161 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
On the complementary quantum capacity of the depolarizing channel
The qubit depolarizing channel with noise parameter transmits an input
qubit perfectly with probability , and outputs the completely mixed
state with probability . We show that its complementary channel has
positive quantum capacity for all . Thus, we find that there exists a
single parameter family of channels having the peculiar property of having
positive quantum capacity even when the outputs of these channels approach a
fixed state independent of the input. Comparisons with other related channels,
and implications on the difficulty of studying the quantum capacity of the
depolarizing channel are discussed.Comment: v4 corrects errors in equation (38
Quantum network communication -- the butterfly and beyond
We study the k-pair communication problem for quantum information in networks
of quantum channels. We consider the asymptotic rates of high fidelity quantum
communication between specific sender-receiver pairs. Four scenarios of
classical communication assistance (none, forward, backward, and two-way) are
considered. (i) We obtain outer and inner bounds of the achievable rate regions
in the most general directed networks. (ii) For two particular networks
(including the butterfly network) routing is proved optimal, and the free
assisting classical communication can at best be used to modify the directions
of quantum channels in the network. Consequently, the achievable rate regions
are given by counting edge avoiding paths, and precise achievable rate regions
in all four assisting scenarios can be obtained. (iii) Optimality of routing
can also be proved in classes of networks. The first class consists of directed
unassisted networks in which (1) the receivers are information sinks, (2) the
maximum distance from senders to receivers is small, and (3) a certain type of
4-cycles are absent, but without further constraints (such as on the number of
communicating and intermediate parties). The second class consists of arbitrary
backward-assisted networks with 2 sender-receiver pairs. (iv) Beyond the k-pair
communication problem, observations are made on quantum multicasting and a
static version of network communication related to the entanglement of
assistance.Comment: 15 pages, 17 figures. Final versio
Bidirectional coherent classical communication
A unitary interaction coupling two parties enables quantum communication in
both the forward and backward directions.
Each communication capacity can be thought of as a tradeoff between the
achievable rates of specific types of forward and backward communication.
Our first result shows that for any bipartite unitary gate, coherent
classical communication is no more difficult than classical communication --
they have the same achievable rate regions. Previously this result was known
only for the unidirectional capacities (i.e., the boundaries of the tradeoff).
We then relate the tradeoff curve for two-way coherent communication to the
tradeoff for two-way quantum communication and the tradeoff for coherent
communiation in one direction and quantum communication in the other.Comment: 11 pages, v2 extensive modification and rewriting of the main proof,
v3 published version with only a few more change
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