Topic

Channel degradability

8 records: 4 unsolved, 4 solved. Filter the catalog by this topic →

Strict inclusion of degradable channels in the less-noisy class
Do there exist finite-dimensional quantum channels that are less noisy in Watanabe’s regularized sense but are not degradable?

Equivalent question: Regularized less-noisy channels beyond degradability. Counted once in question totals.
Solved
Regularized less-noisy channels beyond degradability
Does there exist a finite-dimensional regularized less-noisy quantum channel that is not degradable?

Equivalent question: Strict inclusion of degradable channels in the less-noisy class. Counted once in question totals.
Solved
Exactly solvable nondegradable quantum channels
Does there exist a finite-dimensional quantum channel that is neither degradable nor antidegradable and whose unassisted quantum capacity is known exactly?
Solved
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
Nontrivial mutually degradable channel pairs
Does there exist an integer \(d\geq2\) and a pair of distinct channels \(\mathcal M,\mathcal N:\mathcal L(A)\to\mathcal L(B)\), with \(A\simeq B\simeq\mathbb C^d\), that both have Choi rank exactly \(d\), are mutually degradable, and are each nondegradable?
Unsolved
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?
Unsolved
Transpose degradability beyond degradability
Does there exist a finite-dimensional transpose-degradable quantum channel that is not degradable?
Unsolved
Minimal dimensions for strict transpose degradability
What are the componentwise-minimal dimension triples \((d_A,d_B,d_E)\) that admit a transpose-degradable but nondegradable channel?
Unsolved