Related papers: Quantum circuits with classical versus quantum con…
The consistent histories approach to quantum mechanics is traditionally based on linearly ordered sequences of events. We extend the histories formalism to sets of events whose causal ordering is described by directed acyclic graphs. The…
Quantum computation is a novel way of information processing which allows, for certain classes of problems, exponential speedups over classical computation. Various models of quantum computation exist, such as the adiabatic, circuit and…
We develop an extension of the process matrix (PM) framework for correlations between quantum operations with no causal order that allows multiple rounds of information exchange for each party compatibly with the assumption of well-defined…
We reformulate Pearl's three rules of do-calculus in the language of completely positive (CP) trace-preserving maps, thereby extending them to quantum systems with entanglement. We prove that Rule~2 fails whenever the underlying process…
Memory is the fundamental form of temporal complexity: when present but uncontrollable, it manifests as non-Markovian noise; conversely, if controllable, memory can be a powerful resource for information processing. Memory effects arise…
The quantization of particle trajectories gives rise to remarkable features such as the coherent superposition of quantum channels and the quantum switch, which offer significant advantages in the communication of both classical and quantum…
A causal set C can describe a discrete spacetime, but this discrete spacetime is not quantum, because C is endowed with Boolean logic, as it does not allow cycles. In a quasi-ordered set Q, cycles are allowed. In this paper, we consider a…
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…
We derive the category-theoretic backbone of quantum theory from a process ontology. More specifically, we treat quantum theory as a theory of systems, processes and their interactions. In this first part of a three-part overview, we first…
An astonishing feature of higher-order quantum theory is that it can accommodate indefinite causal order. In the simplest bipartite setting, there exist signaling correlations for which it is fundamentally impossible to ascribe a definite…
Quantum mechanics allows the occurrence of events without having any definite causal order. Here, it is shown that the application of two different thermal channels in the causally inseparable order can enhance the potential to extract…
Higher-order transformations acting on input quantum channels in an indefinite causal order, such as the quantum switch, cannot be described by quantum circuits using the same number of calls to the input channels. A natural question is…
Similarly to quantum states, quantum operations can also be transformed by means of quantum superchannels, also known as process matrices. Quantum superchannels with multiple slots are deterministic transformations whichtake independent…
The Swap gate is a ubiquitous tool for moving information on quantum hardware, yet it can be considered a classical operation because it does not entangle product states. Genuinely quantum operations could outperform Swap for the task of…
Identifying the causal structures between two statistically correlated events has been widely investigated in many fields of science. While some of the well-studied classical methods are carefully generalized to quantum version of causal…
A new model of quantum computation is considered, in which the connections between gates are programmed by the state of a quantum register. This new model of computation is shown to be more powerful than the usual quantum computation, e. g.…
A quantum switch is a superoperator that, in general, creates a superposition of various causal orders of two or more quantum dynamics that are all divisible in the complete positivity (CP) sense. We introduce a process that we term as the…
There are good motivations for considering some type of quantum histories formalism. Several possible formalisms are known, defined by different definitions of event and by different selection criteria for sets of histories. These…
It has long been recognized as a difficult problem to determine whether the observed statistical correlation between two classical variables arise from causality or from common causes. Recent research has shown that in quantum theoretical…
Allowing the order of quantum operations to exist in superposition is known to open new routes for thermodynamic tasks. We investigate a quantum heat engine where energy exchanges are driven by generalized measurements, and the sequence of…