Kavli Affiliate: Matthew P. A. Fisher
| First 5 Authors: Shane P. Kelly, Ulrich Poschinger, Ferdinand Schmidt-Kaler, Matthew P. A. Fisher, Jamir Marino
| Summary:
The coherent superposition of quantum states is an important resource for
quantum information processing which distinguishes quantum dynamics and
information from their classical counterparts. In this article we investigate
the coherence requirements to communicate quantum information by using, as a
test bed, a class of hybrid random circuits which show a phase transition in
the quantum and classical channel capacities. The hybrid random circuits are
generated by a quantum information game played between two opponents, Alice and
Eve, who compete by applying random unitaries and measurements on a fixed
number of qubits. Alice applies unitaries in an attempt to maintain quantum
channel capacity, while Eve applies measurements in an attempt to destroy it.
By limiting the coherence generating or destroying operations available to each
opponent, we can control who wins or looses the game and tune a phase
transitions in entanglement and quantum channel capacity. Such transitions
allow us to identify the coherence requirements for quantum communication and,
in particular, prove that the coherence in any local basis gives an upper bound
for the quantum code distance of any stabilizer quantum error correction code.
Such a bound provides a rigorous quantification of the coherence resource
requirements for quantum error correction.
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