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arXiv:1704.07036 · Physical Review A

Beating the classical limits of information transmission using a quantum decoder

Robert J. Chapman, Akib Karim, Zixin Huang, Steven T. Flammia, Marco Tomamichel, Alberto Peruzzo

Published Jan 16, 2018• 11 citations

Abstract

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 $20%$ 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.

DOI: 10.1103/physreva.97.012315

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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.

We present and experimentally demonstrate a communication protocol that employs shared entanglement to reduce errors when sending a bit over a particular noisy classical channel. Specifically, it is shown that given a single use of this channel, one can transmit a bit with higher success probability when the sender and receiver share entanglement compared to the best possible strategy when they do not. The experiment is realized using polarization-entangled photon pairs, whose quantum correlations play a critical role in both the encoding and decoding of the classical message. Experimentally, we find that a bit can be successfully transmitted with probability 0.891±0.002, which is close to the theoretical maximum of (2+2(-1/2))/3≈0.902 and is significantly above the optimal classical strategy, which yields 5/6≈0.833.

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.

Quantum dense coding enables the transmission of two classical bits of information through the exchange of a single qubit, provided that an entangled state is shared between the communicating parties. While this protocol achieves a fundamental increase in channel capacity, its practical realization is strongly influenced by the presence of noise in realistic quantum channels. This work presents a simulation-based study of dense coding performance under two representative noise models: the depolarizing channel and the amplitude damping channel. Using Qiskit Aer, the bit error rate (BER), frame error rate (FER), and effective channel capacity are evaluated across a range of noise parameters. In addition, a classical threefold repetition strategy is examined as a lightweight error-mitigation technique. Results indicate that depolarizing noise produces more rapid degradation in both BER and channel capacity compared to amplitude damping, while repetition coding provides partial improvement in reliability at the expense of resource overhead. These findings highlight the trade-offs between efficiency and robustness in noisy implementations of dense coding and motivate further exploration of more advanced quantum error correction methods.

We investigate practical finite-blocklength classical–quantum channel coding over the quantum amplitude damping channel (ADC), aiming to transmit classical information reliably through quantum outputs. Our findings indicate that for any finite blocklength, a naive (uncoded) approach fails to offer any advantage over the ADC. Instead, sophisticated encoding strategies that leverage both classical error-correcting codes and quantum input states are crucial for realizing quantum performance gains at finite blocklengths.

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.