Quantum capacity of the depolarizing and qubit Pauli channels
Determine the quantum capacity of qubit Pauli channels; even the depolarizing channel's zero-capacity threshold is only known to lie between 0.064956 and 1/12.
Problems
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Matching problems
Seven qubits protecting a qutrit: does a ((7,3,3)) code exist?
Find a three-dimensional subspace of seven qubits that corrects any single-qubit error, or prove that no ((7,3,3)) code exists.
The quantum MDS conjecture
Prove that stabilizer quantum MDS codes on qudits of dimension q have length at most q²+1, apart from one even-q family, or find a longer one.
Fewest CNOT gates to prepare the Golay code's logical zero
Prepare the 23-qubit Golay code's logical zero with fewer than 44 CNOT gates, or prove 44 optimal; at depth 7 the record is 45.
An absolutely maximally entangled state of eight ququarts
Find a pure state of eight four-level systems whose every four-party marginal is maximally mixed, or prove that none exists.