Quantum Information Processing

Superadditivity relations of the $$l_1$$ l 1 norm of coherence

Piyu Li, Feng Liu, Yan-Qin Xu

Published Dec 14, 2017• 5 citations

Publisher

DOI: 10.1007/s11128-017-1790-9

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Superadditivity relations of the $l_1$ l 1 norm of coherenceSuperadditivity relations of the $$l_1$$ l 1 norm of coherence

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Quantum coherence serves as a crucial physical resource, with its quantification emerging as a focal point in contemporary research. Superadditivity constitutes one of the most fundamental attributes in characterizing the coherence distribution in multipartite quantum systems. In this paper, we provide a way to derive tighter superadditivity inequalities of [Formula: see text]-norm coherence measure for arbitrary multiqubit states. We present a category of superadditivity relations related to the [Formula: see text]th [Formula: see text] power of [Formula: see text]-norm coherence [Formula: see text] under certain conditions. Our results are better than the existing ones and are illustrated in detail with examples.Quantum coherence serves as a crucial physical resource, with its quantification emerging as a focal point in contemporary research. Superadditivity constitutes one of the most fundamental attributes in characterizing the coherence distribution in multipartite quantum systems. In this paper, we provide a way to derive tighter superadditivity inequalities of [Formula: see text]-norm coherence measure for arbitrary multiqubit states. We present a category of superadditivity relations related to the [Formula: see text]th [Formula: see text] power of [Formula: see text]-norm coherence [Formula: see text] under certain conditions. Our results are better than the existing ones and are illustrated in detail with examples.

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Superadditivity relations of the

l_1

l 1 norm of coherence

Trade-off relations of

l_1

-norm coherence for multipartite systems

Bell-type inequalities of

l_1

-norm of coherence

We employ a basic formalism from convex analysis to show a simple relation between the entanglement of formation

E_F

and the conjugate function

E^*

of the entanglement function

E(\\rho)=S(\\trace_A\\rho)

. We then consider the conjectured strong superadditivity of the entanglement of formation

E_F(\\rho) \\ge E_F(\\rho_I)+E_F(\\rho_{II})

, where

\\rho_I

and

\\rho_{II}

are the reductions of

\\rho

to the different Hilbert space copies, and prove that it is equivalent with subadditivity of

E^*

. As an application, we show that strong superadditivity would follow from multiplicativity of the maximal channel output purity for all non-trace-preserving quantum channels, when purity is measured by Schatten

p

-norms for

p

tending to 1.