Deterministic entanglement concentration assisted by generalized XZ basis (2410.15892v1)

Abstract: We propose a protocol for concentrating bipartite entanglement over a qubit-qudit system from arbitrary number of qubit-qudit states via a truncation of the Hilbert space corresponding to the subsystem containing the qubits to a space that hosts a single qubit. We achieve this truncation via a multi-qubit measurement in the generalized XZ basis, and show that the protocol is effectively deterministic. We also design a repetitive two-qubit measurement protocol, where the measurements on the qubit-parts is performed taking two qubit-qudit system at a time, and establish its equivalence with the protocol involving the multi-qubit measurement. We show that a concentration of entanglement is possible in each round of two-qubit measurements in the latter scheme, and derive lower and upper bounds of the entanglement concentrated after a given number of rounds of measurements, where the entanglement of the initial qubit-qudit systems are not-necessarily equal. We apply the repetitive two-qubit measurement protocol to concentrate entanglement using arbitrary two-qubit states with unequal entanglement, and discuss the entanglement properties of the multi-qubit state created in this process. We also show that the protocol can be used to create generalized GHZ states on arbitrary number of qubits, which highlights the possibility of creating maximally entangled qubit pairs via qubit-local projection measurements.