Uncertainty relations in the theory of open quantum systems

Hamid Reza Naeij, Afshin Shafiee

Thibaut Lacroix

Aleksander Sukhanov

The quantum oscillator in the thermostat is considered as the model of an open quantum system. Our analysis will be heavily founded on the use of the Schroedinger generalized uncertainties relations (SUR). Our first aim is to demonstrate that for the quantum oscillator the state of thermal equilibrium belongs to the correlated coherent states (CCS), which imply the saturation of SUR at any temperature. The obtained results open the perspective for the search of some statistical theory, which unifies the elements of quantum mechanics and GDT; this in turn will give the foundation for the modification of the standard thermodynamics.

Shang-Bin Han, Shuaijie Li, Jing-Jun Zhang +1 more

The fine-grained uncertainty relation (FUR) is investigated for accelerating open quantum system, which manifests the celebrated Unruh effect, a crucial piece of the jigsaw for combining relativity and quantum physics. For a single detector, we show that the inevitable Unruh decoherence can induce a smaller FUR uncertainty bound, which indicates an additional measurement uncertainty may exist. For an open system combined with two detectors, via a nonlocal retrieval game, the related FUR uncertainty bound is determined by the non-classical correlation of the system. By estimating the maximal violation of Bell inequality for an accelerating system, we show that the FUR uncertainty bound can be protected from Unruh decoherence, due to quantum correlation generated through Markovian dynamics.

Jitendra777 J.B.S mandloi

This work introduces SPQT (Stillness–Periphery Quantum Theory), an operational framework for parameterizing uncertainty relations in open quantum systems. Rather than treating quantum uncertainty as purely fundamental, SPQT characterizes how observable uncertainties scale with two measurable system properties: - Stillness (S): the purity or coherence of the quantum state- Periphery (Γ): environmental interaction strength and decoherence Using these quantities, we define an effective operational scale:ℏ_eff = ℏ(1 + λΓ/S) and derive a phenomenological uncertainty relation applicable to Gaussian and weakly perturbed states. The paper provides three complementary derivations:1. Diffusion of Gaussian wavepackets2. Steady-state variances from Lindblad dynamics3. Purity–covariance relations for Gaussian states SPQT recovers standard Heisenberg uncertainty for pure, isolated systems (S=1, Γ=0) and predicts measurable variance increases in realistic environments including cold atoms, trapped ions, cavity QED, and superconducting circuits. This framework offers a compact, experimentally testable parameterization of how decoherence and mixedness modify observable quantum uncertainties, while preserving the fundamental commutation relation [x,p]=iℏ. Note: SPQT is a phenomenological reframing of known open quantum system effects, presented as an alternative operational perspective rather than a fundamental extension of quantum mechanics. The parameter λ is phenomenological and must be determined from microscopic models or fitted to experimental data.