Locally implementable product unitaries can be globally distinguishable but LOCC-indistinguishable, and vice versa, depending on whether probing states are adaptive or fixed and whether probes are separable or entangled.
Distinguishing quantum operations having few Kraus operators
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abstract
Entanglement is sometimes helpful in distinguishing between quantum operations, as differences between quantum operations can become magnified when their inputs are entangled with auxiliary systems. Bounds on the dimension of the auxiliary system needed to optimally distinguish quantum operations are known in several situations. For instance, the dimension of the auxiliary space never needs to exceed the dimension of the input space of the operations for optimal distinguishability, while no auxiliary system whatsoever is needed to optimally distinguish unitary operations. Another bound, which follows from work of R. Timoney, is that optimal distinguishability is always possible when the dimension of the auxiliary system is twice the number of operators needed to express the difference between the quantum operations in Kraus form. This paper provides an alternate proof of this fact that is based on concepts and tools that are familiar to quantum information theorists.
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Global versus Local Discrimination of Locally Implementable Multipartite Unitaries
Locally implementable product unitaries can be globally distinguishable but LOCC-indistinguishable, and vice versa, depending on whether probing states are adaptive or fixed and whether probes are separable or entangled.