1,890 research outputs found
Communicating over adversarial quantum channels using quantum list codes
We study quantum communication in the presence of adversarial noise. In this
setting, communicating with perfect fidelity requires using a quantum code of
bounded minimum distance, for which the best known rates are given by the
quantum Gilbert-Varshamov (QGV) bound. By asking only for arbitrarily high
fidelity and allowing the sender and reciever to use a secret key with length
logarithmic in the number of qubits sent, we achieve a dramatic improvement
over the QGV rates. In fact, we find protocols that achieve arbitrarily high
fidelity at noise levels for which perfect fidelity is impossible. To achieve
such communication rates, we introduce fully quantum list codes, which may be
of independent interest.Comment: 6 pages. Discussion expanded and more details provided in proofs. Far
less unclear than previous versio
Pauli Manipulation Detection codes and Applications to Quantum Communication over Adversarial Channels
We introduce and explicitly construct a quantum code we coin a "Pauli
Manipulation Detection" code (or PMD), which detects every Pauli error with
high probability. We apply them to construct the first near-optimal codes for
two tasks in quantum communication over adversarial channels. Our main
application is an approximate quantum code over qubits which can efficiently
correct from a number of (worst-case) erasure errors approaching the quantum
Singleton bound. Our construction is based on the composition of a PMD code
with a stabilizer code which is list-decodable from erasures.
Our second application is a quantum authentication code for "qubit-wise"
channels, which does not require a secret key. Remarkably, this gives an
example of a task in quantum communication which is provably impossible
classically. Our construction is based on a combination of PMD codes,
stabilizer codes, and classical non-malleable codes (Dziembowski et al., 2009),
and achieves "minimal redundancy" (rate )
On Zero-Error Communication via Quantum Channels in the Presence of Noiseless Feedback
© 1963-2012 IEEE. We initiate the study of zero-error communication via quantum channels when the receiver and the sender have at their disposal a noiseless feedback channel of unlimited quantum capacity, generalizing Shannon's zero-error communication theory with instantaneous feedback. We first show that this capacity is only a function of the linear span of Choi-Kraus operators of the channel, which generalizes the bipartite equivocation graph of a classical channel, and which we dub non-commutative bipartite graph. Then, we go on to show that the feedback-assisted capacity is non-zero (allowing for a constant amount of activating noiseless communication) if and only if the non-commutative bipartite graph is non-trivial, and give a number of equivalent characterizations. This result involves a far-reaching extension of the conclusive exclusion of quantum states. We then present an upper bound on the feedback-assisted zero-error capacity, motivated by a conjecture originally made by Shannon and proved later by Ahlswede. We demonstrate that this bound to have many good properties, including being additive and given by a minimax formula. We also prove a coding theorem showing that this quantity is the entanglement-assisted capacity against an adversarially chosen channel from the set of all channels with the same Choi-Kraus span, which can also be interpreted as the feedback-assisted unambiguous capacity. The proof relies on a generalization of the Postselection Lemma (de Finetti reduction) that allows to reflect additional constraints, and which we believe to be of independent interest. This capacity is a relaxation of the feedback-assisted zero-error capacity; however, we have to leave open the question of whether they coincide in general. We illustrate our ideas with a number of examples, including classical-quantum channels and Weyl diagonal channels, and close with an extensive discussion of open questions
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