Magic states play an important role in fault-tolerant quantum computation, and so the quantification of magic for quantum states is of great significance. In this work, we propose two new magic quantifiers by introducing two versions of quantum $(α,β)$ Jensen-Shannon divergence based on the quantum $(α,β)$ entropy and the quantum $(α,β)$ -relative entropy, respectively. We derive many desirable properties for our magic quantifiers, and find that they are efficiently computable in low-dimensional Hilbert spaces. We also show that the initial nonstabilizerness in the input state can boost the magic generating power for our magic quantifiers with appropriate parameter ranges for a certain class of quantum gates. Our magic quantifiers may provide new tools for addressing some specific problems in magic resource theory.Magic states play an important role in fault-tolerant quantum computation, and so the quantification of magic for quantum states is of great significance. In this work, we propose two new magic quantifiers by introducing two versions of quantum $(α,β)$ Jensen-Shannon divergence based on the quantum $(α,β)$ entropy and the quantum $(α,β)$-relative entropy, respectively. We derive many desirable properties for our magic quantifiers, and find that they are efficiently computable in low-dimensional Hilbert spaces. We also show that the initial nonstabilizerness in the input state can boost the magic generating power for our magic quantifiers with appropriate parameter ranges for a certain class of quantum gates. Our magic quantifiers may provide new tools for addressing some specific problems in magic resource theory.

quant-pharXiv:2604.06604Communications in Theoretical PhysicsApr 9, 20261 citation

New Quantum Divergences Associated with Monotone Functions and Weighted Wasserstein Means

Ho Thien Long Truong, Trung Hoa Dinh, Ngoc Yen Phan

Mediterranean Journal of MathematicsAug 27, 20260 citations

Quantum q-divergence

Sumiyoshi Abe

Physica A Statistical Mechanics and its ApplicationsJul 6, 200423 citations

Maps preserving a new version of quantum

f

-divergence

Quantifying magic via quantum

(α,β)

Jensen-Shannon divergence

(α,β)

Jensen-Shannon divergence based on the quantum

(α,β)

entropy and the quantum

(α,β)

-relative entropy, respectively. We derive many desirable properties for our magic quantifiers, and find that they are efficiently computable in low-dimensional Hilbert spaces. We also show that the initial nonstabilizerness in the input state can boost the magic generating power for our magic quantifiers with appropriate parameter ranges for a certain class of quantum gates. Our magic quantifiers may provide new tools for addressing some specific problems in magic resource theory.