Related papers: Probabilistic theories with purification
We introduce the concept of a physical process that purifies a mixed quantum state, taken from a set of states, and investigate the conditions under which such a purification map exists. Here, a purification of a mixed quantum state is a…
The recently introduced random purification channel, which converts $n$ i.i.d. copies of any mixed quantum state into a uniform convex combination of $n$ i.i.d. copies of its purifications, has proved to be an extremely useful tool in…
Using the existing classification of all alternatives to the measurement postulates of quantum theory we study the properties of bi-partite systems in these alternative theories. We prove that in all these theories the purification…
We discuss how to reconstruct quantum theory from operational postulates. In particular, the following postulates are consistent only with for classical probability theory and quantum theory. Logical Sharpness: There is a one-to-one map…
To study which are the most general causal structures which are compatible with local quantum mechanics, Oreshkov et al. introduced the notion of a process: a resource shared between some parties that allows for quantum communication…
We present a reconstruction of finite-dimensional quantum theory where all of the postulates are stated in diagrammatic terms, making them intuitive. Equivalently, they are stated in category-theoretic terms, making them mathematically…
Process tomography, the experimental characterization of physical processes, is a central task in science and engineering. Here we investigate the axiomatic requirements that guarantee the in-principle feasibility of process tomography in…
Quantum theory combines density matrices, Born probabilities, tensor-product composites, positive-operator-valued measures (POVMs), and quantum channels. In a finite-dimensional causal operational theory, we prove that two postulates…
We study the task of lifting arbitrary quantum states and channels to purifications and Stinespring dilations, respectively, in both the probabilistic exact and deterministic approximate settings. We formalize this task through a general…
The random purification channel maps n copies of any mixed quantum state to n copies of a random purification of the state. We generalize this construction to arbitrary symmetries: for any group G of unitaries, we construct a quantum…
We show how to reconstruct a process theory of local systems starting from a global theory of reversible processes on a single global system, by using the purification principle. In such a process theory, local systems are not given, but…
It is well-known that pure quantum states are typically almost maximally entangled, and thus have close to maximally mixed subsystems. We consider whether this is true for probabilistic theories more generally, and not just for quantum…
Starting from the observation that reversible processes cannot increase the purity of any input state, we study deterministic physical processes, which map a set of states to a set of pure states. Such a process must map any state to the…
We prove that the linearity and positivity of quantum mechanics impose general restrictions on quantum purification, unveiling a new fundamental limitation of quantum information processing. In particular, no quantum operation can transform…
In quantum theory every state can be diagonalized, i.e. decomposed as a convex combination of perfectly distinguishable pure states. This elementary structure plays an ubiquitous role in quantum mechanics, quantum information theory, and…
Filtered probability spaces (called "filtrations" for short) are shown to satisfy such a topological zero-one law: for every property of filtrations, either the property holds for almost all filtrations, or its negation does. In particular,…
In this paper, we investigate a characterization of Quantum Mechanics by two physical principles based on general probabilistic theories. We first give the operationally motivated definition of the physical equivalence of states and…
Predictions for measurement outcomes in physical theories are usually computed by combining two distinct notions: a state, describing the physical system, and an observable, describing the measurement which is performed. In quantum theory,…
Preparing a quantum system in a pure state is ultimately limited by the nature of the system's evolution in the presence of its environment and by the initial state of the environment itself. We show that, when the system and environment…
Quantum state purification is crucial in quantum communication and computation, aiming to recover a purified state from multiple copies of an unknown noisy state. This work introduces a general state purification framework designed to…