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Impossibility of cloning and deleting of unknown states are importantrestrictions on processing of information in the quantum world. On the otherhand, a known quantum state can always be cloned or deleted. However if werestrict the class of allowed operations, there will arise restrictions on theability of cloning and deleting machines. We have shown that cloning anddeleting of known states is in general not possible by local operations. Thisimpossibility hints at quantum correlation in the state. We propose dualmeasures of quantum correlation based on the dual restrictions of no localcloning and no local deleting. The measures are relative entropy distances ofthe desired states in a (generally impossible) perfect local cloning or localdeleting process from the best approximate state that is actually obtained byimperfect local cloning or deleting machines. Just like the dual measures ofentanglement cost and distillable entanglement, the proposed measures are basedon important processes in quantum information. We discuss their properties. Forthe case of pure states, estimations of these two measures are also provided.Interestingly, the entanglement of cloning for a maximally entangled state oftwo two-level systems is not unity.Comment: 13 pages, 3 figures, RevTeX4; v2: published versio

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