Abstract We introduce a nonunitary partial-swap gate for fusing arbitrary small-sized photonic W-states into a large-scale entangled network of W-state efficiently without ancillary photons. A partial-swap gate is designed in an optical architecture based on linear optics elements. By introducing auxiliary degree of freedom, this gate provides a higher success probability with less cost. Our implementation can create a larger target state with a simpler set-up than previous proposals for W-state fusion. Also all ‘garbage’ states are recyclable, i.e., there is no complete failure output in our scheme in principle.
Abstract We introduce a nonunitary partial-swap gate for fusing arbitrary small-sized photonic W-states into a large-scale entangled network of W-state efficiently without ancillary photons. A partial-swap gate is designed in an optical architecture based on linear optics elements. By introducing auxiliary degree of freedom, this gate provides a higher success probability with less cost. Our implementation can create a larger target state with a simpler set-up than previous proposals for W-state fusion. Also all ‘garbage’ states are recyclable, i.e., there is no complete failure output in our scheme in principle.
With the assistance of weak cross-Kerr nonlinearities, we introduce an optical scheme to fuse two small-size polarization entangled photonic W states into a large-scale W state without qubit loss, i.e.,Wn+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 remaining states are recyclable. In addition, there is no need for any controlled quantum gate and any ancillary photon, so this fusion scheme may be implemented with current experimental techniques.
We propose an optical scheme to prepare large-scale entangled networks of W states. The scheme works by simultaneously fusing three polarization-encoded W states of arbitrary size via accessing only one qubit of each W state. It is composed of a Fredkin gate (controlled-swap gate), two fusion gates [as proposed in S. K. Ozdemir et al., New J. Phys. 13, 103003 (2011)], and an H-polarized ancilla photon. Starting with three n-qubit W states, the scheme prepares a new W state with $3(n\ensuremath{-}1)$ qubits after postselection if both fusion gates operate successfully, i.e., a fourfold coincidence at the detectors. The proposed scheme reduces the cost of creating arbitrarily large W states considerably when compared to previously reported schemes.
Integrating a single Fredkin (controlled swap) gate to the previously introduced W state fusion mechanism [Ozdemir et al., New J. Phys. 13, 103003 (2011)] and using an ancillary photon, we increase the size of the fused W states and essentially, we improve the success probability of the fusion process in a promising way for a possible deterministic W-state fusion mechanism. Besides fusing arbitrary size W states, our setup can also fuse Bell states to create W states with a success probability 3/4 which is much higher than the previous works. Therefore using only this setup, it is now possible to start with Bell pairs to create and expand arbitrary size W states. Since a higher probability of success implies a lower cost of resource in terms of the number of the states spent to achieve a target size, our setup gives rise to more cost-efficient scenarios.
Fusion measurements are a key primitive for linear-optical quantum computing and quantum networks. Type-I and type-II fusion gates are widely used to combine small entangled resource states into larger photonic states, but without ancillary resources their success probability is limited to 1/2. Existing 3/4-efficient type-I schemes rely on entangled Bell-pair ancillary states, whose preparation is itself probabilistic and resource-intensive. Here we propose a boosted type-I fusion gate using only four ancillary single photons and standard linear-optical primitives. For multiqubit GHZ and graph states, the gate succeeds directly with probability 5/8, while a distillation protocol converts partially entangled outcomes into additional successful events, raising the total success probability to 11/16 after one stage and asymptotically to 3/4. We quantify the practical advantage of this scheme by estimating the photonic resources required for generating representative large entangled photonic states and show that the proposed gate significantly reduces the required overhead compared with existing schemes. These results expand the set of resource-efficient linear-optical primitives and enable a substantial reduction in the resource requirements for scalable photonic quantum computing and quantum communication.
Fusion gates enable the creation of large entangled photonic states for linear-optical quantum computing and communication protocols. However, their success probability is limited to 1/2 without additional photonic resources. Previous schemes for boosting type-I fusion have used four ancillary single photons or a two-qubit Bell state, whose preparation is probabilistic and resource intensive. Here we propose a boosted type-I fusion gate using only two independent ancillary single photons and no entangled ancillary input. It achieves a direct success probability of 5/8, matching that of the previous four-single-photon proposal while using half as many ancillary photons. The circuit is predominantly passive, with a single active element that applies a phase shift or swaps two modes according to intermediate photodetection outcomes. Unlike the previous schemes, successful outputs occupy fixed modes and require no further conditional output routing. In particular, we show that the gate is more robust to heralded ancillary-photon loss than previously proposed boosted gates and reduces the average number of single photons required to generate a six-qubit ring graph state by more than 4.6% compared with other type-I schemes. It therefore offers a resource-efficient primitive for scalable fusion-based photonic quantum information processing.
We introduce a simple optical gate to fuse arbitrary-size polarization entangled W-states to prepare larger W-states. The gate requires a polarizing beam splitter (PBS), a half-wave plate (HWP) and two photon detectors. We study, numerically and analytically, the necessary resource consumption for preparing larger W-states by fusing smaller ones with the proposed fusion gate. We show analytically that resource requirement scales at most sub-exponentially with the increasing size of the state to be prepared. We numerically determine the resource cost for fusion without recycling where W-states of arbitrary size can be optimally prepared. Moreover, we introduce another strategy that is based on recycling and outperforms the optimal strategy for the non-recycling case.