Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery (CyberC)

Generalization of Quantum Strassen Theorem

Jingtong Ge

Published Oct 1, 2019• 2 citations
Publisher

Abstract

In a recent paper, L.Zhou, S.Ying, N.Yu and M.Ying proved a quantum Strassen theorem for the quantum marginal problem. By using SDP method, a more general quantum Strassen theorem has been proved here, with which the quantum Strassen theorem can be generalized to infinite dimensional case more easily.
DOI
10.1109/cyberc.2019.00072

Related papers

A note on the infinite-dimensional quantum Strassen’s theorem

Luigi Accardi, Abdallah Dhahri, Yun Gang Lu

In Ref. 3, the quantum Strassen’s theorem has been extended to the infinite-dimensional case. This theorem consists in the solution of the coupling problem for two states on the algebra of bounded operators on two Hilbert spaces [Formula: see text], [Formula: see text] with the additional constraint that the coupling state has support in a pre-assigned sub-space of [Formula: see text]. In this paper, we give an alternative proof of the main theorem in Ref. 3 that allows such extension.

Infinite Dimensional Analysis Quantum Probability and Related Topics•Apr 18, 2022•0 citations

Quantum Coupling and Strassen Theorem

Li Zhou, Shenggang Ying, Nengkun Yu +1 more

We introduce a quantum generalisation of the notion of coupling in probability theory. Several interesting examples and basic properties of quantum couplings are presented. In particular, we prove a quantum extension of Strassen theorem for probabilistic couplings, a fundamental theorem in probability theory that can be used to bound the probability of an event in a distribution by the probability of an event in another distribution coupled with the first.

arXiv:1803.10393•Mar 28, 2018•5 citations

Strassen's support functionals coincide with the quantum functionals

Keiya Sakabe, Mahmut Levent Doğan, Michael Walter

Strassen's asymptotic spectrum offers a framework for analyzing the complexity of tensors. It has found applications in diverse areas, from computer science to additive combinatorics and quantum information. A long-standing open problem, dating back to 1991, asks whether Strassen's support functionals are universal spectral points, that is, points in the asymptotic spectrum of tensors. In this paper, we answer this question in the affirmative for tensors over complex numbers by proving that the support functionals coincide with the quantum functionals - universal spectral points that are defined via entropy optimization on entanglement polytopes. We obtain this result as a special case of a general minimax formula for convex optimization on entanglement polytopes (and more general moment polytopes). Our formula can be interpreted as a very general "classical-quantum correspondence" analogous to the well-known relation between the Shannon entropy and the von Neumann entropy. Its proof is based on a recent Fenchel-type duality theorem on Hadamard manifolds due to Hirai. In addition to settling Strassen's question, our results yield a unified and simpler approach to several other tensor invariants, including the asymptotic slice rank, the symmetric quantum functional, the $G$-stable rank, and the non-commutative rank.

cs.CCCross-listedarXiv:2601.21553•Jan 30, 2026•0 citations

Quantum Strassen’s theorem

Shmuel Friedland, Jingtong Ge, Lihong Zhi

Strassen’s theorem circa 1965 gives necessary and sufficient conditions on the existence of a probability measure on two product spaces with given support and two marginals. In the case where each product space is finite, Strassen’s theorem is reduced to a linear programming problem which can be solved using flow theory. A density matrix of bipartite quantum system is a quantum analog of a probability matrix on two finite product spaces. Partial traces of the density matrix are analogs of marginals. The support of the density matrix is its range. The analog of Strassen’s theorem in this case can be stated and solved using semidefinite programming. The aim of this paper is to give analogs of Strassen’s theorem to density trace class operators on a product of two separable Hilbert spaces, where at least one of the Hilbert spaces is infinite-dimensional.

Infinite Dimensional Analysis Quantum Probability and Related Topics•Sep 1, 2020•5 citations

On quantum Strassen's theorem

Shmuel Friedland, Jingtong Ge, Lihong Zhi

Strassen's theorem circa 1965 gives necessary and sufficient conditions on the existence of a probability measure on two product spaces with given support and two marginals. In the case where each product space is finite Strassen's theorem is reduced to a linear programming problem which can be solved using flow theory. A density matrix of bipartite quantum system is a quantum analog of a probability matrix on two finite product spaces. Partial traces of the density matrix are analogs of marginals. The support of the density matrix is its range. The analog of Strassen's theorem in this case can be stated and solved using semidefinite programming. The aim of this paper is to give analogs of Strassen's theorem to density trace class operators on a product of two separable Hilbert spaces, where at least one of the Hilbert spaces is infinite dimensional.

arXiv:1905.06865•May 14, 2019•2 citations

All $S_p$ notions of quantum expansion are equivalent

Francisco Escudero Gutiérrez, Garazi Muguruza

In a recent work Li, Qiao, Wigderson, Wigderson and Zhang introduced notions of quantum expansion based on $S_p$ norms and posed as an open question if they were all equivalent. We give an affirmative answer to this question.

arXiv:2405.03517•May 6, 2024•0 citations
Strassen's asymptotic spectrum offers a framework for analyzing the complexity of tensors. It has found applications in diverse areas, from computer science to additive combinatorics and quantum information. A long-standing open problem, dating back to 1991, asks whether Strassen's support functionals are universal spectral points, that is, points in the asymptotic spectrum of tensors. In this paper, we answer this question in the affirmative for tensors over complex numbers by proving that the support functionals coincide with the quantum functionals - universal spectral points that are defined via entropy optimization on entanglement polytopes. We obtain this result as a special case of a general minimax formula for convex optimization on entanglement polytopes (and more general moment polytopes). Our formula can be interpreted as a very general "classical-quantum correspondence" analogous to the well-known relation between the Shannon entropy and the von Neumann entropy. Its proof is based on a recent Fenchel-type duality theorem on Hadamard manifolds due to Hirai. In addition to settling Strassen's question, our results yield a unified and simpler approach to several other tensor invariants, including the asymptotic slice rank, the symmetric quantum functional, the GGG-stable rank, and the non-commutative rank.
Strassen’s theorem circa 1965 gives necessary and sufficient conditions on the existence of a probability measure on two product spaces with given support and two marginals. In the case where each product space is finite, Strassen’s theorem is reduced to a linear programming problem which can be solved using flow theory. A density matrix of bipartite quantum system is a quantum analog of a probability matrix on two finite product spaces. Partial traces of the density matrix are analogs of marginals. The support of the density matrix is its range. The analog of Strassen’s theorem in this case can be stated and solved using semidefinite programming. The aim of this paper is to give analogs of Strassen’s theorem to density trace class operators on a product of two separable Hilbert spaces, where at least one of the Hilbert spaces is infinite-dimensional.
Strassen's theorem circa 1965 gives necessary and sufficient conditions on the existence of a probability measure on two product spaces with given support and two marginals. In the case where each product space is finite Strassen's theorem is reduced to a linear programming problem which can be solved using flow theory. A density matrix of bipartite quantum system is a quantum analog of a probability matrix on two finite product spaces. Partial traces of the density matrix are analogs of marginals. The support of the density matrix is its range. The analog of Strassen's theorem in this case can be stated and solved using semidefinite programming. The aim of this paper is to give analogs of Strassen's theorem to density trace class operators on a product of two separable Hilbert spaces, where at least one of the Hilbert spaces is infinite dimensional.
All SpS_pSp​ notions of quantum expansion are equivalent
In a recent work Li, Qiao, Wigderson, Wigderson and Zhang introduced notions of quantum expansion based on SpS_pSp​ norms and posed as an open question if they were all equivalent. We give an affirmative answer to this question.