Topic
Channel degradability
8 records: 3 unsolved, 5 solved. Filter the catalog by this topic →
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Channels superactivated by antidegradable helpers
What necessary and sufficient structural conditions characterize the finite-dimensional channels of zero quantum capacity, and separately those of zero private capacity, that acquire a positive capacity of the same kind when used in parallel with some antidegradable…
Unsolved -
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 -
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 -
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?
Solved -
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 -
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?
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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?
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Transpose degradability beyond degradability
Does there exist a finite-dimensional transpose-degradable quantum channel that is not degradable?
Unsolved