Details
| Original language | English |
|---|---|
| Journal | Quantum |
| Volume | 1 |
| Publication status | Published - 21 Jul 2017 |
Abstract
We investigate decoupling, one of the most important primitives in quantum Shannon theory, by replacing the uniformly distributed random unitaries commonly used to achieve the protocol, with repeated applications of random unitaries diagonal in the Pauli-Z and -X bases. This strategy was recently shown to achieve an approximate unitary 2-design after a number of repetitions of the process, which implies that the strategy gradually achieves decoupling. Here, we prove that even fewer repetitions of the process achieve decoupling at the same rate as that with the uniform ones, showing that rather imprecise approximations of unitary 2-designs are sufficient for decoupling. We also briefly discuss efficient implementations of them and implications of our decoupling theorem to coherent state merging and relative thermalisation.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics
- Physics and Astronomy(all)
- Physics and Astronomy (miscellaneous)
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In: Quantum, Vol. 1, 21.07.2017.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Decoupling with random diagonal unitaries
AU - Nakata, Yoshifumi
AU - Hirche, Christoph
AU - Morgan, Ciara
AU - Winter, Andreas
N1 - Funding Information: The authors are grateful to R. F. Werner and O. Fawzi for interesting and fruitful discussions. YN is a JSPS Research Fellow and is supported in part by JSPS Postdoctoral Fellowships for Research Abroad, and by JSPS KAKENHI Grant Number 272650. CH and CM acknowledge support from the EU grants SIQS and QFTCMPS and by the cluster of excellence EXC 201 Quantum Engineering and Space-Time Research. AW is supported by the European Commission (STREP “RAQUEL”), the European Research Council (Advanced Grant “IRQUAT”), the Spanish MINECO, project FIS2008-01236, with the support of FEDER funds. CH and AW are also supported by the Generalitat de Catalunya, CIRIT project no. 2014 SGR 966, as well as the Spanish MINECO, projects FIS2013-40627-P and FIS2016-80681-P (AEI/FEDER, UE) and CH by FPI Grant No. BES-2014-068888.
PY - 2017/7/21
Y1 - 2017/7/21
N2 - We investigate decoupling, one of the most important primitives in quantum Shannon theory, by replacing the uniformly distributed random unitaries commonly used to achieve the protocol, with repeated applications of random unitaries diagonal in the Pauli-Z and -X bases. This strategy was recently shown to achieve an approximate unitary 2-design after a number of repetitions of the process, which implies that the strategy gradually achieves decoupling. Here, we prove that even fewer repetitions of the process achieve decoupling at the same rate as that with the uniform ones, showing that rather imprecise approximations of unitary 2-designs are sufficient for decoupling. We also briefly discuss efficient implementations of them and implications of our decoupling theorem to coherent state merging and relative thermalisation.
AB - We investigate decoupling, one of the most important primitives in quantum Shannon theory, by replacing the uniformly distributed random unitaries commonly used to achieve the protocol, with repeated applications of random unitaries diagonal in the Pauli-Z and -X bases. This strategy was recently shown to achieve an approximate unitary 2-design after a number of repetitions of the process, which implies that the strategy gradually achieves decoupling. Here, we prove that even fewer repetitions of the process achieve decoupling at the same rate as that with the uniform ones, showing that rather imprecise approximations of unitary 2-designs are sufficient for decoupling. We also briefly discuss efficient implementations of them and implications of our decoupling theorem to coherent state merging and relative thermalisation.
UR - http://www.scopus.com/inward/record.url?scp=85066001320&partnerID=8YFLogxK
U2 - 10.22331/q-2017-07-21-18
DO - 10.22331/q-2017-07-21-18
M3 - Article
AN - SCOPUS:85066001320
VL - 1
JO - Quantum
JF - Quantum
SN - 2521-327X
ER -