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Multiparty quantum secret splitting and quantum state sharing
A protocol for multiparty quantum secret splitting is proposed with an
ordered EPR pairs and Bell state measurements. It is secure and has the
high intrinsic efficiency and source capacity as almost all the instances are
useful and each EPR pair carries two bits of message securely. Moreover, we
modify it for multiparty quantum state sharing of an arbitrary -particle
entangled state based on quantum teleportation with only Bell state
measurements and local unitary operations which make this protocol more
convenient in a practical application than others.Comment: 7 pages, 1 figure. The revision of the manuscript appeared in PLA.
Some procedures for detecting cheat have been added. Then the security
loophole in the original manuscript has been eliminate
Concatenation of the Gottesman-Kitaev-Preskill code with the XZZX surface code
Bosonic codes provide an alternative option for quantum error correction. An
important category of bosonic codes called the Gottesman-Kitaev-Preskill (GKP)
code has aroused much interest recently. Theoretically, the error correction
ability of GKP code is limited since it can only correct small shift errors in
position and momentum quadratures. A natural approach to promote the GKP error
correction for large-scale, fault-tolerant quantum computation is concatenating
encoded GKP states with a stabilizer code. The performance of the XZZX
surface-GKP code, i.e., the single-mode GKP code concatenated with the XZZX
surface code is investigated in this paper under two different noise models.
Firstly, in the code-capacity noise model, the asymmetric rectangular GKP code
with parameter is introduced. Using the minimum weight perfect
matching decoder combined with the continuous-variable GKP information, the
optimal threshold of the XZZX-surface GKP code reaches when
, compared with the threshold of the standard
surface-GKP code. Secondly, we analyze the shift errors of two-qubit gates in
the actual implementation and build the full circuit-level noise model. By
setting the appropriate bias parameters, the logical error rate is reduced by
several times in some cases. These results indicate the XZZX surface-GKP codes
are more suitable for asymmetric concatenation under the general noise models.
We also estimate the overhead of the XZZX-surface GKP code which uses about 291
GKP states with the noise parameter 18.5 dB () to
encode a logical qubit with the error rate , compared with
the qubit-based surface code using 3041 qubits to achieve almost the same
logical error rate.Comment: 17 pages, 10 figure
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