Quantum States Seen by a Probe: Partial Trace Over a Region of Space (2403.10501v1)
Abstract: The partial trace operation is usually considered in composite quantum systems, to reduce the state on a single subsystem. This operation has a key role in the decoherence effect and quantum measurements. However, partial trace operations can be defined in more generic situations. In particular, it can be used to restrict a quantum state (for a single or several quantum entities) on a specific region of space, the rest of the universe being treated as an environment. The reduced state is then interpreted as the state that can be detected by an ideal probe with a limited spatial extent. In this paper, such an operation is investigated for systems defined on a Fock Hilbert space. A generic expression of the reduced density matrix is computed, and it is applied to several case studies: eigenstates of the number operator, coherent states, and thermal states. These states admit very different behaviors. In particular, (i) a decoherence effect happens on eigenstates of the number operator (ii) coherent or thermal states remain coherent or thermal, but with an amplitude/temperature reduced non-trivially by the overlap between the field and the region of interest.
- “The Theory of Open Quantum Systems”. Oxford University Press. (2007).
- Kurt Jacobs. “Quantum measurement theory and its applications”. Cambridge University Press. (2014).
- “Quantum noise: a handbook of markovian and non-markovian quantum stochastic methods with applications to quantum optics”. Springer Science & Business Media. (2004). url: https://link.springer.com/book/9783540223016.
- “Adiabatic elimination for open quantum systems with effective lindblad master equations”. In 2016 IEEE 55th Conference on Decision and Control (CDC). Pages 4559–4565. (2016).
- “Quantum field theory on curved spacetimes: Axiomatic framework and examples”. Journal of Mathematical Physics 57, 031101 (2016). arXiv:https://pubs.aip.org/aip/jmp/article-pdf/doi/10.1063/1.4939955/14803718/031101_1_online.pdf.
- “Covariant loop quantum gravity: an elementary introduction to quantum gravity and spinfoam theory”. Cambridge University Press. (2015).
- Quentin Ansel. “A model of spinfoam coupled with an environment”. General Relativity and Gravitation 53, 39 (2021).
- S. W. Hawking. “Particle creation by black holes”. Communications in Mathematical Physics 43, 199–220 (1975).
- “The unruh effect and its applications”. Rev. Mod. Phys. 80, 787–838 (2008).
- “Tomography of quantum detectors”. Nature Physics 5, 27–30 (2009).
- “Local mapping of detector response for reliable quantum state estimation”. Nature communications 5, 4332 (2014).
- “Quantum state reconstruction of the single-photon fock state”. Phys. Rev. Lett. 87, 050402 (2001).
- “Photon counting probabilities in quantum optics”. Optica Acta: International Journal of Optics 28, 981–996 (1981).
- Anthony Mark Fox. “Quantum optics: an introduction”. Volume 15. Oxford University Press, USA. (2006).
- “Exploring the quantum: Atoms, cavities, and photons”. OUP Oxford. (2006).
- “Photonic quantum metrology”. AVS Quantum Science 2, 024703 (2020).
- Eberhard Zeidler. “Creation and annihilation operators”. Pages 771–791. Springer Berlin, Heidelberg. Berlin, Heidelberg (2009).
- R. Honegger and A. Rieckers. “Photons in fock space and beyond”. G - Reference,Information and Interdisciplinary Subjects Series. World Scientific. (2015).
- S. N. M. Ruijsenaars. “On bogoliubov transformations. II. the general case”. Annals of Physics 116, 105–134 (1978).
- “Holstein-primakoff/bogoliubov transformations and the multiboson system”. Fortschritte der Physik/Progress of Physics 45, 145–156 (1997).
- B. Yurke and D. Stoler. “Measurement of amplitude probability distributions for photon-number-operator eigenstates”. Phys. Rev. A 36, 1955–1958 (1987).
- “Lorentzian quantum gravity via pachner moves: one-loop evaluation”. Journal of High Energy Physics 2023, 1–50 (2023).
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