[Paper Review] Schemes for generating W state of paths and W state of polarization photons

Bao‐Sen Shi, Akihisa Tomita|ArXiv.org|Aug 28, 2002

Semiconductor Lasers and Optical Devices3 citations

TL;DR

This paper proposes two simple, experimentally feasible schemes for generating two types of W states using only commercial multiport fiber couplers and single-photon sources: (1) a path W state with one photon and 100% success probability via a symmetric N×N tritter, and (2) a multiphoton polarization W state via postselection using the same couplers, achieving higher success probabilities than prior schemes. The methods are scalable and require no complex entangled state sources or additional optical elements.

ABSTRACT

In this paper, we give two very simple schemes to produce two kinds of W states, one kind is path W state with one photon and the other is multiphoton photon polarization W state. These schemes just need a common commercial multiport fiber coupler and single photon sources, they are feasible by current technologies.

Motivation & Objective

• To develop experimentally viable, low-complexity schemes for generating W states—key resources in quantum information processing—using only available optical components.
• To address the challenge of producing W states, particularly multiphoton polarization W states, with higher success probabilities and simpler setups than existing linear-optical schemes.
• To demonstrate that a single commercial multiport fiber coupler and standard single-photon sources are sufficient to generate arbitrary N-mode path W states and N-photon polarization W states.
• To enable practical implementation of W states for applications such as quantum teleportation, telecloning, and dense coding by minimizing resource requirements.
• To generalize existing schemes by eliminating the need for maximal entangled state sources and complex interferometric setups.

Proposed method

• A symmetric N×N multiport fiber coupler (tritter) is used to coherently split a single photon across N spatial modes, generating a path W state via unitary transformation with equal amplitude distribution.
• The transformation is described by a unitary matrix M, where input state |10…0⟩ is mapped to ∑ₙ Mₙ₁|0…1…0⟩, producing a superposition of Fock states with one photon in any of the N modes.
• For multiphoton polarization W states, three or more single-photon sources prepare photons in specific polarization states (H or V), which are fed into the N×N coupler simultaneously.
• Postselection is applied to select only the output events where each output port contains exactly one photon, yielding the desired W state with probability |∑ₙ exp(iφₙ)|² / N².
• The use of a symmetric tritter matrix T with equal complex phases (e^{i2π/3}, e^{i4π/3}) ensures uniform amplitude distribution across all output modes.
• The scheme is scalable: any N-mode path W state or N-photon polarization W state can be generated by using an N×N coupler and N single-photon sources, with success probabilities of 100% and 1/N² respectively.

Experimental results

Research questions

• RQ1 Can a path W state of one photon in N spatial modes be generated with 100% success probability using only standard optical components?
• RQ2 Can multiphoton polarization W states be generated with higher success probabilities than existing linear-optical schemes using only a multiport coupler and single-photon sources?
• RQ3 Is it possible to generate arbitrary multimode or multiphoton W states without requiring a source of maximally entangled states or complex interferometric setups?
• RQ4 How does the use of a symmetric multiport coupler affect the fidelity and probability of W state generation?
• RQ5 Can postselection be effectively used to probabilistically generate multiphoton W states while minimizing resource overhead?

Key findings

• A path W state of one photon in N spatial modes is generated with 100% success probability using a symmetric N×N multiport fiber coupler and a single-photon source.
• The three-mode path W state |W⟩ = 1/√3 (|100⟩ + |010⟩ + |001⟩) is generated with unit probability using a 3×3 tritter and a single photon in one input port.
• For three-photon polarization W states, the scheme achieves a success probability of 1/9 when postselecting for one-photon-per-output configurations, exceeding the 2/27 probability in Ref. [15].
• The four-photon W state |W⟩ = 1/2 (|HHHV⟩ + |HHVH⟩ + |HVHH⟩ + |VHHH⟩) is generated with a success probability of 1/16 using a 4×4 coupler and postselection.
• The method is scalable: arbitrary N-mode path W states and N-photon polarization W states can be generated in principle using the same setup, with success probabilities of 1 and 1/N², respectively.
• The schemes eliminate the need for additional entangled state sources or complex optical elements, making them significantly simpler and more practical than prior approaches.