241 research outputs found
Quantum entropic security and approximate quantum encryption
We present full generalisations of entropic security and entropic
indistinguishability to the quantum world where no assumption but a limit on
the knowledge of the adversary is made. This limit is quantified using the
quantum conditional min-entropy as introduced by Renato Renner. A proof of the
equivalence between the two security definitions is presented. We also provide
proofs of security for two different cyphers in this model and a proof for a
lower bound on the key length required by any such cypher. These cyphers
generalise existing schemes for approximate quantum encryption to the entropic
security model.Comment: Corrected mistakes in the proofs of Theorems 3 and 6; results
unchanged. To appear in IEEE Transactions on Information Theory
Entanglement sampling and applications
A natural measure for the amount of quantum information that a physical
system E holds about another system A = A_1,...,A_n is given by the min-entropy
Hmin(A|E). Specifically, the min-entropy measures the amount of entanglement
between E and A, and is the relevant measure when analyzing a wide variety of
problems ranging from randomness extraction in quantum cryptography, decoupling
used in channel coding, to physical processes such as thermalization or the
thermodynamic work cost (or gain) of erasing a quantum system. As such, it is a
central question to determine the behaviour of the min-entropy after some
process M is applied to the system A. Here we introduce a new generic tool
relating the resulting min-entropy to the original one, and apply it to several
settings of interest, including sampling of subsystems and measuring in a
randomly chosen basis. The sampling results lead to new upper bounds on quantum
random access codes, and imply the existence of "local decouplers". The results
on random measurements yield new high-order entropic uncertainty relations with
which we prove the optimality of cryptographic schemes in the bounded quantum
storage model.Comment: v3: fixed some typos, v2: fixed minor issue with the definition of
entropy and improved presentatio
A decoupling approach to classical data transmission over quantum channels
Most coding theorems in quantum Shannon theory can be proven using the
decoupling technique: to send data through a channel, one guarantees that the
environment gets no information about it; Uhlmann's theorem then ensures that
the receiver must be able to decode. While a wide range of problems can be
solved this way, one of the most basic coding problems remains impervious to a
direct application of this method: sending classical information through a
quantum channel. We will show that this problem can, in fact, be solved using
decoupling ideas, specifically by proving a "dequantizing" theorem, which
ensures that the environment is only classically correlated with the sent data.
Our techniques naturally yield a generalization of the
Holevo-Schumacher-Westmoreland Theorem to the one-shot scenario, where a
quantum channel can be applied only once
A father protocol for quantum broadcast channels
A new protocol for quantum broadcast channels based on the fully quantum
Slepian-Wolf protocol is presented. The protocol yields an achievable rate
region for entanglement-assisted transmission of quantum information through a
quantum broadcast channel that can be considered the quantum analogue of
Marton's region for classical broadcast channels. The protocol can be adapted
to yield achievable rate regions for unassisted quantum communication and for
entanglement-assisted classical communication; in the case of unassisted
transmission, the region we obtain has no independent constraint on the sum
rate, only on the individual transmission rates. Regularized versions of all
three rate regions are provably optimal.Comment: Typo in statement of Theorem 4 fixe
The decoupling approach to quantum information theory
Quantum information theory studies the fundamental limits that physical laws
impose on information processing tasks such as data compression and data
transmission on noisy channels. This thesis presents general techniques that
allow one to solve many fundamental problems of quantum information theory in a
unified framework. The central theorem of this thesis proves the existence of a
protocol that transmits quantum data that is partially known to the receiver
through a single use of an arbitrary noisy quantum channel. In addition to the
intrinsic interest of this problem, this theorem has as immediate corollaries
several central theorems of quantum information theory. The following chapters
use this theorem to prove the existence of new protocols for two other types of
quantum channels, namely quantum broadcast channels and quantum channels with
side information at the transmitter. These protocols also involve sending
quantum information partially known by the receiver with a single use of the
channel, and have as corollaries entanglement-assisted and unassisted
asymptotic coding theorems. The entanglement-assisted asymptotic versions can,
in both cases, be considered as quantum versions of the best coding theorems
known for the classical versions of these problems. The last chapter deals with
a purely quantum phenomenon called locking. We demonstrate that it is possible
to encode a classical message into a quantum state such that, by removing a
subsystem of logarithmic size with respect to its total size, no measurement
can have significant correlations with the message. The message is therefore
"locked" by a logarithmic-size key. This thesis presents the first locking
protocol for which the success criterion is that the trace distance between the
joint distribution of the message and the measurement result and the product of
their marginals be sufficiently small.Comment: PhD Thesis, Universit\'e de Montr\'eal, defended December 2009. 133
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