Topic

Strong converses

All-code exponential strong converse for degradable channels
Does every finite-dimensional degradable quantum channel satisfy an all-code exponential strong converse for quantum communication at its quantum capacity?
Solved
Fixed-error parallel Stein lemma for quantum channels
Let \(\mathcal N,\mathcal M:\mathcal L(A)\to\mathcal L(B)\) be quantum channels on finite-dimensional systems.
Unsolved
Strong converse for the quantum capacity of a general channel
Does every finite-dimensional memoryless quantum channel obey the strong converse at its unassisted quantum capacity?
Solved
Exponential strong converse for transpose-degradable channels
Does every finite-dimensional transpose-degradable channel satisfy an exponential strong converse for quantum communication at its single-letter quantum capacity?
Solved
Universal strong converse for the classical capacity
Does every finite-dimensional quantum channel satisfy the strong converse property at its unassisted classical capacity, or does some channel admit a sequence of codes above capacity whose average success probability stays bounded away from zero?
Solved
Strong converse for general mixed-state quantum compression
Does general finite-dimensional i.i.d.
Unsolved