Related papers: Transference Plans and Uncertainty
An efficient method for computing solutions to the Optimal Transportation (OT) problem with a wide class of cost functions is presented. The standard linear programming (LP) discretization of the continuous problem becomes intractible for…
We consider Monge-Kantorovich optimal transport problems on $\mathbb{R}^d$, $d\ge 1$, with a convex cost function given by the cumulant generating function of a probability measure. Examples include the Wasserstein-2 transport whose cost…
A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic…
We revisit the duality theorem for multimarginal optimal transportation problems. In particular, we focus on the Coulomb cost. We use a discrete approximation to prove equality of the extremal values and some careful estimates of the…
Semidiscrete optimal transport is a challenging generalization of the classical transportation problem in linear programming. The goal is to design a joint distribution for two random variables (one continuous, one discrete) with fixed…
Many research has been conducted about quadratic programming and inverse optimization. In this paper we present the combination aspect of these subjects, applying on transportation problem. First, we obtain the inverse form of quadratic…
We analyse the problem of transmitting a number of unknown quantum states or one composite system in one go. We derive a lower bound on the performance of such process, measured in the entanglement fidelity. The obtained bound is…
Optimal Transport, a theory for optimal allocation of resources, is widely used in various fields such as astrophysics, machine learning, and imaging science. However, many applications impose elementwise constraints on the transport plan…
Recent experiments confirm that quantum teleportation is possible at least for states of photons and nuclear spins. The quantum teleportation is not only a curious effect but a fundamental protocol of quantum communication and quantum…
Quantum field theory can be a new medium for communication through quantum energy teleportation. We performed a demonstration of quantum energy teleportation with a relativistic fermionic field theory of self-coupled fermions, called the…
A general framework is given to analyze the falsifiability of economic models based on a sample of their observable components. It is shown that, when the restrictions implied by the economic theory are insufficient to identify the unknown…
The basic problem of optimal transportation consists in minimizing the expected costs $\mathbb {E}[c(X_1,X_2)]$ by varying the joint distribution $(X_1,X_2)$ where the marginal distributions of the random variables $X_1$ and $X_2$ are…
Teleportation for pure states, mixed states with standard and optimal protocols are introduced and investigated systematically. An explicit equation governing the teleportation of finite dimensional quantum pure states by a generally given…
Entropy regularized optimal transport and its multi-marginal generalization have attracted increasing attention in various applications, in particular due to efficient Sinkhorn-like algorithms for computing optimal transport plans. However,…
A quantum version of the Monge--Kantorovich optimal transport problem is analyzed. The transport cost is minimized over the set of all bipartite coupling states $\rho^{AB}$, such that both of its reduced density matrices $\rho^A$ and…
We present a minimization problem with a horizontal divergence-type constraint in the Heisenberg group. Our study explores its dual formulation and examines its relationship with the congested optimal transport problem, for $1 < p <…
Theories describing electrical transport in semiconductor superlattices can essentially be divided in three disjoint categories: i) transport in a miniband; ii) hopping between Wannier-Stark ladders; and iii) sequential tunneling. We…
The effects of the propagation of particles which have a finite life time and an according width in their mass spectrum are discussed in the context of transport descriptions. In the first part the coupling of soft photon modes to a source…
A programmable quantum networks model is used in this paper for development of methods of control of a quantum state transport. These methods may be applied for a wide variety of patterns of controlled state transmission and spreading in…
We bring together the semiclassical approximation, matrix integrals and the theory of symmetric polynomials in order to solve a long standing problem in the field of quantum chaos: to compute transport moments when tunnel barriers are…