Abstract
We investigate how two pieces of localized quantum information represented by a tensor product of two unknown qudit states are delocalized by performing two-qudit global unitary operations. To characterize the delocalization power of global unitary operations on quantum information, we analyze the necessary and sufficient condition to deterministically relocalize one of the two pieces of quantum information to its original Hilbert space by using only local operation and classical communication (LOCC). We prove that this LOCC one-piece relocalization is possible if and only if the global unitary operation is local unitary equivalent to a controlled-unitary operation. The delocalization power and the entangling power characterize different non-local properties of global unitary operations.
Highlights
Quantum information processing (QIP) aims to achieve more efficient information processing or to perform tasks that are not classically possible, by utilizing the superposition principle of quantum states
We derive a necessary condition on the local operation and classical communication (LOCC) protocol for one-piece relocalization for a particular input state by introducing accumulated operators representing LOCC. We show that this condition restricts the operators representing the protocol and this restriction implies that any LOCC one-piece relocalization protocol can be reduced to a oneway LOCC protocol
We investigated how originally localized two pieces of quantum information represented by the tensor product of two unknown qudit states is delocalized by performing two-qudit global unitary operations
Summary
Quantum information processing (QIP) aims to achieve more efficient information processing or to perform tasks that are not classically possible, by utilizing the superposition principle of quantum states. Our idea is to evaluate the power of delocalization of global unitary operations by analyzing non-local properties of the quantum operations required for relocalizing one of the two pieces of delocalized quantum information. This restriction on the measurement is equivalent to restricting general LOCC to more limited one-way LOCC They have investigated the condition on the completely positive and trace-preserving (CPTP) map of the non-environmental qudit alone, not global unitary operations, for the delocalized piece of quantum information to be relocalizable by LOCC. Ogata and Murao [12] have considered a related problem to find a necessary and sufficient condition for a restricted class of delocalized two pieces of qubit quantum information in the two-qubit Hilbert space to be relocalized by LOCC In their work, they considered general LOCC, but their LOCC operations required partial knowledge of one of the qubit states.
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