Topic
Quantum channel structure
12 records: 9 unsolved, 3 solved. Filter the catalog by this topic →
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The PPT-squared conjecture
Must the composition of any two compatible PPT completely positive maps be entanglement breaking?
Solved -
Smallest output dimension violating minimum output entropy additivity
What is the smallest output dimension in which the minimum output von Neumann entropy of quantum channels fails to be additive?
Unsolved -
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 -
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 -
Loss of mixed unitarity after a positive time in a quantum dynamical semigroup
Does there exist a norm-continuous semigroup \((\Phi_t)_{t\geq0}\) of unital completely positive trace-preserving maps on \(\mathcal L(\mathbb C^d)\), for some finite integer \(d\geq3\), such that \(\Phi_s\) is mixed unitary and \(\Phi_t\) is not mixed unitary for some \(0<s<t\)?
Unsolved -
Minimum output entropy additivity for qubit channels
Is minimum output von Neumann entropy additive whenever one channel is a qubit channel?
Unsolved -
Gaussian-input preservation under a Gaussian reference extension
Does preservation of Gaussian inputs by a trace-decreasing operation imply preservation when a Gaussian reference is attached?
Solved -
Optimal random-unitary decomposition of symmetric Werner–Holevo channels
For every odd integer \(d\geq5\), do there exist \(r=d(d+1)/2\) unitary operators \(U_1,\ldots,U_r\) on \(\mathbb C^d\) such that
Unsolved -
Equal-weight low-Choi-rank decompositions of quantum channels
Can every finite-dimensional quantum channel be written as the uniform mixture of \(d_B\) channels whose Choi ranks are at most the input dimension?
Unsolved -
Multiplicativity for polarized Werner–Holevo channels
For every integer \(d\geq3\), every \(x\in(0,1)\), and every \(1<p<2\), is the maximal output Schatten \(p\)-norm of the polarized Werner–Holevo channel multiplicative on two identical copies?
Unsolved -
Delayed-onset additivity violation for minimum output Rényi entropy
Does there exist a finite-dimensional quantum channel whose minimum output Rényi entropy is additive for every tensor power below some order and first becomes strictly subadditive at that order?
Unsolved