Quantum Coherence
More accurately, the resource theory of quantum coherence, aims to describe the phenomenon of quantum superposition, and clarify its connections with other sui generis quantum effects such as (in the case of several particles) entanglement. It is a particular (but possibly the most illustrative, along with entanglement) case of quantum resource theory:
A quantum resource theory is based on two main ingredients, the free states and the free operations. [...] The free states — states which do not possess any resource and are cheap to prepare — are the incoherent states, that is, quantum states which are diagonal in a fixed reference basis.
coherence is basis dependent, so wherever we talk about coherence we must be clear which basis is presupposed.
The most important paper is by Baumgratz et al.[1] who study it in finite-dimensional Hilbert spaces, measuring coherence through the distance between the state and its closest incoherent state. The first work in that direction, however, is an unpublished arXiv preprint by Johan Aberg with a better terminology than "coherence" (namely, "superpositions").[2] Streltsov et al.[3] used entanglement.
Marc Aßmann et al. brought those concepts within the problem of polariton condensation.[4][5][6][7]
A crime in terminology
From Streltsov et al.[8]
From Wu et al.[9]
From Killoran et al.[10]
Interesting papers
- Quantum resource theories. E. Chitambar and G. Gour in Rev. Mod. Phys. 91:025001 (2019). (review)
- Quantifying Coherence. T. Baumgratz, M. Cramer and M. Plenio in Phys. Rev. Lett. 113:140401 (2014).
- How to quantify coherence: Distinguishing speakable and unspeakable notions. I. Marvian and R. W. Spekkens in Phys. Rev. A 94:052324 (2016).
- Quantum coherence as a resource. A. Streltsov, G. Adesso and M. B. Plenio in Rev. Mod. Phys. 89:041003 (2017). (review)
- Maximal coherence and the resource theory of purity. A. Streltsov, H. Kampermann, S. Wölk, M. Gessner and D. Bruß in New J. Phys. 20:053058 (2018). links quantum coherence to purity.
- Converting Nonclassicality into Entanglement. N. Killoran, F. Steinh and n. M. Plenio in Phys. Rev. Lett. 116:080402 (2016).
- Two novel pure-state coherence measures in quantifying coherence. M. Hazra and D. Goswami in Quantum Inf. Comput. 24:945 (2024).
Continuous variables
The original theory[1] was developped for finite-dimensional Hilbert spaces. There has been several attempts at extending it to infinite spaces:
- Quantifying coherence of Gaussian states. J. Xu in Phys. Rev. A 93:032111 (2016).
- Quantifying coherence in infinite-dimensional systems. Y. Zhang, L. Shao, Y. Li and H. Fan in Phys. Rev. A 93:012334 (2016).
- Quantifying the Coherence between Coherent States. K. C. Tan, T. Volkoff, H. Kwon and H. Jeong in Phys. Rev. Lett. 119:190405 (2017).
- Hierarchy of continuous-variable quantum resource theories. G. Gianfelici, H. Kampermann and D. Bruß in New J. Phys. 23:113008 (2021).
As a variation, or precursor, to that lies the problem of the phase of coherent states. Chief papers on that question include:
- Quantum Phase of a Bose-Einstein Condensate with an Arbitrary Number of Atoms. J. Javanainen and S. M. Yoo in Phys. Rev. Lett. 76:161 (1996).
- Optical coherence: A convenient fiction. K. Molmer in Phys. Rev. A 55:3195 (1997).
- Quantum entanglement and classical behaviour. K. Molmer in J. Mod. Opt. 44:1937 (1997).
- Reply to "Comment on 'Optical coherence: A convenient fiction'''. K. Molmer in Phys. Rev. A 58:4247 (1998).
- Macroscopic Entanglement and Relative Phase. G. Nienhuis in 🕮Modern Challenges in Quantum Optics, Springer Nature, page 95 (2001) [ISBN: 978-3-540-41957-0].
- Dialogue concerning two views on quantum coherence: factist and fictionist. S. D. Bartlett, T. Rudolph and R. W. Spekkens in Int. J. Quantum Inform. 04:17 (2006).
- Decoherence of a two-state atom driven by coherent light. H. Nha and H. J. Carmichael in Phys. Rev. A 71:013805 (2005).
- Disentanglement of Source and Target and the Laser Quantum State. C. Noh and H. J. Carmichael in Phys. Rev. Lett. 100:120405 (2008).
- Open system entanglement and the laser quantum state. H. Carmichael and C. Noh in Physica E 42:399 (2010).
- Decoherence and the conditions for the classical control of quantum systems. G. J. Milburn in Phil. Trans. R. Soc. A 370:4469 (2012).
References
- ↑ 1.0 1.1 Quantifying Coherence. T. Baumgratz, M. Cramer and M. Plenio in Phys. Rev. Lett. 113:140401 (2014).
- ↑ Template:Aberg arXiv06a
- ↑ Measuring Quantum Coherence with Entanglement. A. Streltsov, U. Singh, H. S. Dhar, M. N. Bera and G. Adesso in Phys. Rev. Lett. 115:020403 (2015).
- ↑ Quantifying Quantum Coherence in Polariton Condensates. C. Lüders, M. Pukrop, E. Rozas, C. Schneider, S. Höfling, J. Sperling, S. Schumacher and M. Aßmann in Phys. Rev. X Quantum 2:030320 (2021).
- ↑ Tracking Quantum Coherence in Polariton Condensates with Time-Resolved Tomography. C. Lüders, M. Pukrop, F. Barkhausen, E. Rozas, C. Schneider, S. Höfling, J. Sperling, S. Schumacher and M. Aßmann in Phys. Rev. Lett. 130:113601 (2023).
- ↑ Continuous-variable quantum optics and resource theory for ultrafast semiconductor spectroscopy [Invited]. C. Lüders, F. Barkhausen, M. Pukrop, E. Rozas, J. Sperling, S. Schumacher and M. Aßmann in Opt. Mater. Express 13:2997 (2023).
- ↑ Quantum coherence of a long-lifetime exciton-polariton condensate. Y. Brune, E. Rozas, K. West, K. Baldwin, L. Pfeiffer, J. Beaumariage, H. Alnatah, D. Snoke and M. Aßmann in Commun. Mater. 6:123 (2025).
- ↑ Quantum coherence as a resource. A. Streltsov, G. Adesso and M. B. Plenio in Rev. Mod. Phys. 89:041003 (2017).
- ↑ Experimental Progress on Quantum Coherence: Detection, Quantification and Manipulation. K. Wu, A. Streltsov, B. Regula, G. Xiang, C. Li and G. Guo in Adv. Quantum Technol. 4:2100040 (2021).
- ↑ Converting Nonclassicality into Entanglement. N. Killoran, F. Steinh and n. M. Plenio in Phys. Rev. Lett. 116:080402 (2016).