Saved in:
Bibliographic Details
Main Authors: Camacho, Gonzalo, de Vicente, Julio I.
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2511.08285
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866910018329116672
author Camacho, Gonzalo
de Vicente, Julio I.
author_facet Camacho, Gonzalo
de Vicente, Julio I.
contents The existence of a maximally entangled pure state is a cornerstone result of entanglement theory that has paramount consequences in quantum information theory. A natural generalization of this property is to consider whether a notion of maximal entanglement is possible among all states with the same spectrum (where the aforementioned case of pure states corresponds to the particular choice in which the spectrum is a delta distribution, i.e., rank-1 states). Despite positive evidence in the past that such a notion might exist at least in the case of two-qubit states, it was recently shown in [Phys. Rev. Lett. 133, 050202 (2024)] that the answer to the above question is negative. This reference proved this for particular choices of the spectrum in the case of rank-2 two-qubit density matrices. While this settles the problem in general, it still leaves open whether there are other choices of the spectrum outside the case of pure states where a maximally entangled state for a fixed spectrum might exist. In this work we extend this impossibility result to all rank-2 and rank-3 two-qubit states as well as for a large class of eigenvalue distributions in the case where the rank equals four.
format Preprint
id arxiv_https___arxiv_org_abs_2511_08285
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Nonexistence of maximally entangled mixed states for a fixed spectrum
Camacho, Gonzalo
de Vicente, Julio I.
Quantum Physics
The existence of a maximally entangled pure state is a cornerstone result of entanglement theory that has paramount consequences in quantum information theory. A natural generalization of this property is to consider whether a notion of maximal entanglement is possible among all states with the same spectrum (where the aforementioned case of pure states corresponds to the particular choice in which the spectrum is a delta distribution, i.e., rank-1 states). Despite positive evidence in the past that such a notion might exist at least in the case of two-qubit states, it was recently shown in [Phys. Rev. Lett. 133, 050202 (2024)] that the answer to the above question is negative. This reference proved this for particular choices of the spectrum in the case of rank-2 two-qubit density matrices. While this settles the problem in general, it still leaves open whether there are other choices of the spectrum outside the case of pure states where a maximally entangled state for a fixed spectrum might exist. In this work we extend this impossibility result to all rank-2 and rank-3 two-qubit states as well as for a large class of eigenvalue distributions in the case where the rank equals four.
title Nonexistence of maximally entangled mixed states for a fixed spectrum
topic Quantum Physics
url https://arxiv.org/abs/2511.08285