The Squeezed State — Quadrature Squeezing and Quantum-Enhanced Sensing
Act 19 of the NexusOS physics sequence. First disclosed 2026-07-21. AGPL-3.0. Founder: Te Rata Pou.
Definition
A squeezed state reduces one quadrature's noise below vacuum while increasing conjugate noise. Heisenberg uncertainty is preserved: ΔX₁ΔX₂≥¼ for X̂₁=(â+â†)/2, X̂₂=(â−â†)/2i. Ideal pure squeezed vacuum aligned with these axes saturates the bound. Single-mode operator: S(ξ)=exp(ξ★â²/2−ξ↲/2), with ξ=r·e^(iθ).
Quadrature Noise
For θ=0: ΔX₁=e^(−r)/2 and ΔX₂=e^r/2. At r≈1.15 (10 dB squeezing), the squeezed uncertainty is 31.6% of vacuum. Record squeezing: −15 dB (Vahlbruch 2016).
Photon-Number Statistics and Wigner Function
Ideal single-mode squeezed vacuum is a pure Gaussian state with n̄=sinh²(r) and Var(n)=2n̄(n̄+1). For r≠0 it is super-Poissonian: Var(n)>n̄ and Mandel Q=2n̄+1>0. At r=0, Q is undefined because the mean is zero. Some displaced amplitude-squeezed states can be sub-Poissonian depending on displacement and squeezing angle; quadrature squeezing alone does not imply reduced photon-number noise. Squeezed vacuum has a non-negative Gaussian Wigner function. Gaussian squeezing alone does not imply Wigner negativity; negativity requires a non-Gaussian state.
Two-Mode Squeezing and EPR Entanglement
S₂(ξ)=exp(ξ★â_sâ_i−ξâ†_sâ†_i) produces an ideal pure entangled pair. Tracing out one partner gives a mixed thermal reduced state with n̄=sinh²(r), unlike pure single-mode squeezed vacuum. For the stated real positive squeeze convention, x_s+x_i and p_s−p_i become arbitrarily quiet as r→∞.
WNSP Connection — Hypothesis
NexusOS proposes squeezed-light sensing at λ=1550 nm in SNIC WGM cavities. Ideally, 10 dB phase-quadrature squeezing reduces phase uncertainty by √10 relative to vacuum noise for the same sensing carrier. This does not remove the energy cost of the external pump. WNSP integration, channel capacity and security benefits remain hypotheses requiring hardware tests and protocol-specific security analysis, not demonstrated guarantees.
The 20-Act Sequence
The Squeezed State
Act 19 of the NexusOS research sequence.
Established basis
Squeezing reduces one quadrature's noise while increasing the conjugate noise. Ideal squeezed vacuum is super-Poissonian and has a non-negative Gaussian Wigner function.
NexusOS proposal
Squeezed Ψ readout is a proposed integration of established optical techniques.
Evidence limits
Quadrature squeezing does not automatically suppress photon-number noise or establish hardware performance.
Hardware fundraising and promotions paused pending engineering review. Working software models; reported electrical tests on three Coiltek bifilar coils. Integrated SNIC, optical relay, quantum memory and ZERO-G performance have not been demonstrated by those tests.
Original numbered disclosures are research claims, not independent experimental validation or granted patents.
Read the research transparency recordExplore the Act and its research context