Correlations for subsets of particles in symmetric states: what photons are doing within a beam of light when the rest are ignored
arXiv:2401.05484 · doi:10.1364/OPTICAQ.501218
Abstract
Given a state of light, how do its properties change when only some of the constituent photons are observed and the rest are neglected (traced out)? By developing formulae for mode-agnostic removal of photons from a beam, we show how the expectation value of any operator changes when only photons are inspected from a beam, ignoring the rest. We use this to reexpress expectation values of operators in terms of the state obtained by randomly selecting photons. Remarkably, this only equals the true expectation value for a unique value of : expressing the operator as a monomial in normally ordered form, must be equal to the number of photons annihilated by the operator. A useful corollary is that the coefficients of any -photon state chosen at random from an arbitrary state are exactly the th order correlations of the original state; one can inspect the intensity moments to learn what any random photon will be doing and, conversely, one need only look at the -photon subspace to discern what all of the th order correlation functions are. The astute reader will be pleased to find no surprises here, only mathematical justification for intuition. Our results hold for any completely symmetric state of any type of particle with any combination of numbers of particles and can be used wherever bosonic correlations are found.
11+3 pages, 1 figure, comments always welcome
References in corpus (19)
- Generation of Optical Coherent State Superpositions by Number-Resolved Photon Subtraction from Squeezed Vacuum
- Generation of large-amplitude coherent-state superposition via ancilla-assisted photon-subtraction
- Experimental nonclassicality of single-photon-added thermal light states
- Testing nonclassicality in multimode fields: a unified derivation of classical inequalities
- Generation of optical Schrödinger's cat states by generalized photon subtraction
- Exploring pure quantum states with maximally mixed reductions
- Direct, Loss-Tolerant Characterization of Nonclassical Photon Statistics
- Strategies for enhancing quantum entanglement by local photon subtraction
- Quantum correlations in optical metrology: Heisenberg-limited phase estimation without mode entanglement
- Tensor Representation of Spin States
- Quantum correlations in separable multi-mode states and in classically entangled light
- Multiqubit symmetric states with maximally mixed one-qubit reductions
- Higher-order sub-Poissonian-like nonclassical fields: Theoretical and experimental comparison
- Controlled multi-photon subtraction with cascaded Rydberg superatoms as single-photon absorbers
- Anticoherence measures for pure spin states
- Modifying quantum optical states by zero-photon subtraction
- Tailored quantum statistics from broadband states of light
- A theoretical framework for photon-subtraction with non-mode selective resources
- Quantum Polarimetry