Predictability as a quantum resource

Abstract

Just recently, complementarity relations (CRs) have been derived from the basic rules of Quantum Mechanics. The complete CRs are equalities involving quantum coherence, $C$, quantum entanglement, and predictability, $P$. While the first two are already quantified in the resource theory framework, such a characterization lacks for the last. In this article, we start showing that, for a system prepared in a state $\rho$, $P$ of $\rho$, with reference to an observable $X$, is equal to $C$, with reference to observables mutually unbiased (MU) to $X$, of the state ${\Phi }_X(\rho )$, which is obtained from a non-revealing von Neumann measurement (NRvNM) of $X$. We also show that $P^X(\rho )>C^Y({\Phi }_X(\rho ))$ for observables not MU. Afterwards, we provide quantum circuits for implementing NRvNMs and use these circuits to experimentally test these (in)equalities using the IBM's quantum computers. Furthermore, we give a resource theory for predictability, identifying its free quantum states and free quantum operations and discussing some predictability monotones. Besides, after applying one of these predictability monotones to study bipartite systems, we discuss the relation among the resource theories of quantum coherence, predictability, and purity.

10 pages, 5 figures, 1 table

References in corpus (8)

• Reference frames, superselection rules, and quantum information
• The resource theory of quantum reference frames: manipulations and monotones
• Bloch vectors for qudits
• Maximally coherent mixed states: Complementarity between maximal coherence and mixedness
• Predictability, Distinguishability and Entanglement
• Entanglement Monotones from Complementarity Relations
• Entanglement monotones connect distinguishability and predictability
• Experimental tests of density matrix's properties-based complementarity relations

Cited by in corpus (4)

• Reality variation under monitoring with weak measurements
• Operational connection between predictability and entanglement in entanglement swapping from partially entangled pure states
• Local predictability and coherence versus distributed entanglement in entanglement swapping from partially entangled pure states
• Simulation of Afshar's Double Slit Experiment