Mutual Conversions Between Knill–Laflamme–Milburn and W States

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.

Conversion of Knill–Laflamme–Milburn Entanglement to Greenberger–Horne–Zeilinger Entanglement in Decoherence‐Free Subspace

“…With the rapid development of quantum information processing, quantum DOI: 10.1002/andp.202100365 entanglement has attracted extensive attention to analysis, application, intrinsic characteristics, and conversion between different entangled states. [19][20][21][22][23] The common quantum entangled states include Bell state, Greenberger-Horne-Zeilinger (GHZ) state, [24] W state, [25] and Knill-Laflamme-Milburn (KLM) state. [26] For multi-qubit KLM state and W state, if any qubit is lost, the remaining qubits may still keep entangled with certain probability.…”

“…Many researchers have proposed the conversion schemes between entangled states. [19][20][21][22][23] Studies have demonstrated that KLM can be converted into W state, and W state can be converted into GHZ state, it is of great importance to study the conversion between GHZ state and KLM state. The KLM and GHZ entangled states represent two different kinds of multi-qubit entanglement, which cannot be converted to each other by local operation and classical communication.…”

Distinguishment of Greenberger–Horne–Zeilinger States in Rydberg Atoms via Noncyclic Geometric Quantum Computation

“…Quantum entanglement is a very attractive resource, playing an irreplaceable role in quantum information processing (QIP), such as quantum dense coding, [1,2] quantum teleportation, [3][4][5] quantum key distribution, [6,7] quantum secret sharing, [8,9] and entanglement conversion. [10][11][12][13] The Greenberger-Horne-Zeilinger (GHZ) state is one of the significant entangled states, which owns more quantum nonlocality than Bell states, and has DOI: 10.1002/andp.202100057 a wide range of applications in quantum computing, [14,15] quantum networks, [5,8,16,17] etc. Thus, both preparing and analyzing GHZ states are highly demanding.…”

Preparation of Steady 3D Dark State Entanglement in Dissipative Rydberg Atoms via Electromagnetic Induced Transparency

“…Very recently, we show that the entanglement conversion would be influenced by the dissipation. [29,30] Commonly, there are three methods to deal with the dissipation: i) Quantum error correction method, [32] which relies on the high-fidelity quantum gate for detecting and correcting errors. ii) Dynamical decoupling method, [33] which seeks to minimize the unwanted systembath interactions in an open quantum system but can never completely avoid all unitary errors.…”