New Additivity Properties of the Relative Entropy of Entanglement and Its Generalizations

Rubboli, Roberto; Tomamichel, Marco

doi:10.1007/s00220-024-05025-3

Commun. Math. Phys.

2024

DOI: 10.1007/s00220-024-05025-3

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New Additivity Properties of the Relative Entropy of Entanglement and Its Generalizations

Roberto Rubboli,

Marco Tomamichel

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2024

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Cited by 3 publications

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On the optimal error exponents for classical and quantum antidistinguishability

Mishra,

Nussbaum,

Wilde

2024

Lett Math Phys

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On the optimal error exponents for classical and quantum antidistinguishability

Mishra,

Nussbaum,

Wilde

2024

Lett Math Phys

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Black Box Work Extraction and Composite Hypothesis Testing

Watanabe,

Takagi

2024

Phys. Rev. Lett.

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Mixed-state additivity properties of magic monotones based on quantum relative entropies for single-qubit states and beyond

Rubboli,

Takagi,

Tomamichel

2024

Quantum

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We prove that the stabilizer fidelity is multiplicative for the tensor product of an arbitrary number of single-qubit states. We also show that the relative entropy of magic becomes additive if all the single-qubit states but one belong to a symmetry axis of the stabilizer octahedron. We extend the latter results to include all the α-z Rényi relative entropy of magic. This allows us to identify a continuous set of magic monotones that are additive for single-qubit states. We also show that all the monotones mentioned above are additive for several standard two and three-qubit states subject to depolarizing noise. Finally, we obtain closed-form expressions for several states and tighter lower bounds for the overhead of probabilistic one-shot magic state distillation.

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New Additivity Properties of the Relative Entropy of Entanglement and Its Generalizations

Cited by 3 publications

References 57 publications

On the optimal error exponents for classical and quantum antidistinguishability

On the optimal error exponents for classical and quantum antidistinguishability

Black Box Work Extraction and Composite Hypothesis Testing

Mixed-state additivity properties of magic monotones based on quantum relative entropies for single-qubit states and beyond

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