The Coherent State Projection Eigenvalue Theorem

Peter D. Drummond; Margaret D. Reid

Home/Archive/arXiv

arXiv · 2610.33613

The Coherent State Projection Eigenvalue Theorem

Peter D. Drummond·Margaret D. Reid

View original source ↗Read source document ↗Export metadata ↓

Abstract

Recent papers have developed a cyclic symmetry projected extension for coherent state representations of bosonic Hilbert space. This extension can greatly reduce sampling errors in phase-space simulations of bosonic quantum systems that have symmetries. Here we prove an eigenvalue theorem for the continuum limit of the projected coherent states. Our intuitively appealing result is that in the continuum limit the projected coherent states are eigenstates of the symmetry generating operator. This result gives a differential identity in phase-space that includes the conserved eigenvalues. Detailed applications of these differential identities to obtaining improved Fokker-Planck and stochastic equations in many-body physics will be given elsewhere.

Explore related subjects

quant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Peter D. Drummond, Margaret D. Reid. 2026-10-24. The Coherent State Projection Eigenvalue Theorem. https://arxiv.org/abs/2610.33613

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Conditional Motional Squeezing of an Optomechanical Oscillator Approaching the Quantum Regime

Squeezed mechanical states are a highly coveted resource for quantum-enhanced sensing and serve as a compelling platform for probing the interplay between gravity and quantum mechanics. It has been predicted that a mechanical oscillator can be prepared into a quantum squeezed state if the applied measurement rate is fast relative to its mechanical resonance frequency. However, the experimental feasibility of this protocol has remained uncertain because of the difficulty in achieving low-frequency oscillators with sufficiently strong read-out. Here, we demonstrate that a careful selection of parameters in an optomechanical system, combined with optimal filtering techniques, enables the preparation of a 50 ng GaAs cantilever in a conditional classical squeezed state, achieving a minimum uncertainty of just 1.07 plus/minus 0.04 times the zero-point fluctuation level. This minimum variance is 3 orders of magnitude smaller than what has been achieved in previous experiments using the same protocol. Although we do not fully achieve the quantum squeezed regime, our demonstration provides definitive evidence that a measurement-based protocol is a practical and effective approach for the real-time preparation of macroscopic oscillators in quantum squeezed states.

quant-ph↗

arXiv2026

Quantum Counting in the Rydberg Blockade

We propose a quantum algorithm for approximately counting the number of solutions to planar 2-satisfiability (2SAT) formulas natively on neutral-atom quantum computers (NAQC). Our algorithm maps Boolean variables to atomic registers arranged in space according to a given formula, so that 2SAT constraints are enforced via the Rydberg blockade between neighboring atoms. A quench of an initial computational basis state then produces a superposition of all solutions after sufficiently long evolution. For almost uniform superpositions, a polynomial number of measurements is enough to estimate the solution count up to any constant multiplicative factor via sampling-based counting. Numerical simulations show that the protocol leads to almost uniform solution sampling in 1D and 2D grids and produces accurate counts for small random 2SAT instances on punctured grids. We implement our algorithm on Pasqal's Orion Alpha NAQC and demonstrate approximate counts within small multiplicative factors of the exact count for a planar grid instance with 81 atoms.

quant-ph↗

arXiv2026

Proofs of Quantum Memory

In this paper, we introduce a new concept, proofs of quantum memory (PoQM). A PoQM is an interactive protocol between a classical verifier and a quantum prover over a classical channel where the verifier can verify that the prover has possessed a specified number of qubits for a specified period of time. PoQM generalize proofs of quantumness (PoQ) [Brakerski, Christiano, Mahadev, Vazirani, and Vidick, JACM 2021] where a classical verifier can verify that the prover is not classical. Our contributions are summarized as follows: We introduce PoQM. We also introduce a variant of PoQM, which we call inefficient-verifier PoQM (IV-PoQM), where the verifier's final computation to make the decision is not necessarily efficient. We construct PoQM based on the hardness of LWE. Specifically, we give two constructions of PoQM. The first one is of two-round and has negligible soundness error under the subexponential-hardness of LWE. The second one is of polynomial-round and has inverse-polynomial soundness error under the polynomial-hardness of LWE. We show that IV-PoQM imply one-way puzzles. Moreover, we show that a certain restricted version of PoQM implies quantum computation classical communication key exchange, which suggests the difficulty of black-box constructing PoQM from one-way functions. We show that constant-round PoQ imply PoQM or single-round PoQ (with a quantum verifier). Single-round PoQ are ``trivial'' PoQ in the sense that the verifier asks the prover to solve a classical problem which is quantumly easy but classically hard. The result therefore demonstrates that PoQM capture ``genuinely-interactive'' PoQ. We show that if constant-round IV-PoQ that are black-box constructed from quantumly-secure falsifiable assumptions exist then IV-PoQM exist. This result implies that IV-PoQM can be constructed from quantumly-secure constant-round statistically-hiding commitments.

quant-ph↗