Related papers: Causal structures and the classification of higher…
Quantum processes with indefinite causal structure emerge when we wonder which are the most general evolutions, allowed by quantum theory, of a set of local systems which are not assumed to be in any particular causal order. These processes…
Higher-order quantum theory is an extension of quantum theory where one introduces transformations whose input and output are transformations, thus generalizing the notion of channels and quantum operations. The generalization then goes…
Quantum supermaps are transformations that map quantum operations to quantum operations. It is known that quantum supermaps which respect a definite, predefined causal order between their input operations correspond to fixed-order quantum…
We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and…
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…
We show that quantum theory allows for transformations of black boxes that cannot be realized by inserting the input black boxes within a circuit in a pre-defined causal order. The simplest example of such a transformation is the classical…
Unitary operations are a fundamental component of quantum algorithms, but they seem to be far more useful if given with a "quantum control" as a controlled unitary operation. However, quantum operations are not limited to unitary…
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…
In the past decade, the toolkit of quantum information has been expanded to include processes in which the basic operations do not have definite causal relations. Originally considered in the context of the unification of quantum mechanics…
Quantum resources exist in a hierarchy of multiple levels. At order zero, quantum states are transformed by linear maps (channels, or gates) in order to perform computations or simulate other states. At order one, gates and channels are…
We present a framework to treat quantum networks and all possible transformations thereof, including as special cases all possible manipulations of quantum states, measurements, and channels, such as, e.g., cloning, discrimination,…
Quantum supermaps provide a framework in which higher order quantum processes can act on lower order quantum processes. In doing so, they enable the definition and analysis of new quantum protocols and causal structures. Recently, key…
Complex information-processing systems, for example quantum circuits, cryptographic protocols, or multi-player games, are naturally described as networks composed of more basic information-processing systems. A modular analysis of such…
Quantum theory is in principle compatible with scenarios where physical processes occur in an indefinite order, potentially yielding advantages in a broad range of information processing tasks. However, advantages in communication, the most…
Many fundamental and key objects in quantum mechanics are linear mappings between particular affine/linear spaces. This structure includes basic quantum elements such as states, measurements, channels, instruments, non-signalling channels…
We present a categorical construction for modelling causal structures within a general class of process theories that include the theory of classical probabilistic processes as well as quantum theory. Unlike prior constructions within…
Causal nonseparability refers to processes where events take place in a coherent superposition of different causal orders. These may be the key resource for experimental violations of causal inequalities and have been recently identified as…
Given black-box access to the input and output systems, we develop the first efficient quantum causal order discovery algorithm with polynomial query complexity with respect to the number of systems. We model the causal order with quantum…
A sequential network of quantum operations is efficiently described by its quantum comb, a non-negative operator with suitable normalization constraints. Here we analyze the case of networks enjoying symmetry with respect to the action of a…
In quantum computing, the computation is achieved by linear operators in or between Hilbert spaces. In this work, we explore a new computation scheme, in which the linear operators in quantum computing are replaced by (higher) functors…