Mutual Conversions Between Knill–Laflamme–Milburn and <i>W</i> States

Abstract

Abstract Herein, two proposals are speculated to realize mutual conversions between Knill–Laflamme–Milburn (KLM) and W entangled states via X homodyne measurement (HM). By one of these proposals three‐qubit mutual conversions can be realized between these two photonic polarization entangled states. The other can be generalized to convert an arbitrary‐qubit KLM state to a W state adopting a control‐NOT gate. With the increasing number of qubits, the utilization ratio of photons in the second proposal would be close to unity. Analyses of the three‐qubit mutual conversions show that the proposal has a low error rate and high utilization ratio of photons. Moreover, the fidelity can also be very high even in consideration of decoherence. The P homodyne measurement is analyzed as well to improve the precision. The proposals, especially the second one, are expected to be helpful to reveal the relationship between these two robust multiple‐qubit entanglements.