相关论文: Choi-Defined Resource Theories
This paper deals with the unconstrained and constrained cases for continuous-time Markov decision processes under the finite-horizon expected total cost criterion. The state space is denumerable and the transition and cost rates are allowed…
In this article, I use an operational formulation of the Choi-Jamio\l{}kowski isomorphism to explore an approach to quantum mechanics in which the state is not the fundamental object. I first situate this project in the context of…
The goal of this work is to develop, in a systematic way and in a full natural generality, the foundations of a theory of functions of (free) noncommuting variables.
We develop a resource theory for non-absolutely separable states (non-AS) in which absolutely separable states (AS) that cannot be entangled by any global unitaries are recognised as free states and any convex mixture of global unitary…
We study the class $\mathcal{M}_{\mathrm{ratio}}$ of those probability distributions for which the free $R$-transforms are rational functions. This class is closed under the additive free convolution, additive free powers and under the…
It is known that distillation in continuous variable resource theories is impossible when restricted to Gaussian states and operations. To overcome this limitation, we enlarge the theories to include convex mixtures of Gaussian states and…
We derive sufficient conditions for theories consisting of multiple vector fields, which could also couple to external fields, to be multi-field generalised Proca theories. The conditions are derived by demanding that the theories have the…
In this work we examine quantum states which have non-negative amplitudes (in a fixed basis) and the channels which preserve them. These states include the ground states of stoquastic Hamiltonians and they are of interest since they avoid…
We identify and explore the intriguing property of resource resonance arising within resource theories of entanglement, coherence and thermodynamics. While the theories considered are reversible asymptotically, the same is generally not…
We present an operational framework for Einstein-Podolsky-Rosen steering as a physical resource. To begin with, we characterize the set of steering non-increasing operations (SNIOs) --i.e., those that do not create steering-- on…
There are several important abstract operator systems with the convex cone of positive semidefinite matrices at the first level. Well-known are the operator systems of separable matrices, of positive semidefinite matrices, and of block…
A short proof is given for the well-known Choi-Effros theorem on the structure of ranges of completely positive projections.
We provide a reformulation of finite dimensional quantum theory in the circuit framework in terms of mathematical axioms, and a reconstruction of quantum theory from operational postulates. The mathematical axioms for quantum theory are the…
We study the one-shot distillation of general quantum resources, providing a unified quantitative description of the maximal fidelity achievable in this task, and revealing similarities shared by broad classes of resources. We establish…
We show how any system with morphological degrees of freedom and locally limited free energy will, under the constraints of the free energy principle, evolve toward a neuromorphic morphology that supports hierarchical computations in which…
Hierarchical inductive biases are hypothesized to promote generalizable policies in reinforcement learning, as demonstrated by explicit hyperbolic latent representations and architectures. Therefore, a more flexible approach is to have…
The definition of Choi matrices for linear maps on the n x n matrices is extended to factors, and the basic theorems for Choi matrices are proved in this general context.
This paper develops limit theorems for random variables with network dependence, without requiring the individuals in the network to be located in a Euclidean or metric space. This distinguishes our approach from most existing limit…
The study of state revivals has a long history in dynamical systems. We introduce a resource theory to understand the use of state revivals in quantum physics, especially in quantum many-body scarred systems. In this theory, a state is said…
Using the technique developed in approximation theory, we construct examples of exponential families of infinitely divisible laws which can be viewed as deformations of the normal, gamma, and Poisson exponential families. Replacing the…