a quick journey through its different flavours. We will start with a broad conceptual motivation for studying indefinite causal order, based on the…
We address the study of quantum metrology enhanced by indefinite causal order, demonstrating a quadratic advantage in the estimation of the product of two average displacements in a continuous variable system. We prove that no setup where…
Quantum theory is compatible with scenarios in which the order of operations is indefinite. Experimental investigations of such scenarios, all of which have been based on a process known as the quantum switch, have provided demonstrations…
It was recently suggested that causal structures are both dynamical, because of general relativity, and indefinite, due to quantum theory. The process matrix formalism furnishes a framework for quantum mechanics on indefinite causal…
In all existing quantum walk models, the assumption about a pre-existing fixed background causal structure is always made and has been taken for granted. Nevertheless, in this work we will get rid of this tacit assumption especially by…
It was recently found that the indefinite causal order in the quantum switch can be certified device-independently when assuming the impossibility of superluminal influences. Here we strengthen this result in two ways. First, we give a…
The quantum switch has been widely studied as a prototypical example of indefinite causal order in quantum information processing. However, the potential advantages of utilising more general forms of indefinite causal orders remain largely…
Indefinite causal order (ICO), in which the order of quantum operations is placed in a coherent superposition, has been demonstrated to enhance various information-processing tasks. Here, we investigate its impact on the thermodynamic…
The standard model of quantum circuits assumes operations are applied in a fixed sequential "causal" order. In recent years, the possibility of relaxing this constraint to obtain causally indefinite computations has received significant…
We demonstrate non-classical cooling on the IBMq cloud quantum computer. We implement a recently proposed refrigeration protocol which relies upon indefinite causal order for its quantum advantage. We use quantum channels which, when used…
Indefinite causal order has found numerous applications in quantum computation, quantum communication, and quantum metrology. Before its usage, the quality of the indefinite causal order needs to be first certified, and the certification…
In theories of communication, it is usually presumed that the involved parties perform actions in a fixed causal order. However, practical and fundamental reasons can induce uncertainties in the causal order. Here we show that a maximal…
Indefinite causal order (ICO) has the potential to be a new resource for quantum information processing. In most of its experiments, ICO has been investigated in a photonic platform. Here we investigate ICO in a cavity quantum…
We report an experimental certification of indefinite causal order that relies only on the characterization of the operations of a single party. We do so in the semi-device-independent scenario with the fewest possible assumptions of…
Treating the time of an event as a quantum variable, we derive a scheme in which superpositions in time are used to perform operations in an indefinite causal order. We use some aspects of a recently developed space-time-symmetric formalism…
Quantum theory is consistent with a computational model permitting black-box operations to be applied in an indefinite causal order, going beyond the standard circuit model of computation. The quantum switch -- the simplest such example --…