Order 2 Quantum Wasserstein Distance Advances State Discrimination For

Order 2 Quantum Wasserstein Distance Advances State Discrimination For By offering a closed form solution for quantifying differences between these quantum states, this research establishes a powerful new approach for state discrimination and opens avenues for advancements in quantum information theory. In this paper, we study the computational aspects of the order 2 quantum wasserstein distance, formulating it as an infinite dimensional linear program in the space of positive borel measures supported on products of two unit spheres.

Advances Quantum State Discrimination Beating Helstrom Limit With In this paper, we study the computational aspects of the order 2 quantum wasserstein distance, formulating it as an infinite dimensional linear program in the space of positive borel measures supported on products of two unit spheres. Order 2 quantum wasserstein distance advances state discrimination for gaussian states researchers have derived a precise mathematical formula to calculate the minimal ‘cost’ of. Quantum wasserstein distances extend optimal transport theory to quantum states and channels, offering geometric, computational, and operational insights. In this paper, we study the computational aspects of the order 2 quantum wasserstein distance, formulating it as an infinite dimensional linear program in the space of positive borel measures supported on products of two unit spheres.

Sequential Quantum State Discrimination Quantum wasserstein distances extend optimal transport theory to quantum states and channels, offering geometric, computational, and operational insights. In this paper, we study the computational aspects of the order 2 quantum wasserstein distance, formulating it as an infinite dimensional linear program in the space of positive borel measures supported on products of two unit spheres. Numerical experiments are presented for $n=2$ qubit systems. for pure states, the minimal relaxation order $t=2$ yields the exact distance. for mixed states, the hierarchy provides lower bounds that increase with $t$. an example maximizing the distance shows saturation of the theoretical upper bound $w 2^2 (\rho, \nu) \le 2$. Distinguishing quantum states with minimal sampling overhead is of fundamental importance to teach quantum data to an algorithm. recently, the quantum wasserstein distance emerged from the theory of quantum optimal transport as a promising tool in this context. In this paper we study isometries of quantum wasserstein distances and divergences on the quantum bit state space. we describe isometries with respect to the symmetric quantum wasserstein divergence d sym, the divergence induced by all of the pauli matrices. Relying on this general machinery, we introduce p p wasserstein distances and divergences and study their fundamental geometric properties.

Distributed Quantum State Discrimination At Two Quantum Enabled Numerical experiments are presented for $n=2$ qubit systems. for pure states, the minimal relaxation order $t=2$ yields the exact distance. for mixed states, the hierarchy provides lower bounds that increase with $t$. an example maximizing the distance shows saturation of the theoretical upper bound $w 2^2 (\rho, \nu) \le 2$. Distinguishing quantum states with minimal sampling overhead is of fundamental importance to teach quantum data to an algorithm. recently, the quantum wasserstein distance emerged from the theory of quantum optimal transport as a promising tool in this context. In this paper we study isometries of quantum wasserstein distances and divergences on the quantum bit state space. we describe isometries with respect to the symmetric quantum wasserstein divergence d sym, the divergence induced by all of the pauli matrices. Relying on this general machinery, we introduce p p wasserstein distances and divergences and study their fundamental geometric properties.