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Chinese Physics

Entanglement-enhanced classical communication through generalized amplitude damping channel

Hou Li-Zhen, Mao-Fa Fang

Published Jan 24, 2007• 2 citations
Publisher

Abstract

The problem of sending a single classical bit through a generalized amplitude damping channel is considered. When two transmissions through the channel are available as a resource, we find that two entangled transmissions can enhance the capability of receiver's judging information correctly under certain conditions compared with two product-state transmissions. In addition, we find a special case in which the two entangled transmissions can always make a classical bit more effectively disable the noise influence.

DOI
10.1088/1009-1963/16/2/008

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The problem of sending a single classical bit through a generalized amplitude damping channel is considered. When two transmissions through the channel are available as a resource, we find that two entangled transmissions can enhance the capability of receiver's judging information correctly under certain conditions compared with two product-state transmissions. In addition, we find a special case in which the two entangled transmissions can always make a classical bit more effectively disable the noise influence.
Encoding schemes and error-correcting codes are widely used in information technology to improve the reliability of data transmission over real-world communication channels. Quantum information protocols can further enhance the performance in data transmission by encoding a message in quantum states; however, most proposals to date have focused on the regime of a large number of uses of the noisy channel, which is unfeasible with current quantum technology. We experimentally demonstrate quantum enhanced communication over an amplitude damping noisy channel with only two uses of the channel per bit and a single entangling gate at the decoder. By simulating the channel using a photonic interferometric setup, we experimentally increase the reliability of transmitting a data bit by greater than 2020%20 for a certain damping range over classically sending the message twice. We show how our methodology can be extended to larger systems by simulating the transmission of a single bit with up to eight uses of the channel and a two-bit message with three uses of the channel, predicting a quantum enhancement in all cases.
Entanglement is an important resource for various applications of quantum computation. Another important endeavor is to establish the role of entanglement in practical implementation where system of interest is affected by various kinds of noisy channels. Here, a single classical bit is used to send information under the influence of a noisy quantum channel. The entanglement content of quantum states is computed under noisy channels such as amplitude damping, phase damping, squeesed generalised amplitude damping, Pauli channels and various collective noise models on the protocols of quantum key distribution.
The entanglement-assisted capacity of a generalized amplitude damping channel is investigated by using the properties of partial symmetry and concavity of mutual information. The numerical and analytical results of the entanglement-assisted capacity are obtained under certain conditions. It is shown that the entanglement-assisted capacity depends on the channel parameters representing the ambient temperature and dissipation, and the prior entanglement between sender and receiver can approximately double the classical capacity of the generalized amplitude damping channel.
Entanglement of quantum states is a very important resource in quantum communication systems. For many special tasks, entanglement is found to be helpful. But it is still a problem how to find the relationship between the amount of entanglement and the effect of doing the task. In this work, we consider a particular task—trying to send a single classical bit as effective as possible through a noisy quantum channel and two transmissions through the channel are available as a resource. For two special channels—amplitude damping channel and two-Pauli channel, we separately establish the quantitative connections, and try to find whether the relationship is always monotonous, i.e., the states with the larger entanglement necessarily result in the better effect. Unfortunately, this is not true. At the same time, we can get the optimal codes for the task using this method.
Can entangling codewords across independent uses of a quantum channel improve the rate of classical communication? An old conjecture states that there is no such entanglement advantage for all channels. Although Hastings's result and follow-up works disproved this conjecture, it turns out that enormous dimension is required to construct a channel where entanglement enhances classical communication. This indicates that there might be no entanglement advantage for many physical channels, or for all low dimensional channels. Motivated by recent progress on (generalized) amplitude damping channels, we propose a general Schur-weighted block entropy inequality, and show that there is no entanglement advantage for all phase-covariant channels including multi-level amplitude damping channels, generalized dephasing channels, and damping-dephasing channels. As a by-product, we also recover the recently established result that there is no entanglement advantage for all qubit channels.