Neural networks can identify an optical quantum state from an image of its phase-space function, but a real measurement gives a finite record of $N$ detection events. Heterodyne detection samples the Husimi $Q$ function directly, whereas homodyne detection gives the Wigner function only after a reconstruction from several phases. We ask which scheme better identifies one of seven families of states, including Gottesman-Kitaev-Preskill (GKP) states, under loss, dephasing and Gaussian noise. We simulate finite records on identical states for two sets of families, one with equal mean photon number and one built from the code of Ahmed et al. For convolutional networks, heterodyne detection outperforms homodyne detection with filtered back-projection by 14.1 percentage points at $N=100$ events and 20% dephasing in the first set (adjusted $p=0.003$ over $24$ cells across training runs), and it depends on the number of phases and on the reconstruction. At $N=10^3$ and $10^4$ no difference is significant, but the intervals are wide. At $N=100$ , a homodyne network without reconstruction does not differ significantly from heterodyne detection in the first set and is nominally worse in the second. Near thermal states we show to leading order that heterodyne detection damps phase-space structure of order $n$ exponentially, whereas homodyne detection shares unit weight among $n+1$ angular components, a local result that does not explain the finite-record differences. Experimental records of a GKP state, photon-subtracted squeezed states and one mode of an Einstein-Podolsky-Rosen source are classified like simulated ones, but these low-power tests probe our counting-noise model, not the seven-class accuracy. A likelihood-ratio observer shows no such gap at $N=100$ , so our evidence concerns a reconstruction-based pipeline, not homodyne detection in general.Neural networks can identify an optical quantum state from an image of its phase-space function, but a real measurement gives a finite record of $N$ detection events. Heterodyne detection samples the Husimi $Q$ function directly, whereas homodyne detection gives the Wigner function only after a reconstruction from several phases. We ask which scheme better identifies one of seven families of states, including Gottesman-Kitaev-Preskill (GKP) states, under loss, dephasing and Gaussian noise. We simulate finite records on identical states for two sets of families, one with equal mean photon number and one built from the code of Ahmed et al. For convolutional networks, heterodyne detection outperforms homodyne detection with filtered back-projection by 14.1 percentage points at $N=100$ events and 20% dephasing in the first set (adjusted $p=0.003$ over $24$ cells across training runs), and it depends on the number of phases and on the reconstruction. At $N=10^3$ and $10^4$ no difference is significant, but the intervals are wide. At $N=100$, a homodyne network without reconstruction does not differ significantly from heterodyne detection in the first set and is nominally worse in the second. Near thermal states we show to leading order that heterodyne detection damps phase-space structure of order $n$ exponentially, whereas homodyne detection shares unit weight among $n+1$ angular components, a local result that does not explain the finite-record differences. Experimental records of a GKP state, photon-subtracted squeezed states and one mode of an Einstein-Podolsky-Rosen source are classified like simulated ones, but these low-power tests probe our counting-noise model, not the seven-class accuracy. A likelihood-ratio observer shows no such gap at $N=100$, so our evidence concerns a reconstruction-based pipeline, not homodyne detection in general.

quant-pharXiv:2610.38671Oct 30, 20260 citations

Experimental study of balanced optical homodyne and heterodyne detection by controlling sideband modulation

Wei Li, Xudong Yu, Zengming Meng +2 more

arXiv:1508.04974Science China Physics Mechanics and AstronomySep 4, 20156 citations

Experimental study of balanced optical homodyne and heterodyne detection by controlling sideband modulation

Li We

We experimentally study optical homodyne and heterodyne detections with the same setup, which is flexible to manipulate the signal sideband modulation. When the modulation only generates a single signal sideband, the light field measurement by mixing the single sideband at ω0 ±? with a strong local oscillator at the carrier frequency ω0on a beam splitter becomes balanced heterodyne detection. When two signal sidebands at ω0 ±? are generated and the relative phase of the two sidebands is locked, this measurement corresponds to optical balanced homodyne detection. With this setup, we may confirm directly that the signal-to-noise ratio with heterodyne detection is two-fold worse than that with homodyne detection. This work will have important applications in quantum state measurement and quantum information.We experimentally study optical homodyne and heterodyne detections with the same setup, which is flexible to manipulate the signal sideband modulation. When the modulation only generates a single signal sideband, the light field measurement by mixing the single sideband at ω0 ±? with a strong local oscillator at the carrier frequency ω0on a beam splitter becomes balanced heterodyne detection. When two signal sidebands at ω0 ±? are generated and the relative phase of the two sidebands is locked, this measurement corresponds to optical balanced homodyne detection. With this setup, we may confirm directly that the signal-to-noise ratio with heterodyne detection is two-fold worse than that with homodyne detection. This work will have important applications in quantum state measurement and quantum information.

Science in China. Series G, Physics, mechanics & astronomy/Science in China. Series G, Physics, Mechanics & AstronomyJan 1, 20150 citations

Neural networks can identify an optical quantum state from an image of its phase-space function, but a real measurement gives a finite record of

N

detection events. Heterodyne detection samples the Husimi

Q

function directly, whereas homodyne detection gives the Wigner function only after a reconstruction from several phases. We ask which scheme better identifies one of seven families of states, including Gottesman-Kitaev-Preskill (GKP) states, under loss, dephasing and Gaussian noise. We simulate finite records on identical states for two sets of families, one with equal mean photon number and one built from the code of Ahmed et al. For convolutional networks, heterodyne detection outperforms homodyne detection with filtered back-projection by 14.1 percentage points at

N=100

events and 20% dephasing in the first set (adjusted

p=0.003

over

24

cells across training runs), and it depends on the number of phases and on the reconstruction. At

N=10^3

and

10^4

no difference is significant, but the intervals are wide. At

N=100

, a homodyne network without reconstruction does not differ significantly from heterodyne detection in the first set and is nominally worse in the second. Near thermal states we show to leading order that heterodyne detection damps phase-space structure of order

n

exponentially, whereas homodyne detection shares unit weight among

n+1

angular components, a local result that does not explain the finite-record differences. Experimental records of a GKP state, photon-subtracted squeezed states and one mode of an Einstein-Podolsky-Rosen source are classified like simulated ones, but these low-power tests probe our counting-noise model, not the seven-class accuracy. A likelihood-ratio observer shows no such gap at

N=100

, so our evidence concerns a reconstruction-based pipeline, not homodyne detection in general.