Deciding if a classical-quantum channel can exactly preserve a single bit is QCMA-complete, with optimal witnesses characterized as computational basis states (minimum) and |+>, |-> states (maximum).
QMA-complete problems
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abstract
In this paper we give an overview of the quantum computational complexity class QMA and a description of known QMA-complete problems to date. Such problems are believed to be difficult to solve, even with a quantum computer, but have the property that if a purported solution to the problem is given, a quantum computer would easily be able to verify whether it is correct. An attempt has been made to make this paper as self-contained as possible so that it can be accessible to computer scientists, physicists, mathematicians, and quantum chemists. Problems of interest to all of these professions can be found here.
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quant-ph 1years
2025 1verdicts
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Deciding Whether a C-Q Channel Preserves a Bit is QCMA-Complete
Deciding if a classical-quantum channel can exactly preserve a single bit is QCMA-complete, with optimal witnesses characterized as computational basis states (minimum) and |+>, |-> states (maximum).