A quantum version of Wielandt's inequality

Mikel Sanz; David Perez-Garcia; Michael Marc Wolf; Juan I. Cirac

doi:10.1109/TIT.2010.2054552

A quantum version of Wielandt's inequality

Mikel Sanz, David Perez-Garcia, Michael Marc Wolf, Juan I. Cirac

52 Citationer (Scopus)

Abstract

In this paper, Wielandt's inequality for classical channels is extended to quantum channels. That is, an upper bound to the number of times a channel must be applied, so that it maps any density operator to one with full rank, is found. Using this bound, dichotomy theorems for the zero-error capacity of quantum channels and for the Matrix Product State (MPS) dimension of ground states of frustration-free Hamiltonians are derived. The obtained inequalities also imply new bounds on the required interaction-range of Hamiltonians with unique MPS ground state.

Originalsprog	Engelsk
Tidsskrift	I E E E Transactions on Information Theory
Vol/bind	56
Udgave nummer	9
Sider (fra-til)	4668-4673
Antal sider	5
ISSN	0018-9448
DOI	https://doi.org/10.1109/TIT.2010.2054552
Status	Udgivet - sep. 2010

Adgang til dokumentet

10.1109/TIT.2010.2054552

Citationsformater

@article{742241251c7541f09991ce13c60f8c73,

title = "A quantum version of Wielandt's inequality",

abstract = "In this paper, Wielandt's inequality for classical channels is extended to quantum channels. That is, an upper bound to the number of times a channel must be applied, so that it maps any density operator to one with full rank, is found. Using this bound, dichotomy theorems for the zero-error capacity of quantum channels and for the Matrix Product State (MPS) dimension of ground states of frustration-free Hamiltonians are derived. The obtained inequalities also imply new bounds on the required interaction-range of Hamiltonians with unique MPS ground state.",

author = "Mikel Sanz and David Perez-Garcia and Wolf, {Michael Marc} and Cirac, {Juan I.}",

year = "2010",

month = sep,

doi = "10.1109/TIT.2010.2054552",

language = "English",

volume = "56",

pages = "4668--4673",

journal = "IEEE Transactions on Information Theory",

issn = "0018-9448",

publisher = "Institute of Electrical and Electronics Engineers",

number = "9",

}

TY - JOUR

T1 - A quantum version of Wielandt's inequality

AU - Sanz, Mikel

AU - Perez-Garcia, David

AU - Wolf, Michael Marc

AU - Cirac, Juan I.

PY - 2010/9

Y1 - 2010/9

N2 - In this paper, Wielandt's inequality for classical channels is extended to quantum channels. That is, an upper bound to the number of times a channel must be applied, so that it maps any density operator to one with full rank, is found. Using this bound, dichotomy theorems for the zero-error capacity of quantum channels and for the Matrix Product State (MPS) dimension of ground states of frustration-free Hamiltonians are derived. The obtained inequalities also imply new bounds on the required interaction-range of Hamiltonians with unique MPS ground state.

AB - In this paper, Wielandt's inequality for classical channels is extended to quantum channels. That is, an upper bound to the number of times a channel must be applied, so that it maps any density operator to one with full rank, is found. Using this bound, dichotomy theorems for the zero-error capacity of quantum channels and for the Matrix Product State (MPS) dimension of ground states of frustration-free Hamiltonians are derived. The obtained inequalities also imply new bounds on the required interaction-range of Hamiltonians with unique MPS ground state.

U2 - 10.1109/TIT.2010.2054552

DO - 10.1109/TIT.2010.2054552

M3 - Journal article

SN - 0018-9448

VL - 56

SP - 4668

EP - 4673

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 9

ER -

A quantum version of Wielandt's inequality

Abstract

Adgang til dokumentet

Fingeraftryk

Citationsformater