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Discord, Quantum Knowledge and Private Communications

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Lectures on General Quantum Correlations and their Applications

Part of the book series: Quantum Science and Technology ((QST))

Abstract

In this brief review, we discuss the role that quantum correlations, as quantified by quantum discord, play in two interesting settings. The first one is discerning which unitaries have been applied on a quantum system, by taking advantage of knowledge regarding its initial configuration. Here discord captures the ‘quantum’ component of this knowledge, useful only when we have access to a quantum memory. In particular, discord can be used to detect whether an untrusted party has certain quantum capabilities. The second setting is quantum cryptography. Here discord represents an important resource for trusted-noise quantum key distribution and also provides a general upper bound for the optimal secret key rates that are achievable by ideal protocols. In particular, the (two-way assisted) secret key capacity of a lossy bosonic channel exactly coincides with the maximum discord that can be distributed between the remote parties at the two ends of the channel.

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Acknowledgements

Authors acknowledge financial support from the National Research Foundation of Singapore (NRF), NRF-Fellowship (Reference No: NRF-NRFF2016-02), the John Templeton Foundation (Grant No 54914) and the EPSRC via the ‘UK Quantum Communications Hub’ (EP/M013472/1).

Author information

Authors and Affiliations

  1. School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 639673, Singapore

    Mile Gu

  2. Complexity Institute, Nanyang Technological University, Singapore, 637723, Singapore

    Mile Gu

  3. Centre for Quantum Technologies, National University of Singapore, Singapore, 117543, Singapore

    Mile Gu

  4. Computer Science & York Centre for Quantum Technologies, University of York, York, YO10 5GH, UK

    Stefano Pirandola

Authors
  1. Mile Gu
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  2. Stefano Pirandola
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Corresponding author

Correspondence to Stefano Pirandola .

Editor information

Editors and Affiliations

  1. São Paulo State University, São Paulo, Brazil

    Felipe Fernandes Fanchini

  2. São Carlos Institute of Physics, University of São Paulo, São Paulo, Brazil

    Diogo de Oliveira Soares Pinto

  3. School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom

    Gerardo Adesso

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Gu, M., Pirandola, S. (2017). Discord, Quantum Knowledge and Private Communications. In: Fanchini, F., Soares Pinto, D., Adesso, G. (eds) Lectures on General Quantum Correlations and their Applications. Quantum Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-53412-1_11

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