The Beta-Bound: Drift constraints for Gated Quantum Probabilities

• URL: http://arxiv.org/abs/2601.22188v1
• Date: Thu, 29 Jan 2026 01:36:31 GMT
• Title: The Beta-Bound: Drift constraints for Gated Quantum Probabilities
• Abstract summary: This paper develops a measurement-theoretic framework for projective gating.<n>The central object is the $$-bound, an inequality that controls how much probability assignments can drift when gating and measurement fail to commute.<n>Three experimental vignettes demonstrate falsifiability.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum mechanics provides extraordinarily accurate probabilistic predictions, yet the framework remains silent on what distinguishes quantum systems from definite measurement outcomes. This paper develops a measurement-theoretic framework for projective gating. The central object is the $β$-bound, an inequality that controls how much probability assignments can drift when gating and measurement fail to commute. For a density operator $ρ$, projector $F$, and effect $E$, with gate-passage probability $s = {\rm Tr}(ρF)$ and commutator norm $\varepsilon = \|[F, E]\|$, the symmetric partial-gating drift satisfies $|Δp_F(E)| \leq 2 \sqrt{(1 - s)/s} \cdot \varepsilon$. The constant 2 is sharp. We introduce two diagnostic quantities: the coherence witness $W(ρ, F) = \|F ρ(I - F)\|_1$, measuring cross-boundary coherence, and the record fidelity gap $Δ_T(ρ_F, R)$, measuring expectation-value change under symmetrisation. Three experimental vignettes demonstrate falsifiability: Hong--Ou--Mandel interferometry, atomic energy-basis dephasing, and decoherence-induced classicality. The framework is operational and interpretation-neutral, compatible with Everettian, Bohmian, QBist, and collapse approaches. It provides quantitative structure that any interpretation must accommodate, along with a template for experimental tests.

Related papers

• Quantifying Multipartite Entanglement Based on unified entropy [8.011717889271603]
  We show that our lower bounds provide tighter estimates of quantum entanglement than several existing analytical bounds.<n>We rigorously prove that when the parameters $q$ and $s$ are in certain ranges, $Ak_q,s()$ and $Gk_q,s()$ also satisfy monotonicity and strong monotonicity.
  arXiv  Detail & Related papers  (2026-08-24T00:54:24Z)
• Robust quantum state certification and uncertainty principles for total influence [5.7531205491708945]
  We show that nonadaptive single-qubit Pauli measurements suffice to test whether an unknown $n$-qubit state $$ is $varepsilon$-close to or $O(varepsilon)$-far from an ideal target state $|rangle$.<n>The test uses $O(varepsilon-2log (1/)$ copies of $$ to achieve confidence $1-$, which is information-theoretically optimal even among protocols with arbitrary joint measurements.
  arXiv  Detail & Related papers  (2026-07-29T17:53:23Z)
• Effective Dimension Governs Generalization in Quantum Kernel Vision Models [31.082191748525137]
  We show that entanglement structure and quantum noise are two knobs that move $d_rm eff$.<n>Amplitude damping contracts $d_rm eff$ and lifts test accuracy by up to $+13%$ along an inverted-U sweet spot.
  arXiv  Detail & Related papers  (2026-06-18T12:55:59Z)
• Wavelet Variance Equipartition as a Threshold for World-Model Quality and Quantum Kernel TN-Simulability [0.0]
  We identify the wavelet scaling exponent $$ as a critical diagnostic.<n>We establish $= 1/2$ as a sharp transition boundary for the classical simulability of amplitude-encoded quantum kernels.<n>We prove this variance scales strictly as $Var[X] = (d-2)$.
  arXiv  Detail & Related papers  (2026-05-12T05:41:12Z)
• Universal Description of Decoherence in Scale-Invariant Environments [0.0]
  We show that when a quantum system couples to a scale-invariant environment, what form must its decoherence take?<n>We validate the framework using multi-channel transport data from the unitary Fermi gas.<n>We show that quantum Ising criticality, inflationary cosmology, and high-energy astrophysical neutrinos are unified as specific realizations of the same structure.
  arXiv  Detail & Related papers  (2026-04-16T18:03:43Z)
• Theta-term in Russian Doll Model: phase structure, quantum metric and BPS multifractality [45.88028371034407]
  We investigate the phase structure of the deterministic and disordered versions of the Russian Doll Model (RDM)<n>We find the pattern of phase transitions in the global charge $Q(theta,gamma)$, which arises from the BA equation.<n>We conjecture that the Hamiltonian of the RDM model describes the mixing in particular 2d-4d BPS sector of the Hilbert space.
  arXiv  Detail & Related papers  (2025-10-23T17:25:01Z)
• Mesoscopic Fluctuations and Multifractality at and across Measurement-Induced Phase Transition [46.176861415532095]
  We explore statistical fluctuations over the ensemble of quantum trajectories in a model of two-dimensional free fermions.<n>Our results exhibit a remarkable analogy to Anderson localization, with $G_AB$ corresponding to two-terminal conductance.<n>Our findings lay the groundwork for mesoscopic theory of monitored systems, paving the way for various extensions.
  arXiv  Detail & Related papers  (2025-07-15T13:44:14Z)
• Entropic characterization of Tunneling and State Pairing in a Quasi-Exactly Solvable Sextic Potential [0.0]
  We analyze a quasi-exactly solvable (QES) sextic potential $V_textQES(x) = frac12(x6 + 2x4 - 2(2lambda + 1)x2)$ as a function of the parameter $lambda in [-frac34, 6]$.<n>For $lambda > -frac12$, the potential exhibits a symmetric double-well structure, with tunneling emerging for the ground state level at $lambda approx
  arXiv  Detail & Related papers  (2025-06-27T23:31:49Z)
• Controlling Symmetries and Quantum Criticality in the Anisotropic Coupled-Top Model [32.553027955412986]
  We investigate the anisotropic coupled-top model, which describes the interactions between two large spins along both $x-$ and $y-$directions.<n>We can manipulate the system's symmetry, inducing either discrete $Z$ or continuous U(1) symmetry.<n>The framework provides an ideal platform for experimentally controlling symmetries and investigating associated physical phenomena.
  arXiv  Detail & Related papers  (2025-02-13T15:14:29Z)
• The role of shared randomness in quantum state certification with unentangled measurements [36.19846254657676]
  We study quantum state certification using unentangled quantum measurements. $Theta(d2/varepsilon2)$ copies are necessary and sufficient for state certification. We develop a unified lower bound framework for both fixed and randomized measurements.
  arXiv  Detail & Related papers  (2024-01-17T23:44:52Z)
• One-dimensional pseudoharmonic oscillator: classical remarks and quantum-information theory [0.0]
  Motion of a potential that is a combination of positive quadratic and inverse quadratic functions of the position is considered. The dependence on the particle energy and the factor $mathfraka$ describing a relative strength of its constituents is described.
  arXiv  Detail & Related papers  (2023-04-13T11:50:51Z)
• Full Counting Statistics across the Entanglement Phase Transition of Non-Hermitian Hamiltonians with Charge Conservations [4.923287660970805]
  We study the full counting statistics (FCS) $Z(phi, O)equiv sum_o eiphi oP(o)$ for 1D systems described by non-Hermitian SYK-like models. In both the volume-law entangled phase for interacting systems and the critical phase for non-interacting systems, the conformal symmetry emerges, which gives $F(phi, Q_A)equiv log Z(phi, Q_A)sim phi2log |A|$
  arXiv  Detail & Related papers  (2023-02-19T03:51:04Z)
• A Quantum Algorithm Framework for Discrete Probability Distributions with Applications to Rényi Entropy Estimation [13.810917492304565]
  We propose a unified quantum algorithm framework for estimating properties of discrete probability distributions. Our framework estimates $alpha$-R'enyi entropy $H_alpha(p)$ to within additive error $epsilon$ with probability at least $2/3$.
  arXiv  Detail & Related papers  (2022-12-03T08:01:55Z)
• Laboratory-frame tests of quantum entanglement in $H \to WW$ [0.0]
  Quantum entanglement between the two $W$ bosons resulting from the decay of a Higgs boson may be investigated in the dilepton channel $H to WW to ell nu ell nu$ The dilepton invariant mass distribution, already measured by the ATLAS and CMS Collaborations at the LHC, can be used to observe the quantum entanglement of the $WW$ pair.
  arXiv  Detail & Related papers  (2022-09-28T12:22:12Z)
• Consistent Density Estimation Under Discrete Mixture Models [20.935152220339056]
  This work considers a problem of estimating a mixing probability density $f$ in the setting of discrete mixture models. In particular, it is shown that there exists an estimator $f_n$ such that for every density $f$ $lim_nto infty mathbbE left[ int |f_n -f | right]=0$.
  arXiv  Detail & Related papers  (2021-05-03T18:30:02Z)
• Energy-Time Uncertainty Relation for Absorbing Boundaries [0.0]
  We prove the uncertainty relation $sigma_T, sigma_E geq hbar/2$ between the time $T$ of detection of a quantum particle on the surface.
  arXiv  Detail & Related papers  (2020-05-29T12:04:57Z)
• Quantum Algorithms for Simulating the Lattice Schwinger Model [63.18141027763459]
  We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x-1/2$ and electric field cutoff $x-1/2Lambda$. We estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density.
  arXiv  Detail & Related papers  (2020-02-25T19:18:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.