Quantum limits on squeezing

• URL: http://arxiv.org/abs/2604.22500v1
• Date: Fri, 24 Apr 2026 12:28:04 GMT
• Title: Quantum limits on squeezing
• Abstract summary: We show how, for a network of bosonic modes, canonical commutation relations constrain the coefficients relating input and internal modes.<n>We derive a lower bound on the total steady-state squeezing achievable in reservoir-engineered (dissipative) squeezing schemes, quantified by the sum of mode-optimal quadrature variances normalized to its corresponding input variance.
• Score: 2.660415540961114
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In our work, we show how, for a network of bosonic modes, canonical commutation relations constrain the coefficients relating input and internal modes. Based on these constraints, we derive a lower bound on the total steady-state squeezing achievable in reservoir-engineered (dissipative) squeezing schemes, quantified by the sum of mode-optimal quadrature variances normalized to its corresponding input variance. The bound follows solely from canonical commutation relations and stability, and is saturated in the strong-coupling limit at 1. Furthermore, we show that adding independent parametric driving terms for each mode changes the quantum noise-gain balance and yields a distinct optimum bound, approaching 1/2. In addition, we show how these constraints allow us to reformulate the Duan inseparability criterion for a three-mode bosonic system in terms of a single parameter-dependent figure of merit. Our results apply directly to current electromechanical and nanomechanical experiments and indicate that the two-mode bounds can be experimentally approached even at room temperature.

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