Quantifying the imaginarity of quantum states via Tsallis relative entropy

Abstract

It is a fundamental question that why quantum mechanics uses complex numbers instead of only real numbers. To address this topic, recently, a rigorous resource theory for the imaginarity of quantum states were established, and several imaginarity measures were proposed. In this work, we propose a new imaginarity measure based on the Tsallis relative entropy. This imaginarity measure has explicit expression, and also, it is computable for bosonic Gaussian states.

9 pages, 1 figure. Any comments are welcome!

References in corpus (15)

• The Quantum Chernoff Bound
• Quantum information with Gaussian states
• Quantum theory based on real numbers can be experimentally falsified
• The Chernoff lower bound for symmetric quantum hypothesis testing
• Computable bounds for the discrimination of Gaussian states
• The quantum Chernoff bound as a measure of distinguishability between density matrices: application to qubit and Gaussian states
• Resource theory of imaginarity: Quantification and state conversion
• Hiding and masking quantum information in complex and real quantum mechanics
• Coherence measures with respect to general quantum measurements
• Real quantum operations and state transformations
• Imaginarity of Gaussian states
• Is there a finite complete set of monotones in any quantum resource theory?
• Flag Additivity in Quantum Resource Theories
• Quantum Chernoff bound as a measure of nonclassicality for one-mode Gaussian states
• Riemannian optimization of photonic quantum circuits in phase and Fock space

Cited by in corpus (8)

• Quantifying imaginarity in terms of pure-state imaginarity
• Two imaginarity monotones induced by unified $(\alpha ,\beta )$-relative entropy
• Imaginarity measures induced by relative entropy
• Coherence and Imaginarity as Resources in Quantum Circuit Complexity
• Imaginarity measures induced by real part states and the complementarity relations
• Off-resonant preservation and generation of imaginarity in distributed scenarios
• Experimental certification of the nonlocal advantages of quantum imaginarity
• Measure of set imaginarity