Computational self-testing for entangled magic states

Mizutani, Akihiro; Takeuchi, Yuki; Hiromasa, Ryo; Aikawa, Yusuke; Tani, Seiichiro

doi:10.1103/PhysRevA.106.L010601

Computational self-testing for entangled magic states

Nov 4, 2021

31 pages

Published in:

Phys.Rev.A 106 (2022) 1, L010601

Published: Jul 25, 2022

e-Print:

2111.02700 [quant-ph]

DOI:

10.1103/PhysRevA.106.L010601 (publication)

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Abstract: (APS)

Can classical systems grasp quantum dynamics executed in an untrusted quantum device? Metger and Vidick answered this question affirmatively by proposing a computational self-testing protocol for Bell states that certifies generation of Bell states and measurements on them. Since their protocol relies on the fact that the target states are stabilizer states, it is highly nontrivial to reveal whether the other class of quantum states, nonstabilizer states, can be self-tested. Among nonstabilizer states, magic states are indispensable resources for universal quantum computation. Here, we show that a magic state for the

C C Z

gate can be self-tested while that for the

T

gate cannot. Our result is applicable to a proof of quantumness, where we can classically verify whether a quantum device generates a quantum state having nonzero magic.

Note:

31 pages, 1 figure, Supplementary material simplied but the results unchanged

stability
entanglement

References(53)

Figures(1)

[1]

Quantum cryptography based on Bell's theorem

Artur K. Ekert
(
- Oxford U.
)

- Phys.Rev.Lett. 67 (1991) 661-663
•
DOI:
- 10.1103/PhysRevLett.67.661

[2]

in Proceedings of the 39th Annual Symposium on Foundations of Computer Science (, Piscataway, NJ, ), pp

D. Mayers
,
A. Yao

[3]

C.C.W. Lim
,
C. Portmann
,
M. Tomamichel
,
R. Renner
,
N. Gisin

- Phys.Rev.X 3 (2013) 031006
•
DOI:
- 10.1103/PhysRevX.3.031006

[4]

Fully device independent quantum key distribution

Umesh Vazirani
(
- UC, Berkeley
)
,
Thomas Vidick
(
- Caltech
)

- Commun.ACM (2019),
- Phys.Rev.Lett. 113 (2014) 14, 140501
•
DOI:
- 10.1145/3310974

[5]

The ultimate physical limits of privacy

Artur Ekert
(
- Oxford U., Inst. Math. and
- Singapore Natl. U. (main)
)
,
Renato Renner
(
- Zurich, ETH
)

- Nature 507 (2014) 7493, 443-447
•
DOI:
- 10.1038/nature13132

[6]

Practical device-independent quantum cryptography via entropy accumulation

Rotem Arnon-Friedman
(
- Zurich, ETH
)
,
Frédéric Dupuis
(
- Masaryk U., Brno and
- Inst. Jean Lamour, Vandoeuvre les Nancy
)
,
Omar Fawzi
(
- Lyon, Ecole Normale Superieure
)
,
Renato Renner
(
- Zurich, ETH
)
,
Thomas Vidick
(
- Caltech
)

- Nature Commun. 9 (2018) 1, 459
•
DOI:
- 10.1038/s41467-017-02307-4

[7]

Device-independent quantum key distribution from computational assumptions

Tony Metger
(
- Zurich, ETH
)
,
Yfke Dulek
(
- Amsterdam, CWI
)
,
Andrea Coladangelo
(
- UC, Berkeley
)
,
Rotem Arnon-Friedman
(
- Weizmann Inst.
)

- New J.Phys. 23 (2021) 12, 123021,
- New J.Phys. 23 (2021) 123021
•
e-Print:
- 2010.04175
•
DOI:
- 10.1088/1367-2630/ac304b

[8]

Classical command of quantum systems

Ben W. Reichardt
(
- Southern California U.
)
,
Falk Unger
(
- Santa Clara U.
)
,
Umesh Vazirani
(
- LBL, Berkeley
)

- Nature 496 (2013) 7446, 456-460
•
DOI:
- 10.1038/nature12035

[9]

Device-Independent Verifiable Blind Quantum Computation

e-Print:
- 1502.02563

[10]

D. Mayers
,
A. Yao

- Quantum Inf. Comput. 4 (2004) 273

[11]

Robust self-testing of the singlet

- J.Phys.A 45 (2012) 45, 455304
•
DOI:
- 10.1088/1751-8113/45/45/455304

[12]

All pure bipartite entangled states can be self-tested

Andrea Coladangelo
(
- Caltech
)
,
Koon Tong Goh
(
- Singapore Natl. U. (main)
)
,
Valerio Scarani
(
- Singapore Natl. U. (main) and
- Singapore Natl. U.
)

- Nature Commun. 8 (2017) 1, 15485
•
DOI:
- 10.1038/ncomms15485

[13]

Self-testing of quantum systems: a review

Ivan Šupić
(
- Geneva U.
)
,
Joseph Bowles
(
- ICFO, Barcelona
)

- Quantum 4 (2020) 337
•
e-Print:
- 1904.10042
•
DOI:
- 10.22331/q-2020-09-30-337

[14]

Self-testing of a single quantum device under computational assumptions

Tony Metger
(
- Zurich, ETH
)
,
Thomas Vidick
(
- Caltech
)

- Quantum 5 (2021) 544
•
e-Print:
- 2001.09161
•
DOI:
- 10.22331/q-2021-09-16-544

[15]

The LWE problem is to solve a noisy system of linear equations, and so far there exists no efficient quantum algorithm to solve this problem

[16]

O. Regev

- J.Assoc.Comput.Machinery 56 (2009) 1
•
DOI:
- 10.1145/1568318.1568324

[17]

Note that encrypted messages using classical public-key cryptography are decrypted once it becomes technologically feasible to break the underlying computational assumption. On the other hand, the LWE assumption supposed in [14] is only exploited to prevent the malicious prover from tricking the verifier into accepting the prover as honest. Hence, as long as the LWE assumption holds during the self-testing protocol, if this assumption is broken after the protocol, the results already obtained never be compromised

[18]