Stabilizer rank of tensor powers of the T state
Decide whether the number of stabilizer states needed to write n copies of the T magic state is bounded by a polynomial in n.
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Decide whether the number of stabilizer states needed to write n copies of the T magic state is bounded by a polynomial in n.
Find the smallest output dimension in which two quantum channels violate additivity of minimum output entropy; it lies between 2 and 182.
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.
Find a three-dimensional subspace of seven qubits that corrects any single-qubit error, or prove that no ((7,3,3)) code exists.
Prove or refute that minimum output entropy is additive when one of two channels is an arbitrary, possibly non-unital, qubit channel.
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.
Decide whether shared randomness and one bit of communication reproduce all projective measurements on every partially entangled qubit pair.
Find the most mutually unbiased bases possible in dimension d when d is not a prime power; for d = 6 it is 3, 4 or 5, and a claimed proof of 3 awaits checking.
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.
Find a pure state of eight four-level systems whose every four-party marginal is maximally mixed, or prove that none exists.