Programmability of covariant quantum channels

Research output: Contribution to journal › Journal article › Research › peer-review

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Programmability of covariant quantum channels. / Gschwendtner, Martina; Bluhm, Andreas; Winter, Andreas.

In: Quantum, Vol. 5, 2021.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Gschwendtner, M, Bluhm, A & Winter, A 2021, 'Programmability of covariant quantum channels', Quantum, vol. 5. https://doi.org/10.22331/q-2021-06-29-488

APA

Gschwendtner, M., Bluhm, A., & Winter, A. (2021). Programmability of covariant quantum channels. Quantum, 5. https://doi.org/10.22331/q-2021-06-29-488

Vancouver

Gschwendtner M, Bluhm A, Winter A. Programmability of covariant quantum channels. Quantum. 2021;5. https://doi.org/10.22331/q-2021-06-29-488

Author

Gschwendtner, Martina ; Bluhm, Andreas ; Winter, Andreas. / Programmability of covariant quantum channels. In: Quantum. 2021 ; Vol. 5.

Bibtex

@article{7c5bb44d49f54fefb13a79a420c1535b,
title = "Programmability of covariant quantum channels",
abstract = " A programmable quantum processor uses the states of a program register to specify one element of a set of quantum channels which is applied to an input register. It is well-known that such a device is impossible with a finite-dimensional program register for any set that contains infinitely many unitary quantum channels (Nielsen and Chuang's No-Programming Theorem), meaning that a universal programmable quantum processor does not exist. The situation changes if the system has symmetries. Indeed, here we consider group-covariant channels. If the group acts irreducibly on the channel input, these channels can be implemented exactly by a programmable quantum processor with finite program dimension (via teleportation simulation, which uses the Choi-Jamiolkowski state of the channel as a program). Moreover, by leveraging the representation theory of the symmetry group action, we show how to remove redundancy in the program and prove that the resulting program register has minimum Hilbert space dimension. Furthermore, we provide upper and lower bounds on the program register dimension of a processor implementing all group-covariant channels approximately. ",
keywords = "quant-ph",
author = "Martina Gschwendtner and Andreas Bluhm and Andreas Winter",
note = "preprint",
year = "2021",
doi = "10.22331/q-2021-06-29-488",
language = "English",
volume = "5",
journal = "Quantum",
issn = "2521-327X",
publisher = "Verein zur F{\"o}rderung des Open Access Publizierens in den Quantenwissenschaften",

}

RIS

TY - JOUR

T1 - Programmability of covariant quantum channels

AU - Gschwendtner, Martina

AU - Bluhm, Andreas

AU - Winter, Andreas

N1 - preprint

PY - 2021

Y1 - 2021

N2 - A programmable quantum processor uses the states of a program register to specify one element of a set of quantum channels which is applied to an input register. It is well-known that such a device is impossible with a finite-dimensional program register for any set that contains infinitely many unitary quantum channels (Nielsen and Chuang's No-Programming Theorem), meaning that a universal programmable quantum processor does not exist. The situation changes if the system has symmetries. Indeed, here we consider group-covariant channels. If the group acts irreducibly on the channel input, these channels can be implemented exactly by a programmable quantum processor with finite program dimension (via teleportation simulation, which uses the Choi-Jamiolkowski state of the channel as a program). Moreover, by leveraging the representation theory of the symmetry group action, we show how to remove redundancy in the program and prove that the resulting program register has minimum Hilbert space dimension. Furthermore, we provide upper and lower bounds on the program register dimension of a processor implementing all group-covariant channels approximately.

AB - A programmable quantum processor uses the states of a program register to specify one element of a set of quantum channels which is applied to an input register. It is well-known that such a device is impossible with a finite-dimensional program register for any set that contains infinitely many unitary quantum channels (Nielsen and Chuang's No-Programming Theorem), meaning that a universal programmable quantum processor does not exist. The situation changes if the system has symmetries. Indeed, here we consider group-covariant channels. If the group acts irreducibly on the channel input, these channels can be implemented exactly by a programmable quantum processor with finite program dimension (via teleportation simulation, which uses the Choi-Jamiolkowski state of the channel as a program). Moreover, by leveraging the representation theory of the symmetry group action, we show how to remove redundancy in the program and prove that the resulting program register has minimum Hilbert space dimension. Furthermore, we provide upper and lower bounds on the program register dimension of a processor implementing all group-covariant channels approximately.

KW - quant-ph

U2 - 10.22331/q-2021-06-29-488

DO - 10.22331/q-2021-06-29-488

M3 - Journal article

VL - 5

JO - Quantum

JF - Quantum

SN - 2521-327X

ER -

ID: 255789646