Sequences of resource monotones from modular Hamiltonian polynomials
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...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2023-10-01
|
| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.5.043082 |
| _version_ | 1797210407053557760 |
|---|---|
| author | Raúl Arias Jan de Boer Giuseppe Di Giulio Esko Keski-Vakkuri Erik Tonni |
| author_facet | Raúl Arias Jan de Boer Giuseppe Di Giulio Esko Keski-Vakkuri Erik Tonni |
| author_sort | Raúl Arias |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T10:10:06Z |
| format | Article |
| id | doaj.art-d9843551ae6446c1bb783fd59f9472cc |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:10:06Z |
| publishDate | 2023-10-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-d9843551ae6446c1bb783fd59f9472cc2024-04-12T17:35:23ZengAmerican Physical SocietyPhysical Review Research2643-15642023-10-015404308210.1103/PhysRevResearch.5.043082Sequences of resource monotones from modular Hamiltonian polynomialsRaúl AriasJan de BoerGiuseppe Di GiulioEsko Keski-VakkuriErik TonniWe 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.http://doi.org/10.1103/PhysRevResearch.5.043082 |
| spellingShingle | Raúl Arias Jan de Boer Giuseppe Di Giulio Esko Keski-Vakkuri Erik Tonni Sequences of resource monotones from modular Hamiltonian polynomials Physical Review Research |
| title | Sequences of resource monotones from modular Hamiltonian polynomials |
| title_full | Sequences of resource monotones from modular Hamiltonian polynomials |
| title_fullStr | Sequences of resource monotones from modular Hamiltonian polynomials |
| title_full_unstemmed | Sequences of resource monotones from modular Hamiltonian polynomials |
| title_short | Sequences of resource monotones from modular Hamiltonian polynomials |
| title_sort | sequences of resource monotones from modular hamiltonian polynomials |
| url | http://doi.org/10.1103/PhysRevResearch.5.043082 |
| work_keys_str_mv | AT raularias sequencesofresourcemonotonesfrommodularhamiltonianpolynomials AT jandeboer sequencesofresourcemonotonesfrommodularhamiltonianpolynomials AT giuseppedigiulio sequencesofresourcemonotonesfrommodularhamiltonianpolynomials AT eskokeskivakkuri sequencesofresourcemonotonesfrommodularhamiltonianpolynomials AT eriktonni sequencesofresourcemonotonesfrommodularhamiltonianpolynomials |