Related papers: State-injection schemes of quantum computation in …
Spekkens' toy model is a non-contextual hidden variable model with an epistemic restriction, a constraint on what an observer can know about reality. The aim of the model, developed for continuous and discrete prime degrees of freedom, is…
We give a complete characterization of the (non)classicality of all stabilizer subtheories. First, we prove that there is a unique nonnegative and diagram-preserving quasiprobability representation of the stabilizer subtheory in all odd…
We provide two mathematical descriptions of Spekkens's toy qubit theory, an inductively one in terms of a small set of generators, as well as an explicit closed form description. It is a subcategory MSpek of the category of finite sets,…
Spekkens has introduced a toy theory [Phys. Rev. A, 75, 032110 (2007)] in order to argue for an epistemic view of quantum states. I describe a notation for the theory (excluding certain joint measurements) which makes its similarities and…
While quantum theory cannot be described by a local hidden variable model, it is nevertheless possible to construct such models that exhibit features commonly associated with quantum mechanics. These models are also used to explore the…
We investigate the strengths and limitations of the Spekkens toy model, which is a local hidden variable model that replicates many important properties of quantum dynamics. First, we present a set of five axioms that fully encapsulate…
We generalize the ZX calculus to quantum systems of dimension higher than two. The resulting calculus is sound and universal for quantum mechanics. We define the notion of a mutually unbiased qudit theory and study two particular instances…
In order to better understand a complex theory like quantum mechanics, it is sometimes useful to take a step back and create alternative theories, with more intuitive foundations, and examine which features of quantum mechanics can be…
Quantum mechanics is known to provide significant improvements in information processing tasks when compared to classical models. These advantages range from computational speeds-up to security improvements. A key question is where these…
We describe a general framework in which we can precisely compare the structures of quantum-like theories which may initially be formulated in quite different mathematical terms. We then use this framework to compare two theories: quantum…
The toy model used by Spekkens [R. Spekkens, Phys. Rev. A 75, 032110 (2007)] to argue in favor of an epistemic view of quantum mechanics is extended by generalizing his definition of pure states (i.e. states of maximal knowledge) and by…
It is a fundamental prediction of quantum theory that states of physical systems are described by complex vectors or density operators on a Hilbert space. However, many experiments admit effective descriptions in terms of other state…
We describe a universal scheme of quantum computation by state injection on rebits (states with real density matrices). For this scheme, we establish contextuality and Wigner function negativity as computational resources, extending results…
This paper describes an algorithmic system called SQT for the computer simulation of a wide class of quantum experiments on entangled particles. SQT maintains a hidden internal state for each particle and it provides an initialization…
The framework of generalized probabilistic theories (GPTs) is a popular approach for studying the physical foundations of quantum theory. The standard framework assumes the no-restriction hypothesis, in which the state space of a physical…
We map Spekkens' toy model to a quantum mechanics defined over the finite field $\mathbb{F}_5$. This allows us to define arbitrary linear combinations of the epistemic states in the model. For Spekkens' elementary system with only $2^2=4$…
We apply the geometric quantization procedure via symplectic groupoids proposed by E. Hawkins to the setting of epistemically restricted toy theories formalized by Spekkens. In the continuous degrees of freedom, this produces the algebraic…
In this paper, we extend the standard formalism of quantum mechanics to a quantum theory for a total system including one internal measuring apparatus. The internality of the measuring apparatus implies that different decomposition of a…
Recent results on the non-universality of fault-tolerant gate sets underline the critical role of resource states, such as magic states, to power scalable, universal quantum computation. Here we develop a resource theory, analogous to the…
A rigorous microscopic theory for the description of quantum-transport phenomena in systems with open boundaries is proposed. We shall show that the application of the conventional Wigner-function formalism to this problem leads to…