In this paper, we prove a quantum union bound that is relevant when performing a sequence of binary-outcome quantum measurements on a quantum state. The quantum union bound proved here involves a tunable parameter that can be optimized, and this tunable parameter plays a similar role to a parameter involved in the Hayashi-Nagaoka inequality (Hayashi & Nagaoka 2003 IEEE Trans. Inf. Theory49, 1753-1768. (doi:10.1109/TIT.2003.813556)), used often in quantum information theory when analysing the error probability of a square-root measurement. An advantage of the proof delivered here is that it is elementary, relying only on basic properties of projectors, Pythagoras' theorem, and the Cauchy-Schwarz inequality. As a non-trivial application of our quantum union bound, we prove that a sequential decoding strategy for classical communication over a quantum channel achieves a lower bound on the channel's second-order coding rate. This demonstrates the advantage of our quantum union bound in the non-asymptotic regime, in which a communication channel is called a finite number of times. We expect that the bound will find a range of applications in quantum communication theory, quantum algorithms and quantum complexity theory.
Union bound for quantum information processing
Mancini, Stefano;
2019-01-01
Abstract
In this paper, we prove a quantum union bound that is relevant when performing a sequence of binary-outcome quantum measurements on a quantum state. The quantum union bound proved here involves a tunable parameter that can be optimized, and this tunable parameter plays a similar role to a parameter involved in the Hayashi-Nagaoka inequality (Hayashi & Nagaoka 2003 IEEE Trans. Inf. Theory49, 1753-1768. (doi:10.1109/TIT.2003.813556)), used often in quantum information theory when analysing the error probability of a square-root measurement. An advantage of the proof delivered here is that it is elementary, relying only on basic properties of projectors, Pythagoras' theorem, and the Cauchy-Schwarz inequality. As a non-trivial application of our quantum union bound, we prove that a sequential decoding strategy for classical communication over a quantum channel achieves a lower bound on the channel's second-order coding rate. This demonstrates the advantage of our quantum union bound in the non-asymptotic regime, in which a communication channel is called a finite number of times. We expect that the bound will find a range of applications in quantum communication theory, quantum algorithms and quantum complexity theory.File | Dimensione | Formato | |
---|---|---|---|
rspa-20180612.pdf
solo gestori di archivio
Descrizione: PDF
Tipologia:
Versione Editoriale
Licenza:
NON PUBBLICO - Accesso privato/ristretto
Dimensione
321.91 kB
Formato
Adobe PDF
|
321.91 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Union bound for quantum information processing.pdf
accesso aperto
Tipologia:
Versione Editoriale
Licenza:
DRM non definito
Dimensione
395.66 kB
Formato
Adobe PDF
|
395.66 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.