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CATEGORIES:CQIF Seminar
SUMMARY:On the quantum capacity of the qubit depolarizing
channel - Felix Leditzky\, JILA\, University of Co
lorado Boulder
DTSTART;TZID=Europe/London:20170427T141500
DTEND;TZID=Europe/London:20170427T151500
UID:TALK71937AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/71937
DESCRIPTION:The qubit depolarizing channel\, defined in terms
of a single depolarizing parameter p\, is a simple
and widely studied quantum channel. However\, an
exact determination of its quantum capacity has re
mained elusive so far\, and we can only give lower
and upper bounds on its capability to transmit qu
antum data faithfully. In this seminar talk\, I wi
ll discuss two upper bounds on the quantum capacit
y of the qubit depolarizing channel (in the sequel
denoted D_p)\, which constitute the best known up
per bounds for low and high values of the depolari
zing parameter p\, respectively.\n\nThe first boun
d is the approximate degradability bound derived b
y Sutter et al. (arXiv:1412.0980). This powerful b
ound uses the fact that D_p is "almost degradable"
for low values of p\, and hence its quantum capac
ity is close to its (computable) channel coherent
information. In joint work with Debbie Leung and G
raeme Smith (soon to be posted on the arXiv)\, we
analyze this bound in greater detail. We prove tha
t the complementary channel of the depolarizing ch
annel (with a tweaked depolarizing parameter) serv
es as an "approximate degrading map"\, and renders
the depolarizing channel O(p^2)-approximate degra
dable. As a result\, the corresponding upper bound
derived by Sutter et al. on the quantum capacity
is tangent to the channel coherent information\, w
hich explains the power of the approximate degrada
bility approach. We can lift this result to all ge
neralized Pauli channels\, and more generally to "
low-noise" channels\, i.e.\, channels that are clo
se to the identity channel with respect to the dia
mond norm.\n\nFor large values of the depolarizing
parameter p\, the best known upper bound has rece
ntly been derived in arXiv:1701.03081\, which is j
oint work with Nilanjana Datta and Graeme Smith. O
ne of our main results in arXiv:1701.03081 is a ge
neral upper bound on the one-way distillable entan
glement of a mixed bipartite state\, based on conv
ex decompositions of this state into degradable an
d antidegradable states. Since the depolarizing ch
annel belongs to the class of so-called teleportat
ion-simulable channels\, quantum data transmission
is equivalent to entanglement distillation using
its Choi state. Hence\, an upper bound on the quan
tum capacity of D_p is obtained from evaluating ou
r bound for the Choi state of D_p\, which is a so-
called isotropic state. Exploiting this symmetry\,
we were able to phrase our general upper bound as
a non-convex optimization problem that can be sol
ved numerically\, yielding the advertised bound.
LOCATION:MR4\, Centre for Mathematical Sciences\, Wilberfor
ce Road\, Cambridge
CONTACT:Steve Brierley
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