Bibliographic Details
| Title: |
On the rank of extremal marginal states. |
| Authors: |
Devendra, Repana1 (AUTHOR) ma16d020@smail.iitm.ac.in, Dey, Pankaj1 (AUTHOR) pankaj@math.iitb.ac.in, Dey, Santanu1 (AUTHOR) dey@math.iitb.ac.in |
| Source: |
Linear Algebra & its Applications. May2026, Vol. 737, p146-172. 27p. |
| Subjects: |
Quantum states, Density matrices, Matrices (Mathematics) |
| Abstract: |
Given two invertible states ρ 1 on C d 1 and ρ 2 on C d 2 , the marginal state space C (ρ 1 , ρ 2) is defined as the set of all states ρ on C d 1 ⊗ C d 2 with partial traces ρ 1 and ρ 2. A fundamental result by K. R. Parthasarathy establishes that if ρ is an extreme point of the set C (ρ 1 , ρ 2) , then the rank of ρ does not exceed d 1 2 + d 2 2 − 1. A naturally raised question, also posed by Rudolph, is that are there any extreme points of C (ρ 1 , ρ 2) whose rank is equal to ⌊ d 1 2 + d 2 2 − 1 ⌋ , where ⌊ a ⌋ indicates the largest integer that does not exceed a. In 2010, Ohno gave an affirmative answer for low-dimensional matrix algebras M 3 and M 4. In this article, we provide a positive answer to the Rudolph question in various matrix algebras by explicitly constructing the extreme points of C (ρ 1 , ρ 2) whose rank is equal to ⌊ d 1 2 + d 2 2 − 1 ⌋. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
