Quantum channel structure

What is the smallest output dimension in which the minimum output von Neumann entropy of quantum channels fails to be additive?

• Quantum Communication
• Additivity and regularization
• Matrix and entropy inequalities
• Quantum channel structure

Must the composition of any two compatible PPT completely positive maps be entanglement breaking?

• Quantum Resource Theory
• Quantum Communication
• Quantum separability
• Quantum channel structure

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?

• Quantum Communication
• Quantum channel structure

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?

• Quantum Communication
• Channel degradability
• Quantum channel structure

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?

• Quantum Communication
• Additivity and regularization
• Quantum channel structure
• Matrix and entropy inequalities

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?

• Quantum Communication
• Additivity and regularization
• Matrix and entropy inequalities
• Quantum channel structure

Does there exist a finite-dimensional transpose-degradable quantum channel that is not degradable?

• Quantum Communication
• Channel degradability
• Quantum channel structure

What are the componentwise-minimal dimension triples \((d_A,d_B,d_E)\) that admit a transpose-degradable but nondegradable channel?

• Quantum Communication
• Channel degradability
• Quantum channel structure