17 research outputs found
Secure communication over fully quantum Gel'fand-Pinsker wiretap channel
In this work we study the problem of secure communication over a fully
quantum Gel'fand-Pinsker channel. The best known achievability rate for this
channel model in the classical case was proven by Goldfeld, Cuff and Permuter
in [Goldfeld, Cuff, Permuter, 2016]. We generalize the result of [Goldfeld,
Cuff, Permuter, 2016]. One key feature of the results obtained in this work is
that all the bounds obtained are in terms of error exponent. We obtain our
achievability result via the technique of simultaneous pinching. This in turn
allows us to show the existence of a simultaneous decoder. Further, to obtain
our encoding technique and to prove the security feature of our coding scheme
we prove a bivariate classical-quantum channel resolvability lemma and a
conditional classical-quantum channel resolvability lemma. As a by product of
the achievability result obtained in this work, we also obtain an achievable
rate for a fully quantum Gel'fand-Pinsker channel in the absence of Eve. The
form of this achievable rate matches with its classical counterpart. The
Gel'fand-Pinsker channel model had earlier only been studied for the
classical-quantum case and in the case where Alice (the sender) and Bob (the
receiver) have shared entanglement between them.Comment: version 2, 1 figure, 26 pages, added some extra proof and corrected
few typo
A hypothesis testing approach for communication over entanglement assisted compound quantum channel
We study the problem of communication over a compound quantum channel in the
presence of entanglement. Classically such channels are modeled as a collection
of conditional probability distributions wherein neither the sender nor the
receiver is aware of the channel being used for transmission, except for the
fact that it belongs to this collection. We provide near optimal achievability
and converse bounds for this problem in the one-shot quantum setting in terms
of quantum hypothesis testing divergence. We also consider the case of informed
sender, showing a one-shot achievability result that converges appropriately in
the asymptotic and i.i.d. setting. Our achievability proof is similar in spirit
to its classical counterpart. To arrive at our result, we use the technique of
position-based decoding along with a new approach for constructing a union of
two projectors, which can be of independent interest. We give another
application of the union of projectors to the problem of testing composite
quantum hypotheses.Comment: 21 pages, version 3. Added an application to the composite quantum
hypothesis testing. Expanded introductio
Convex-split and hypothesis testing approach to one-shot quantum measurement compression and randomness extraction
We consider the problem of quantum measurement compression with side
information in the one-shot setting with shared randomness. In this problem,
Alice shares a pure state with Reference and Bob and she performs a measurement
on her registers. She wishes to communicate the outcome of this measurement to
Bob using shared randomness and classical communication, in such a way that the
outcome that Bob receives is correctly correlated with Reference and Bob's own
registers. Our goal is to simultaneously minimize the classical communication
and randomness cost. We provide a protocol based on convex-split and position
based decoding with its communication upper bounded in terms of smooth max and
hypothesis testing relative entropies.
We also study the randomness cost of our protocol in both one-shot and
asymptotic and i.i.d. setting. By generalizing the convex-split technique to
incorporate pair-wise independent random variables, we show that our one shot
protocol requires small number of bits of shared randomness. This allows us to
construct a new protocol in the asymptotic and i.i.d. setting, which is optimal
in both the number of bits of communication and the number of bits of shared
randomness required.
We construct a new protocol for the task of strong randomness extraction in
the presence of quantum side information. Our protocol achieves error guarantee
in terms of relative entropy (as opposed to trace distance) and extracts close
to optimal number of uniform bits. As an application, we provide new
achievability result for the task of quantum measurement compression without
feedback, in which Alice does not need to know the outcome of the measurement.
This leads to the optimal number of bits communicated and number of bits of
shared randomness required, for this task in the asymptotic and i.i.d. setting.Comment: version 5: 29 pages, 1 figure. Added applications to randomness
extraction (against quantum side information) and measurement compression
without feedbac
On the strong converses for the quantum channel capacity theorems
A unified approach to prove the converses for the quantum channel capacity
theorems is presented. These converses include the strong converse theorems for
classical or quantum information transfer with error exponents and novel
explicit upper bounds on the fidelity measures reminiscent of the Wolfowitz
strong converse for the classical channel capacity theorems. We provide a new
proof for the error exponents for the classical information transfer. A long
standing problem in quantum information theory has been to find out the strong
converse for the channel capacity theorem when quantum information is sent
across the channel. We give the quantum error exponent thereby giving a
one-shot exponential upper bound on the fidelity. We then apply our results to
show that the strong converse holds for the quantum information transfer across
an erasure channel for maximally entangled channel inputs.Comment: Added the strong converse for the erasure channel for maximally
entangled inputs and corrected minor typo