Communication through coherent control of quantum channels

Alastair A. Abbott1,2, Julian Wechs2, Dominic Horsman3, Mehdi Mhalla3, and Cyril Branciard2

1Département de Physique Appliquée, Université de Genève, 1211 Genève, Switzerland
2Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
3Univ. Grenoble Alpes, CNRS, Grenoble INP, LIG, 38000 Grenoble France

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Abstract

A completely depolarising quantum channel always outputs a fully mixed state and thus cannot transmit any information. In a recent Letter[3], it was however shown that if a quantum state passes through two such channels in a quantum superposition of different orders---a setup known as the ``quantum switch''---then information can nevertheless be transmitted through the channels. Here, we show that a similar effect can be obtained when one coherently controls between sending a target system through one of two identical depolarising channels. Whereas it is tempting to attribute this effect in the quantum switch to the indefinite causal order between the channels, causal indefiniteness plays no role in this new scenario. This raises questions about its role in the corresponding effect in the quantum switch. We study this new scenario in detail and we see that, when quantum channels are controlled coherently, information about their specific implementation is accessible in the output state of the joint control-target system. This allows two different implementations of what is usually considered to be the same channel to therefore be differentiated. More generally, we find that to completely describe the action of a coherently controlled quantum channel, one needs to specify not only a description of the channel (e.g., in terms of Kraus operators), but an additional ``transformation matrix'' depending on its implementation.

The standard framework in quantum computing is that of quantum circuits, where quantum operations are applied to physical systems in a definite causal order. Recently, it has been found that one can go beyond this paradigm, and connect quantum operations in more exotic ways – e.g., with no well-defined causal order. Such indefinite orders open up new possibilities for quantum computing and quantum communication.
In that context, a particular quantum communication effect has attracted substantial interest. A completely noisy quantum channel cannot transmit any information by itself. However, information transmission is possible if two such channels are applied in a superposition of orders – or more precisely, in an order that is coherently determined by a control qubit, taken to be in a quantum superposition.
In our work, we show that a similar phenomenon occurs in an even simpler situation where a control qubit determines which of the two channels acts on the target system, rather than their order. This raises interesting questions about how this communication advantage is related to indefinite causal order.
Our study of this example leads us to a more general analysis of the concept of a quantum-controlled channel, which turns out to be ill-defined. We show that for a complete account of the situation one needs more information about the channel implementation than is usually considered.

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Cited by

[1] Giulio Chiribella and Hlér Kristjánsson, "Quantum Shannon theory with superpositions of trajectories", Proceedings of the Royal Society of London Series A 475 2225, 20180903 (2019).

[2] Giulio Chiribella, Manik Banik, Some Sankar Bhattacharya, Tamal Guha, Mir Alimuddin, Arup Roy, Sutapa Saha, Sristy Agrawal, and Guruprasad Kar, "Indefinite causal order enables perfect quantum communication with zero capacity channel", arXiv:1810.10457.

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[5] Yu Guo, Xiao-Min Hu, Zhi-Bo Hou, Huan Cao, Jin-Ming Cui, Bi-Heng Liu, Yun-Feng Huang, Chuan-Feng Li, Guang-Can Guo, and Giulio Chiribella, "Experimental transmission of quantum information using a superposition of causal orders", arXiv:1811.07526.

[6] Philippe Allard Guérin, Giulia Rubino, and Časlav Brukner, "Communication through quantum-controlled noise", Physical Review A 99 6, 062317 (2019).

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[8] Philippe Allard Guérin, Giulia Rubino, and Časlav Brukner, "Communication through quantum-controlled noise", arXiv:1812.06848.

[9] Márcio M. Taddei, Jaime Cariñe, Daniel Martínez, Tania García, Nayda Guerrero, Alastair A. Abbott, Mateus Araújo, Cyril Branciard, Esteban S. Gómez, Stephen P. Walborn, Leandro Aolita, and Gustavo Lima, "Experimental computational advantage from superposition of multiple temporal orders of quantum gates", arXiv:2002.07817.

[10] Lorenzo M. Procopio, Francisco Delgado, Marco Enríquez, Nadia Belabas, and Juan Ariel Levenson, "Sending classical information via three noisy channels in superposition of causal orders", Physical Review A 101 1, 012346 (2020).

[11] Nicolas Loizeau and Alexei Grinbaum, "Channel capacity enhancement with indefinite causal order", Physical Review A 101 1, 012340 (2020).

[12] Qingxiuxiong Dong, Shojun Nakayama, Akihito Soeda, and Mio Murao, "Controlled quantum operations and combs, and their applications to universal controllization of divisible unitary operations", arXiv:1911.01645.

[13] Giulio Chiribella, Matthew Wilson, and H. F. Chau, "Quantum and Classical Data Transmission Through Completely Depolarising Channels in a Superposition of Cyclic Orders", arXiv:2005.00618.

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[22] Matthew Wilson and Giulio Chiribella, "A Diagrammatic Approach to Information Transmission in Generalised Switches", arXiv:2003.08224.

[23] K. Goswami, Y. Cao, G. A. Paz-Silva, J. Romero, and A. G. White, "Increasing communication capacity via superposition of order", Physical Review Research 2 3, 033292 (2020).

[24] Alexandre Clément and Simon Perdrix, "PBS-Calculus: A Graphical Language for Coherent Control of Quantum Computations", arXiv:2002.09387.

[25] Nicola Pinzani and Stefano Gogioso, "Giving Operational Meaning to the Superposition of Causal Orders", arXiv:2003.13306.

[26] Tamal Guha, Mir Alimuddin, and Preeti Parashar, "Thermodynamic advancement in the causally inseparable occurrence of thermal maps", arXiv:2003.01464.

[27] Yujie Zhang, Xinan Chen, and Eric Chitambar, "Building Multiple Access Channels with a Single Particle", arXiv:2006.12475.

[28] K. Goswami and J. Romero, "Experiments on quantum causality", arXiv:2009.00515.

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