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@article{833863,
author = {Ambainis, Andris and Bouda, Jan and Winter, Andreas},
article_location = {USA},
article_number = {4},
keywords = {quantum information processing; encryption; non-malleability; unitary k-design},
language = {eng},
issn = {0022-2488},
journal = {Journal of Mathematical Physics},
title = {Nonmalleable encryption of quantum information},
volume = {50},
year = {2009}
}
TY - JOUR
ID - 833863
AU - Ambainis, Andris - Bouda, Jan - Winter, Andreas
PY - 2009
TI - Nonmalleable encryption of quantum information
JF - Journal of Mathematical Physics
VL - 50
IS - 4
SP - 042106
EP - 042106
PB - American Institute of Physics
SN - 00222488
KW - quantum information processing
KW - encryption
KW - non-malleability
KW - unitary k-design
N2 - We introduce the notion of nonmalleability of a quantum state encryption scheme (in dimension d): in addition to the requirement that an adversary cannot learn information about the state, here we demand that no controlled modification of the encrypted state can be effected. We show that such a scheme is equivalent to a unitary 2-design [Dankert, et al., e-print arXiv:quant-ph/0606161], as opposed to normal encryption which is a unitary 1-design. Our other main results include a new proof of the lower bound of (d2-1)2+1 on the number of unitaries in a 2-design [Gross, et al., J. Math. Phys. 48, 052104 (2007)], which lends itself to a generalization to approximate 2-design. Furthermore, while in prime power dimension there is a unitary 2-design with <=d5 elements, we show that there are always approximate 2-designs with O(\epsilon-2d4 log d) elements.
ER -
AMBAINIS, Andris, Jan BOUDA and Andreas WINTER. Nonmalleable encryption of quantum information. \textit{Journal of Mathematical Physics}. USA: American Institute of Physics, 2009, vol.~50, No~4, p.~042106-42113. ISSN~0022-2488.
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