APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017;
New Orleans, Louisiana
Session S52: Quantum Network and Quantum Communication
11:15 AM–2:03 PM,
Thursday, March 16, 2017
Room: 399
Sponsoring
Unit:
GQI
Abstract ID: BAPS.2017.MAR.S52.1
Abstract: S52.00001 : Reflections on Quantum Data Hiding
11:15 AM–11:51 AM
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Abstract
Author:
Andreas Winter
(Universitat Autonoma de Barcelona)
Quantum data hiding, originally invented as a limitation on
local operations and classical communications (LOCC) in distinguishing
globally orthogonal states, is actually a phenomenon arising generically
in statistics whenever comparing a `strong' set of measurements (\emph{i.e.},
decision rules) with a `weak' one. The classical statistical analogue of
this would be secret sharing, in which two perfectly distinguishable
multi-partite hypotheses appear to be indistinguishable when accessing
only a marginal. The quantum versions are richer in that for example
LOCC allows for state tomography, so the states cannot be come
perfectly indistinguishable but only nearly so, and hence the question
is one of efficiency. I will discuss two concrete examples and associated
sets of problems:
\\
1. Gaussian operations and classical computation (GOCC): Not very
surprisingly, GOCC cannot distinguish optimally even two coherent
states of a single mode [Takeoka \&{} Sasaki, PRA 78:022320, 2008].
Here we find states, each a mixture of multi-mode coherent states,
which are almost perfectly distinguishable by suitable measurements,
by when restricted to GOCC, i.e. linear optics and post-processing, the
states appear almost identical. The construction is random and relies
on coding arguments. Open questions include whether there one can
give a constructive version of the argument, and whether for instance
even thermal states can be used, or how efficient the hiding is.
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2. Local operation and classical communication (LOCC): It is well-known
that in a bipartite dxd-system, asymptotically $\log d$ bits can be hidden
[Hayden \emph{et al.}, CMP 250:371–391, 2004]. Here we show for the first
time, using the calculus of min-entropies, that this is asymptotically
optimal. In fact, we get bounds on the data hiding capacity of any
preparation system; these are however not always tight.
While it is known that data hiding by separable states is possible (i.e.
the state preparation can be done by LOCC), it is open whether the
optimal information efficiency of (asymptotically) log d bits can be
achieved by separable states.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2017.MAR.S52.1