Resource-efficient linear-optical generation of GHZ-like states

TL;DR

The paper addresses the resource bottleneck in heralded, multi-photon GHZ-like state generation within linear-optical quantum computing by enabling variable-entanglement intermediate states (primes) and introducing a bleeding technique. It extends the primate fusion framework to allow tunable entanglement in intermediate states and analyzes sequential fusion and non-exhaustive bleeding to reduce the average photon cost for GHZ-like state generation, validating the approach numerically. Key findings show measurable resource-cost reductions for GHZ-like states, including maximally entangled cases, albeit with trade-offs in single-pass success probability; non-exhaustive bleeding often yields the strongest gains, particularly for larger N. Overall, the work provides a flexible, resource-aware toolkit for photonic quantum state engineering and motivates further exploration of alternative intermediate-state architectures and fusion strategies for scalable quantum computation.

Abstract

Heralded multi-photon entanglement generation is a central bottleneck for photonic quantum computing, where resource costs typically skyrocket with target size. We explore efficient methods for generating photon states with tunable entanglement, providing a flexible tool for quantum state engineering. We introduce a theoretical framework that has been numerically validated, demonstrating the capacity to generate GHZ-like states incrementally from non-logical intermediate states. We demonstrate that in certain scenarios $-$ such as reducing the resource cost for building large maximally entangled GHZ states $-$ these variable-entanglement states can outperform their fixed-entanglement counterparts. By adjusting intermediate states and optimizing interferometer schemes, we improve photon number cost efficiency of GHZ-like states generation. Our findings indicate that while not a universal solution, non-maximally entangled states offer practical advantages for specific photonic quantum information tasks.

Figures (12)

• Figure 1: Schematic of the fusion unit. A success trigger can be added to sum detector signals and output a signal when only one photon is detected. Copper wires represent classical signals, with arrows indicating direction. The logical unit discriminates single-photon detection and sends the corresponding signal.
• Figure 2: The scheme for generating elementary variable primate state $|\pi^{(1)}(1,s)\rangle$.
• Figure 3: The photon resource cost $\nu^{(1)}$ for generating the elementary variable primate state $|\pi^{(1)}(1,s)\rangle$.
• Figure 4: (a) Example of two-primate fusion when the $13$ mode pair is chosen for fusion. (b) The final fusion step that transforms a primate state into a GHZ-like state. Note that the final fusion is always optimal at a beamsplitter transmittance of $1/2$.
• Figure 5: Improved photon resource costs $\nu$ for generating GHZ-like states with a variable parameter of entanglement $s$ for different numbers of qubits $N$ using fusion.