Round Complexity of Quantum State Transformation

E. Chitambar and MH, arXiv:1610.01998

Nature Comm. to appear.

\rho_{AB}
ρAB\rho_{AB}
\mathcal{A}_{M_1}
AM1\mathcal{A}_{M_1}
\mathcal{B}^{(M_1)}_{M_2}
BM2(M1)\mathcal{B}^{(M_1)}_{M_2}
M_1
M1M_1
\mathcal{A}^{(M_1,M_2)}_{M_3}
AM3(M1,M2)\mathcal{A}^{(M_1,M_2)}_{M_3}
M_2
M2M_2
\sigma_{AB}
σAB\sigma_{AB}
P_{XY|Z}
PXY∣ZP_{XY|Z}
\mathcal{A}_{M_1}
AM1\mathcal{A}_{M_1}
\mathcal{B}^{(M_1)}_{M_2}
BM2(M1)\mathcal{B}^{(M_1)}_{M_2}
M_1
M1M_1
\mathcal{A}^{(M_1,M_2)}_{M_3}
AM3(M1,M2)\mathcal{A}^{(M_1,M_2)}_{M_3}
M_2
M2M_2
Q_{XY|Z}
QXY∣ZQ_{XY|Z}
Resource Entanglement Secrecy
Free Operation LOCC LOPC
Unit Resource
\frac{1}{\sqrt{2}}\left(|00\rangle+|11\rangle\right)
12(∣00⟩+∣11⟩)\frac{1}{\sqrt{2}}\left(|00\rangle+|11\rangle\right)
\frac{1}{2}\text{diag}(00,11)
12diag(00,11)\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}
2×n2\times \text{n}
Chitambar and MH  – PRL 2016​

Round Complexity of Quantum State Transformation

By Lawrence Min-Hsiu Hsieh

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Round Complexity of Quantum State Transformation

arXiv:1610.01998

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