24 citations · 84 across the 14 of their papers we have counts for
14 papers
Relations between different definitions of the quantum Wasserstein distance
Géza Tóth, József Pitrik
The quantum Wasserstein distances defined by Golse, Mouhot, Paul, and Caglioti and by De Palma and Trevisan coincide for qubits when a single operator appears in the cost function.…
General method for obtaining the energy minimum of spin Hamiltonians for separable states
Géza Tóth, József Pitrik
We present a general method to determine the energy minimum of spin Hamiltonians over separable states when the single-particle reduced density matrices are fixed. For ferromagneti…
The swap transpose on couplings translates to Petz' recovery map on quantum channels
Gergely Bunth, József Pitrik, Tamás Titkos +1
In [Ann. Henri Poincaré, {\bf 22} (2021), 3199-3234], De Palma and Trevisan described a one-to-one correspondence between quantum couplings and quantum channels realizing transport…
Strong Kantorovich duality for quantum optimal transport with generic cost and optimal couplings on quantum bits
Gergely Bunth, József Pitrik, Tamás Titkos +1
We prove Kantorovich duality for a linearized version of a recently proposed non-quadratic quantum optimal transport problem, where quantum channels realize the transport. As an ap…
Quantum Wasserstein distance and its relation to several types of fidelities
Géza Tóth, József Pitrik
We consider several definitions of the quantum Wasserstein distance based on an optimization over general bipartite quantum states with given marginals. Then, we examine the quanti…
Wasserstein distances and divergences of order by quantum channels
Gergely Bunth, József Pitrik, Tamás Titkos +1
We introduce a non-quadratic generalization of the quantum mechanical optimal transport problem introduced in [De Palma and Trevisan, Ann. Henri Poincaré, {\bf 22} (2021), 3199-323…