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Gaussian entropic inequalities and uncertainty relations for communication and secure quantum key distribution

Total Cost €


EC-Contrib. €






Project "GENIUS" data sheet

The following table provides information about the project.


Organization address
address: NORREGADE 10
postcode: 1165

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Denmark [DK]
 Total cost 200˙194 €
 EC max contribution 200˙194 € (100%)
 Programme 1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
 Code Call H2020-MSCA-IF-2017
 Funding Scheme MSCA-IF-EF-ST
 Starting year 2018
 Duration (year-month-day) from 2018-04-01   to  2020-06-28


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    KOBENHAVNS UNIVERSITET DK (KOBENHAVN) coordinator 200˙194.00


 Project objective

Information and communication technologies are essential to modern society as the internet is pervading all aspects of our lives. Quantum mechanics imposes a fundamental limit to the communication rates. Determining this limit is one of the two challenges addressed by GENIUS. Given the amount of sensitive information sent through the internet, secure communications are essential to our society. To fulfill this need, the EU is investing in quantum key distribution (QKD) with the 1G€ Quantum Technology Flagship. The other challenge addressed by GENIUS is determining the maximum rate for secure communication that can be achieved by the forthcoming generation of QKD devices and proving their perfect security. To address the above challenges, I will firstly apply methods from functional analysis to prove new fundamental entropic inequalities for quantum Gaussian channels. Quantum Gaussian channels provide a mathematical model for the propagation of electromagnetic signals. Entropy is the core of information theory and quantifies the information content of a system. These inequalities will determine the maximum rates allowed by quantum mechanics for communication and QKD. Secondly, I aim to propose and prove a new fundamental entropic uncertainty relation for the heterodyne measurement. This uncertainty relation will prove the perfect security of the most promising QKD protocol. These new insights will have an enormous impact on both quantum communication and quantum cryptography and will stimulate what will be the first realization of quantum devices capable of communication and guaranteed perfectly secure QKD at the maximum possible rates. The experience of my supervisor Prof. Solovej in functional analysis and entropic inequalities combined with the experience of my co-supervisor Prof. Christandl in quantum cryptography make the QMATH group the ideal environment for carrying out this project and establishing myself as a leading independent multidisciplinary researcher.


year authors and title journal last update
List of publications.
2019 Giacomo De Palma
The squashed entanglement of the noiseless quantum Gaussian attenuator and amplifier
published pages: , ISSN: 1089-7658, DOI:
submitted to Journal of Mathematical Physics 2020-01-16
2019 Giacomo De Palma
The entropy power inequality with quantum conditioning
published pages: 08LT03, ISSN: 1751-8113, DOI: 10.1088/1751-8121/aafff4
Journal of Physics A: Mathematical and Theoretical 52/8 2020-01-16
2018 Giacomo De Palma, Dario Trevisan, Vittorio Giovannetti, Luigi Ambrosio
Gaussian optimizers for entropic inequalities in quantum information
published pages: 81101, ISSN: 0022-2488, DOI: 10.1063/1.5038665
Journal of Mathematical Physics 59/8 2020-01-16
2018 Giacomo De Palma, Dario Trevisan, Vittorio Giovannetti
The One-Mode Quantum-Limited Gaussian Attenuator and Amplifier Have GaussianMaximizers
published pages: 2919-2953, ISSN: 1424-0637, DOI: 10.1007/s00023-018-0703-5
Annales Henri Poincaré 19/10 2020-01-16
2018 Giacomo De Palma, Stefan Huber
The conditional entropy power inequality for quantum additive noise channels
published pages: 122201, ISSN: 0022-2488, DOI: 10.1063/1.5027495
Journal of Mathematical Physics 59/12 2020-01-16
2018 Giacomo De Palma, Johannes Borregaard
Minimum error probability of quantum illumination
published pages: 12101, ISSN: 2469-9934, DOI: 10.1103/physreva.98.012101
Physical Review A 98/1 2020-01-16
2019 Giacomo De Palma
New Lower Bounds to the Output Entropy of Multi-Mode Quantum Gaussian Channels
published pages: 5959-5968, ISSN: 0018-9448, DOI: 10.1109/tit.2019.2914434
IEEE Transactions on Information Theory 65/9 2020-01-16

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