Superadditivity of Quantum Channel Coding Rate with Finite Blocklength Joint Measurements

Abstract

The maximum rate at which classical information can be reliably transmitted per use of a quantum channel strictly increases in general with $N$, the number of channel outputs that are detected jointly by the quantum joint-detection receiver (JDR). This phenomenon is known as superadditivity of the maximum achievable information rate over a quantum channel. We study this phenomenon for a pure-state classical-quantum (cq) channel and provide a lower bound on $C_N/N$, the maximum information rate when the JDR is restricted to making joint measurements over no more than $N$ quantum channel outputs, while allowing arbitrary classical error correction. We also show the appearance of a superadditivity phenomenon---of mathematical resemblance to the aforesaid problem---in the channel capacity of a classical discrete memoryless channel (DMC) when a concatenated coding scheme is employed, and the inner decoder is forced to make hard decisions on $N$-length inner codewords. Using this correspondence, we develop a unifying framework for the above two notions of superadditivity, and show that for our lower bound to $C_N/N$ to be equal to a given fraction of the asymptotic capacity $C$ of the respective channel, $N$ must be proportional to $V/C^2$, where $V$ is the respective channel dispersion quantity.

To appear in IEEE Transactions on Information Theory

References in corpus (8)

• The Chernoff lower bound for symmetric quantum hypothesis testing
• Ultimate communication capacity of quantum optical channels by solving the Gaussian minimum-entropy conjecture
• Second-Order Asymptotics for the Classical Capacity of Image-Additive Quantum Channels
• Capacity of optical communication in loss and noise with general Gaussian receivers
• Sequential projective measurements for channel decoding
• Optimal Measurements for Symmetric Quantum States with Applications to Optical Communication
• Achieving the Holevo bound via a bisection decoding protocol
• Second-order coding rates for pure-loss bosonic channels

Cited by in corpus (8)

• Quantum Limits in Optical Communications
• Classical capacity per unit cost for quantum channels
• On capacity of optical communications over a lossy bosonic channel with a receiver employing the most general coherent electro-optic feedback control
• Demonstration of quantum advantage by a joint detection receiver for optical communications using quantum belief propagation on a trapped-ion device
• Capacity of a lossy photon channel with direct detection
• Quantum $f$-divergences via Nussbaum-Szkoła Distributions and Applications to $f$-divergence Inequalities
• How Deep the Theory of Quantum Communications Goes: Superadditivity, Superactivation and Causal Activation
• Attaining classical capacity per unit cost of noisy bosonic Gaussian channels