Skip to content
Shadow Theory

Quantum Source Completions and Memory–Environment Tradeoffs

References

Jeremy RodgersSection 14 of 14Original PDF ↗Publication DOI ↗

References

[1] Alessandro Bisio, Giacomo Mauro D’Ariano, Paolo Perinotti, and Michal Sedlák. Memory cost of quantum protocols. Physical Review A, 85:032333, 2012. doi: 10.1103/PhysRevA.85.032333. URL https://arxiv.org/pdf/1112.3853.

[2] Man-Duen Choi. Completely positive linear maps on complex matrices. Linear Algebra and its Applications, 10(3):285–290, 1975. doi: 10.1016/0024-3795(75)90075-0.

[3] Thomas J. Elliott. Memory compression and thermal efficiency of quantum implementations of nondeterministic hidden markov models. Physical Review A, 103:052615, 2021. doi: 10.1103/Phys RevA.103.052615. URL https://doi.org/10.1103/PhysRevA.103.052615.

[4] Hamza Fawzi, Joao Gouveia, Pablo A. Parrilo, Richard Z. Robinson, and Rekha R. Thomas. Positive semidefinite rank. Mathematical Programming, 153:133–177, 2015. doi: 10.1007/s10107-015-0922-1. URL https://arxiv.org/abs/1407.4095.

[5] David Gross. Hudson’s theorem for finite-dimensional quantum systems. Journal of Mathematical Physics, 47:122107, 2006. doi: 10.1063/1.2393152. URL https://arxiv.org/abs/quant-ph/06 02001.

[6] Rahul Jain, Yaoyun Shi, Zhaohui Wei, and Shengyu Zhang. Efficient protocols for generating bipartite classical distributions and quantum states. IEEE Transactions on Information Theory, 59(8):5171–5178, 2013. URL https://arxiv.org/abs/1203.1153.

[7] Alex Monràs and Andreas Winter. Quantum learning of classical stochastic processes: The completely-positive realization problem. Journal of Mathematical Physics, 57:015219, 2016. doi: 10.1063/1.4936935. URL https://arxiv.org/abs/1412.3634.

[8] Jason D. Padgett. Holographic mathematics: A dual representation of algebra, trigonometry, probability, and calculus in quantum information holography, . Undated supplied PDF manuscript; abstract and Sections 2–3.

[9] Jason D. Padgett. Quantum information holography, . Undated supplied manuscript; pages 64–68.

[10] Juha-Pekka Pellonpää and Mikko Tukiainen. Minimal normal measurement models of quantum instruments. Reports on Mathematical Physics, 79(3):261–278, 2017. doi: 10.1016/S0034-4877(17 )30040-X. URL https://arxiv.org/pdf/1509.08886.

[11] Paul M. Riechers and Thomas J. Elliott. Identifiability and minimality bounds of quantum and post-quantum models of classical stochastic processes, 2025. URL https://arxiv.org/html/250 9.03004v1. Version 1.

[12] Jeremy Rodgers. Exact markov extensions of three-time readouts: Hidden state counts, reversibility obstructions, and nonidentifiability, 2026. Version 1.0, 6 September 2026; supplied manuscript.

[13] Jeremy Rodgers. Source–readout non-equivalence: Descent and equivariant reconstruction ob-structions, 2026. URL https://doi.org/10.5281/zenodo.21369967.

[14] Emanuel Sperner. Ein satz über untermengen einer endlichen menge. Mathematische Zeitschrift, 27:544–548, 1928. URL https://geodesic.mathdoc.fr/item/MZ_1928__27_167993/.

[15] Rishi Sundar and Thomas J. Elliott. Quantum dimension reduction of hidden markov models. Physical Review A, 113:062461, 2026. doi: 10.1103/plt9-cm1x. URL https://arxiv.org/html/2 601.16126v2. Version 2, 1 July 2026.

[16] Michael M. Wolf and David Perez-Garcia. Quantum capacities of channels with small environment. Physical Review A, 75:012303, 2007. doi: 10.1103/PhysRevA.75.012303. URL https://arxiv.or g/abs/quant-ph/0607070.

Back to top ↑