Quantifying magic via quantum (α,β) Jensen-Shannon divergence
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.
Quantum computing is like having a supercharged computer that can do many things at once, thanks to some mind-bending physics tricks. Regular computers use bits that are either 0 or 1. But in quantum computers, we have qubits that can be both 0 and 1 at the same time. It's like having a magic coin that's both heads and tails until you look at it. These qubits can also be connected in a special way called entanglement. Imagine having two magic coins that always show the same side, no matter how far apart they are. This helps quantum computers solve problems crazy fast. The hardware of a quantum computer is made of super-cool stuff like tiny particles kept in special conditions. This keeps them in their magical quantum states. Why is this exciting? Because quantum computers can tackle huge problems much faster than regular ones. They can help us discover new medicines, create better materials, and even make our online data safer with super-secure codes. In short, quantum computing is like having a superhero computer that does things in a whole new, super-fast, and super-cool way because of the strange rules of quantum physics!