[Paper Review] Qubit-loss-free fusion of W states employing weak cross-Kerr nonlinearities

Mei-Yu Wang, Quanzhi Hao+2 more|arXiv (Cornell University)|May 4, 2017

Advanced Fiber Laser Technologies3 citations

TL;DR

This paper proposes a qubit-loss-free fusion scheme for large-scale W states using weak cross-Kerr nonlinearities in an optical setup. By employing two polarization entanglement processes and one spatial entanglement process via cross-Kerr nonlinearities, the scheme achieves a success probability of $(n+m)/(2nm)$, ensures no complete failure output, and recycles all garbage states, making it experimentally feasible without ancillary photons or controlled quantum gates.

ABSTRACT

With the assistance of weak cross-Kerr nonlinearities, we introduce an optical scheme to fuse two small-size polarization entangled W states into a large-scale W state without qubit loss, i.e.,$\mathrm{W}_{n+m}$ state can be generated from an $n$-qubit W state and a $m$-qubit W state. To complete the fusion task, two polarization entanglement processes and one spatial entanglement process are applied. The fulfillments of the above processes are contributed by a cross-Kerr nonlinear interaction between the signal photons and a coherent state via Kerr media. We analyze the resource cost and the success probability of the scheme. There is no complete failure output in our fusion mechanism, and all the garbage states are recyclable. In addition, there is no need for any controlled quantum gate and any ancillary photon, so it is simple and feasible under the current experiment technology.

Motivation & Objective

• To develop a scalable, experimentally feasible method for fusing small W states into larger ones without qubit loss.
• To overcome the limitations of previous schemes that suffer from qubit loss during fusion, reducing efficiency and increasing required fusion steps.
• To eliminate the need for controlled quantum gates and ancillary photons, enhancing experimental practicality.
• To analyze resource cost and success probability under realistic conditions, including decoherence and measurement errors.
• To demonstrate the feasibility of the scheme using current optical technologies and weak nonlinearities.

Proposed method

• The scheme uses weak cross-Kerr nonlinearities to induce phase shifts on coherent probe states proportional to the number of signal photons, enabling non-destructive photon-number measurement.
• Two polarization entanglement processes are implemented via cross-Kerr interactions between signal photons and coherent states to entangle the polarization degrees of freedom of the input W states.
• A spatial entanglement process is realized by interfering the signal photons from the two input W states using a beam splitter, entangling their spatial modes.
• The fusion outcome is heralded by homodyne measurements on the probe beams, with success confirmed by detecting specific phase shifts corresponding to the target W state.
• The scheme avoids any controlled quantum gates or ancillary photons, relying only on linear optics, nonlinear interactions, and standard photodetection.
• All garbage states are recyclable, and the protocol ensures no complete failure output, improving overall resource efficiency.

Experimental results

Research questions

• RQ1 Can W states be fused into larger-scale W states without losing any qubits, using only weak nonlinearities and standard optical components?
• RQ2 What is the success probability of a fusion scheme that avoids ancillary photons and controlled gates while maintaining high fidelity?
• RQ3 How does the resource cost of this qubit-loss-free fusion scheme compare to existing schemes that use Fredkin gates or ancilla?
• RQ4 To what extent can decoherence and measurement errors affect the fidelity of the fused W state in a realistic optical setup?
• RQ5 Can the proposed scheme be extended to fuse more than two W states simultaneously?

Key findings

• The fusion scheme achieves a success probability of $(n+m)/(2nm)$, which is identical to the optimal resource cost reported in prior qubit-loss-free schemes.
• The scheme ensures no complete failure output, and all garbage states are recyclable, enhancing resource efficiency.
• The protocol requires no controlled quantum gates or ancillary photons, significantly reducing experimental complexity.
• The error probability from X homodyne measurements is less than $10^{-5}$ when $\alpha\theta^2 > 9$, making measurement errors negligible in practice.
• The scheme is experimentally feasible using current optical technologies, including weak cross-Kerr nonlinearities and coherent state probing.
• Numerical analysis shows that for small to moderate W state sizes (e.g., $N=50$), the proposed scheme outperforms the Ozdemir scheme in resource cost, despite being less efficient than the Bugu scheme with Fredkin gates.