Round Complexity of Quantum State Transformation
E. Chitambar and MH, arXiv:1610.01998
Nature Comm. to appear.
\rho_{AB}
\mathcal{A}_{M_1}
\mathcal{B}^{(M_1)}_{M_2}
M_1
\mathcal{A}^{(M_1,M_2)}_{M_3}
M_2
\sigma_{AB}
P_{XY|Z}
\mathcal{A}_{M_1}
\mathcal{B}^{(M_1)}_{M_2}
M_1
\mathcal{A}^{(M_1,M_2)}_{M_3}
M_2
Q_{XY|Z}
| Resource | Entanglement | Secrecy |
|---|
| Free Operation | LOCC | LOPC |
|---|
| Unit Resource |
|---|
\frac{1}{\sqrt{2}}\left(|00\rangle+|11\rangle\right)
\frac{1}{2}\text{diag}(00,11)
| Asymptotic Transformation |
Ent. Formation, Ent. Distillation | Secrecy Formation, Secrecy Distillation |
|---|
| Single-copy Transformation |
Majorization | Majorization |
|---|
| Bound Resource | Yes | ??? |
|---|
| Asymp. Reversible Resource |
Flagged states ??? |
|---|
2\times \text{n}
Chitambar and MH – PRL 2016