Dual entanglement measures based on no local cloning and no local deleting

Abstract

Impossibility of cloning and deleting of unknown states are important restrictions on processing of information in the quantum world. On the other hand, a known quantum state can always be cloned or deleted. However if we restrict the class of allowed operations, there will arise restrictions on the ability of cloning and deleting machines. We have shown that cloning and deleting of known states is in general not possible by local operations. This impossibility hints at quantum correlation in the state. We propose dual measures of quantum correlation based on the dual restrictions of no local cloning and no local deleting. The measures are relative entropy distances of the desired states in a (generally impossible) perfect local cloning or local deleting process from the best approximate state that is actually obtained by imperfect local cloning or deleting machines. Just like the dual measures of entanglement cost and distillable entanglement, the proposed measures are based on important processes in quantum information. We discuss their properties. For the case of pure states, estimations of these two measures are also provided. Interestingly, the entanglement of cloning for a maximally entangled state of two two-level systems is not unity.