Sequences of resource monotones from modular Hamiltonian polynomials

• Autores: Arias, Raúl Eduardo; de Boer, Jan; Di Giulio, Giuseppe; Keski Vakkuri, Esko; Tonni, Erik
• Año de publicación: 2023
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: QUANTUM INFORMATION; ENTANGLEMENT MONOTONE; MODULAR HAMILTONIAN; SCHUR CONCAVITY
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

We introduce two infinite sequences of entanglement monotones, which are constructed from expectation values of polynomials in the modular Hamiltonian. These monotones yield infinite sequences of inequalities that must be satisfied in majorizing state transitions. We demonstrate this for information erasure, deriving an infinite sequence of “Landauer inequalities” for the work cost, bounded by linear combinations of expectation values of powers of the modular Hamiltonian. These inequalities give improved lower bounds for the work cost in finite-dimensional systems, and depend on more details of the erased state than just on its entropy and variance of modular Hamiltonian. Similarly one can derive lower bounds for marginal entropy production for a system coupled to an environment. These infinite sequences of entanglement monotones also give rise to relative quantifiers that are monotonic in more general processes, namely those involving so-called σ majorization with respect to a fixed point full rank state σ; such quantifiers are called resource monotones. As an application to thermodynamics, one can use them to derive finite-dimension corrections to the Clausius inequality. Finally, in order to gain some intuition for what (if anything) plays the role of majorization in field theory, we compare pairs of states in discretized theories at criticality and study how majorization depends on the size of the bipartition with respect to the size of the entire chain.
Fil: Arias, Raúl Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Fil: de Boer, Jan. University of Amsterdam; Países Bajos
Fil: Di Giulio, Giuseppe. Institute For Theoretical Physics And Astrophysics; Alemania
Fil: Keski Vakkuri, Esko. University Of Helsinki. Faculty Of Science. Department Of Physics.; Finlandia
Fil: Tonni, Erik. Scuola Internazionale Superiore Di Studi Avanzati (sissa);