On entanglement assistance to a noiseless classical channel

Péter E. Frenkel1,2 and Mihály Weiner3,4

1Eötvös Loránd University, Pázmány Péter sétány 1/C, Budapest, 1117 Hungary
2Rényi Institute, Budapest, Reáltanoda u. 13-15, 1053 Hungary
3Budapest University of Technology and Economics (BME), Department of Analysis, H-1111 Budapest Műegyetem rkp. 3–9 Hungary
4MTA-BME Lendület Quantum Information Theory Research Group

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For a classical channel, neither the Shannon ca-pa-city, nor the sum of conditional probabilities corresponding to the cases of successful transmission can be increased by the use of shared entanglement, or, more generally, a non-signaling resource. Yet, perhaps somewhat counterintuitively, entanglement assistance can help and actually elevate the chances of success even in a one-way communicational task that is to be completed by a single-shot use of a noiseless classical channel.

To quantify the help that a non-signaling resource provides to a noiseless classical channel, one might ask how many extra letters should be added to the alphabet of the channel in order to perform equally well $without$ the specified non-signaling resource. As was observed by Cubitt, Leung, Matthews, and Winter, there is no upper bound on the number of extra letters required for substituting the assistance of a general non-signaling resource to a noiseless one-bit classical channel. In contrast, here we prove that if this resource is a bipartite quantum system in a maximally entangled state, then an extra classical bit always suffices as a replacement.

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[1] Michele Dall'Arno, "The signaling dimension of physical systems", Quantum Views 6, 66 (2022).

[2] Sahil Gopalkrishna Naik, Govind Lal Sidhardh, Samrat Sen, Arup Roy, Ashutosh Rai, and Manik Banik, "Distilling Nonlocality in Quantum Correlations", Physical Review Letters 130 22, 220201 (2023).

[3] Jef Pauwels, Stefano Pironio, Emmanuel Zambrini Cruzeiro, and Armin Tavakoli, "Adaptive Advantage in Entanglement-Assisted Communications", Physical Review Letters 129 12, 120504 (2022).

[4] Martin J. Renner, Armin Tavakoli, and Marco Túlio Quintino, "Classical Cost of Transmitting a Qubit", Physical Review Letters 130 12, 120801 (2023).

[5] Eric Chitambar, Ian George, Brian Doolittle, and Marius Junge, "The Communication Value of a Quantum Channel", IEEE Transactions on Information Theory 69 3, 1660 (2023).

[6] Mir Alimuddin, Ananya Chakraborty, Govind Lal Sidhardh, Ram Krishna Patra, Samrat Sen, Snehasish Roy Chowdhury, Sahil Gopalkrishna Naik, and Manik Banik, "Advantage of Hardy's nonlocal correlation in reverse zero-error channel coding", Physical Review A 108 5, 052430 (2023).

[7] Jef Pauwels, Armin Tavakoli, Erik Woodhead, and Stefano Pironio, "Entanglement in prepare-and-measure scenarios: many questions, a few answers", New Journal of Physics 24 6, 063015 (2022).

[8] Carlos Vieira, Carlos de Gois, Lucas Pollyceno, and Rafael Rabelo, "Interplays between classical and quantum entanglement-assisted communication scenarios", New Journal of Physics 25 11, 113004 (2023).

[9] Armin Tavakoli, Jef Pauwels, Erik Woodhead, and Stefano Pironio, "Correlations in Entanglement-Assisted Prepare-and-Measure Scenarios", PRX Quantum 2 4, 040357 (2021).

[10] Vaisakh M, Ram krishna Patra, Mukta Janpandit, Samrat Sen, Manik Banik, and Anubhav Chaturvedi, "Mutually unbiased balanced functions and generalized random access codes", Physical Review A 104 1, 012420 (2021).

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