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arXiv:quant-ph/0304037 · Physical Review Letters

Exceeding the Classical Capacity Limit in a Quantum Optical Channel

Mikio Fujiwara, Masahiro Takeoka, Jun Mizuno, Masahide Sasaki

Published Apr 24, 2003• 111 citations
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Abstract

The amount of information transmissible through a communications channel is determined by the noise characteristics of the channel and by the quantities of available transmission resources. In classical information theory, the amount of transmissible information can be increased twice at most when the transmission resource is doubled for fixed noise characteristics. In quantum information theory, however, the amount of information transmitted can increase even more than twice. We present a proof-of-principle demonstration of this superadditivity of classical capacity of a quantum channel by using the ternary symmetric states of a single photon, and by event selection from a weak coherent light source. We also show how the superadditive coding gain, even in a small code length, can boost the communication performance of the conventional coding technique.

DOI
10.1103/physrevlett.90.167906

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The amount of information transmissible through a communications channel is determined by the noise characteristics of the channel and by the quantities of available transmission resources. In classical information theory, the amount of transmissible information can be increased twice at most when the transmission resource is doubled for fixed noise characteristics. In quantum information theory, however, the amount of information transmitted can increase even more than twice. We present a proof-of-principle demonstration of this superadditivity of classical capacity of a quantum channel by using the ternary symmetric states of a single photon, and by event selection from a weak coherent light source. We also show how the superadditive coding gain, even in a small code length, can boost the communication performance of the conventional coding technique.
Quantum-information theory predicts that when the transmission resource is doubled in quantum channels, the amount of information transmitted can be increased more than twice by quantum-channel coding technique, whereas the increase is at most twice in classical information theory. This remarkable feature, the superadditive quantum-coding gain, can be implemented by appropriate choices of code words and corresponding quantum decoding which requires a collective quantum measurement. Recently, an experimental demonstration was reported [M. Fujiwara et al., Phys. Rev. Lett. 90, 167906 (2003)]. The purpose of this paper is to describe our experiment in detail. Particularly, a design strategy of quantum-collective decoding in physical quantum circuits is emphasized. We also address the practical implication of the gain on communication performance by introducing the quantum-classical hybrid coding scheme. We show how the superadditive quantum-coding gain, even in a small code length, can boost the communication performance of conventional coding techniques.
We consider a channel coding for sending classical information through a quantum channel with a given ensemble of quantum states (letter states). As is well known, it is generically possible in a quantum channel that the transmittable information in block coding of length nnn can exceed nnn times the maximum amount that can be sent without any coding scheme. This so-called superadditivity in classical capacity of a quantum channel is a distinct feature that cannot be found in a classical memoryless channel. In this paper, a practical model of channel coding that shows this property is presented. It consists of a simple code-word selection and the optimum decoding of the code words minimizing the average error probability. At first, optimization of decoding strategy is discussed. Then the channel coding that shows the superadditivity in classical capacity is demonstrated.
Quantum communication channels differ from their classical counterparts because their capacities can be superadditive. The principle of monogamy of entanglement suggests that superadditive improvements in the transmission capacity of a channel should reduce the amount of information loss to the environment. We challenge this intuition by demonstrating that the coherent and private information of a channel and its complement can be simultaneously superadditive for arbitrarily many channel uses. To quantify the limits of this effect, we consider the notion of max (resp. total) private information of a channel, which represents the maximum (resp. sum) of the private information of the channel itself and its complement, and study its relationship with the coherent information of the individual direct and complementary channels. We show that these quantities can obey different interleaving sequences of inequalities for a varying number of channel uses.
Coherent information quantifies the achievable rate of the reliable quantum information transmission through a communication channel. Use of the correlated quantum states (multiletter codes) instead of the factorized ones (single-letter codes) may result in an increase in the achievable rate, a phenomenon known as the coherent-information superadditivity. However, even for simple physical models of channels it is rather difficult to detect the superadditivity and find the advantageous multiletter codes. Here we consider the case of polarization dependent losses and propose some physically motivated multiletter codes which outperform all single-letter ones in a wide range of the channel parameters. We show that in the asymptotic limit of the infinite code length the superadditivity phenomenon takes place whenever the communication channel is neither degradable nor antidegradable. Besides the superadditivity identification, we also provide a method how to modify the proposed codes and get a higher quantum communication rate by doubling the code length. The obtained results give a deeper understanding of useful multiletter codes and may serve as a benchmark for quantum capacity estimations and future approaches toward an optimal strategy to transfer quantum information.
We investigate superadditivity in the maximum achievable rate of reliable classical communication over a quantum channel. The maximum number of classical information bits extracted per use of the quantum channel strictly increases as the number of channel outputs jointly measured at the receiver increases. This phenomenon is called superadditivity. We provide an explanation of this phenomenon by comparing a quantum channel with a classical discrete memoryless channel (DMC) under concatenated codes. We also give a lower bound on the maximum accessible information per channel use at a finite length of quantum measurements in terms of V, which is the quantum version of channel dispersion, and C, the classical capacity of the quantum channel.
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 channel and provide a lower bound on C[subscript 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 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[subscript N]/N to be equal to a given fraction of the asymptotic capacity C of the respective channel, N must be proportional to V/C², where V is the respective channel dispersion quantity.