Teleportation-based squeezer for bosonic cluster states

TL;DR

This work addresses the squeezing gate needed for one-way quantum computation with bosonic modes of light, where finite squeezing and losses limit gate performance. It compares three teleportation-based squeezers—phase-shift squeezer (PS-sq), beam-splitter squeezer (BS-sq), and the combined BSPS-sq—against a direct BAS-sq baseline, using realistic imperfections modeled by resource squeezing $s$, beam-splitter transmissions $t_1$, $t_2$, phase $\phi$, and efficiencies $\eta_S$, $\eta_H$. Through fidelity with ideally squeezed states, Wigner-function negativity, and Genuine Non-Gaussianity (GnG) metrics, the study finds that BS-sq generally yields higher fidelity and better preservation of non-Gaussian features than PS-sq, with BSPS-sq matching its performance in many regimes. However, realistic noise can trigger entanglement breaking at moderate-to-high squeezing, highlighting trade-offs between noise distribution and non-Gaussianity. The results identify unbalanced beam splitters as a practical route to low-noise, scalable CV cluster-state gates for near-term experiments.

Abstract

The one-way quantum computation utilizing bosonic modes of light offers unmatched scalability of light modes, and it has seen rapid experimental development recently. Scalability requires robust and low-error gates and measurements. Squeezing gate is one of the necessary Gaussian operations. We find the optimal squeezing gate in cluster state architecture. Our approach newly uses amplitude transmission coefficients of unbalanced beam splitters and homodyne detection with subsequent unity-gain feed-forward to squeeze the input state. The approach outperforms the current method based on optimally rotated homodyne detection, but with fixed balanced beam splitters. The performance of both cluster state squeezers is evaluated for Gaussian and non-Gaussian input states. We use different metrics to benchmark the quality of squeezed output states. The result opens a road to low-noise squeezing gates in experimentally achievable cluster states.

Figures (5)

• Figure 1: Quantum circuit of teleportation-based squeezer. HD$_{\text{A}}$ - homodyne measurement in $x$-quadrature, HD$_{\text{B}}$ - homodyne measurement in $p$-quadrature , BS($t_1$) - beam splitter with transmission coefficient $t_1$, for generation of TMSV state. BS($t_2$) with transmission coefficient $t_2$ mixes the input state with one mode of the TMSV. D - feed-forward displacement, displaces the second mode of TMSV according to homodyne measurements. The gain of feed-forward is always set to unity. The gray dashed line indicates classical communication. The quadratures $\hat{x}_{in}$, $\hat{p}_{in}$ and $\hat{x}_{out}$, $\hat{p}_{out}$ describe the input and output states, respectively. The quadratures $\hat{x}_{s_1}$, $\hat{p}_{s_1}$ and $\hat{x}_{s_2}$, $\hat{p}_{s_2}$ correspond to oppositely squeezed vacuum states. The overall homodyne detection efficiency is denoted as $\eta_H$ and includes also mode-matching at the BS($t_2$). The excess noise in the anti-squeezed quadrature in the preparation of the squeezing resource is considered due to the overall outcoupling efficiency of squeezers, denoted as $\eta_S$. It effectively also includes the mode-matching at the BS($t_1$). The phase shift PS($\phi$) adjusts the phase of measured mode B and enables squeezing in output mode if $\phi \neq 0$. Beam splitters BS($t_i$) with variable transmission coefficient $t_i$ also contribute to squeezing in the output mode if $t_i^2 \neq 1/2$. The auxiliary phase shift PS($-\zeta$) and PS$(-\epsilon)$ compensate the rotation caused by PS($\phi$).
• Figure 2: The comparison of fidelities for a given squeezing-gate parameter $s$. a) Vacuum state in the lossless scenario; b) vacuum state in the realistic scenario with $\eta_S = 0.8$ and $\eta_H = 0.9$; c) Single photon state in the lossless scenario; d) Single photon state in the realistic scenario with $\eta_S = 0.8$ and $\eta_H = 0.9$. The different lines distinguish different protocols, PS-sq (full lines with squares) and BS-sq (dashed lines with circles), and three different squeezing levels of the resource squeezed states, 9 dB (blue), 6 dB (brown), and 3 dB (yellow). The lines for BSPS-sq overlap with the lines for BS-sq. An appropriate red marker depicts the entanglement-breaking bound. To the marker's right is a region where entanglement breaks. The combined symbol (circle inscribed in a square) is used when entanglement breaks simultaneously in both cases.
• Figure 3: The comparison of values of the $W(0,0)$ for the given target squeezing $s$ of the single photon state for teleportation-based squeezer. a) Lossless scenario; b) realistic scenario with $\eta_S = 0.8$ and $\eta_H = 0.9$. The different lines distinguish different squeezers, PS-sq (full lines with squares) and BS-sq (dashed lines with circles), and three different squeezing levels of the resource squeezed states, 9 dB (blue), 6 dB (brown), and 3 dB (yellow). The lines for BSPS-sq overlap with the lines for BS-sq. An appropriate red marker depicts the entanglement-breaking bound. To the marker's right is a region where entanglement breaks. The combined symbol (circle inscribed in a square) is used when entanglement breaks simultaneously in both cases.
• Figure 4: The comparison of total noise $N_T$ (noise added before squeezing) for a given squeezing parameter $s$. a) Vacuum state in the lossless scenario; b) vacuum state in the realistic scenario with $\eta_S = 0.8$ and $\eta_H = 0.9$; c) Single photon state in the lossless scenario; d) Single photon state in the realistic scenario with $\eta_S = 0.8$ and $\eta_H = 0.9$. The different lines distinguish different protocols, PS-sq (full lines with squares) and BS-sq (dashed lines with circles), and three different squeezing levels of the resource squeezed states, 9 dB (blue), 6 dB (brown), and 3 dB (yellow). The lines for BSPS-sq overlap with the lines for BS-sq.
• Figure 5: The comparison of the product of variances of noise operators $N_P$ for a given squeezing parameter $s$.a) Vacuum state in the lossless scenario; b) vacuum state in the realistic scenario with $\eta_S = 0.8$ and $\eta_H = 0.9$; c) Single photon state in the lossless scenario; d) Single photon state in the realistic scenario with $\eta_S = 0.8$ and $\eta_H = 0.9$. The different lines distinguish different protocols, PS-sq (full lines with squares) and BS-sq (dashed lines with circles), and three different squeezing levels of the resource squeezed states, 9 dB (blue), 6 dB (brown), and 3 dB (yellow). The lines for BSPS-sq overlap with the lines for BS-sq. The value of $1/4$ corresponds to the entanglement breaking bound, which is denoted by the red full line.