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arXiv:1109.1029

Entanglement enhancement of a noisy classical communication channel

H. T. Williams, Paul Bourdon

Published Sep 5, 2011• 0 citations
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Abstract

We present a formal quantum mechanical analysis of the communication protocol of Prevedel {\it et al.}\ [Phys. Rev. Lett. \textbf{106}, 110505 (2011)], in which entanglement shared by sender and receiver is used to enhance, beyond that achievable via the optimal classical strategy, the probability of successful transmission of a bit through a particular noisy classical channel ${\cal N}$. We provide a full analysis of this protocol when the shared entanglement resides in a two-qubit system. Our analysis shows the measurement choices specified by the protocol yield the maximum possible enhancement of the probability of successful communication of the bit with one use of the channel ${\cal N}$. We determine that shared entanglement residing in a two-qudit system with $d > 2$ cannot provide enhancement beyond that produced by entangled qubits. Finally, we show how the protocol should be extended when probability parameters for the channel ${\cal N}$ are allowed to vary.

DOI
10.48550/arxiv.1109.1029

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We present a formal quantum mechanical analysis of the communication protocol of Prevedel {\it et al.}\ [Phys. Rev. Lett. \textbf{106}, 110505 (2011)], in which entanglement shared by sender and receiver is used to enhance, beyond that achievable via the optimal classical strategy, the probability of successful transmission of a bit through a particular noisy classical channel N{\cal N}N. We provide a full analysis of this protocol when the shared entanglement resides in a two-qubit system. Our analysis shows the measurement choices specified by the protocol yield the maximum possible enhancement of the probability of successful communication of the bit with one use of the channel N{\cal N}N. We determine that shared entanglement residing in a two-qudit system with d>2d > 2d>2 cannot provide enhancement beyond that produced by entangled qubits. Finally, we show how the protocol should be extended when probability parameters for the channel N{\cal N}N are allowed to vary.
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 one-shot success probability of a noisy classical channel for transmitting one classical bit is the optimal probability with which the bit can be successfully sent via a single use of the channel. Prevedel et al. [Phys. Rev. Lett. 106, 110505 (2011)] recently showed that for a specific channel, this quantity can be increased if the parties using the channel share an entangled quantum state. In this paper, we characterize the optimal entanglement-assisted protocols in terms of the radius of a set of operators associated with the channel. This characterization can be used to construct optimal entanglement-assisted protocols for a given classical channel and to prove the limits of such protocols. As an example, we show that the Prevedel et al. protocol is optimal for two-qubit entanglement. We also prove some tight upper bounds on the improvement that can be obtained from quantum and nonsignaling correlations.
A fundamental limitation of quantum communication is that a single qubit can carry at most one bit of classical information. For an important class of quantum communication channels, known as entanglement breaking, this limitation holds even if the sender and receiver share entangled particles. But does this mean that, for the purpose of communicating classical messages, a noisy entanglement-breaking qubit channel can be replaced by a noisy bit channel? Here we answer the question in the negative. We introduce a game, similar to the Monty Hall problem in classical statistics, where a sender assists a receiver in finding a valuable item (the "prize") hidden in one of four possible boxes, while avoiding a hazardous item (the "bomb") hidden in one of the remaining three boxes. We show that no classical strategy using a noisy bit channel can ensure that the bomb is avoided, even if the sender and receiver share arbitrary amounts of randomness. In contrast, communication of a qubit through a class of noisy entanglement-breaking channels, which we call quantum not channels, allows the players to deterministically avoid the bomb and to find the prize with a guaranteed nonzero probability. Our findings show that the communication of classical messages through a noisy entanglement-breaking qubit channel assisted by quantum entanglement cannot, in general, be simulated by communication through a noisy bit channel assisted by classical correlations.
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 Æ 0:002, which is close to the theoretical maximum of ð2 þ 2 À1=2 Þ=3 % 0:902 and is significantly above the optimal classical strategy, which yields 5=6 % 0:833.
A fundamental limitation of quantum communication is that a single qubit can carry at most 1 bit of classical information. For an important class of quantum communication channels, known as entanglement-breaking, this limitation holds even if the sender and receiver share entangled particles. But does this mean that, for the purpose of communicating classical messages, a noisy entanglement-breaking qubit channel can be replaced by a noisy bit channel? Here we answer the question in the negative. We introduce a game, similar to the Monty Hall problem in classical statistics, where a sender assists a receiver in finding a valuable item (the prize) hidden into one of four possible boxes, while avoiding a hazardous item (the bomb) hidden in one of the remaining three boxes. We show that no classical strategy using a noisy bit channel can ensure that the bomb is avoided, even if the sender and receiver share arbitrary amounts of randomness. In contrast, communication of a qubit through a class of noisy entanglement-breaking channels, which we call quantum NOT channels, allows the players to deterministically avoid the bomb and to find the prize with a guaranteed nonzero probability. Our findings show that the communication of classical messages through a noisy entanglement-breaking qubit channel assisted by quantum entanglement cannot, in general, be simulated by communication through a noisy bit channel assisted by classical correlations.
We analyze utility of communication channels in absence of any short of quantum or classical correlation shared between the sender and the receiver. To this aim, we propose a class of two-party communication games, and show that the games cannot be won given a noiseless 1 -bit classical channel from the sender to the receiver. Interestingly, the goal can be perfectly achieved if the channel is assisted with classical shared randomness. This resembles an advantage similar to the quantum superdense coding phenomenon where pre-shared entanglement can enhance the communication utility of a perfect quantum communication line. Quite surprisingly, we show that a qubit communication without any assistance of classical shared randomness can achieve the goal, and hence establishes a novel quantum advantage in the simplest communication scenario. In pursuit of a deeper origin of this advantage, we show that an advantageous quantum strategy must invoke quantum interference both at the encoding step by the sender and at the decoding step by the receiver. We also study communication utility of a class of non-classical toy systems described by symmetric polygonal state spaces. We come up with communication tasks that can be achieved neither with 1 -bit of classical communication nor by communicating a polygon system, whereas 1 -qubit communication yields a perfect strategy, establishing quantum advantage over them. To this end, we show that the quantum advantages are robust against imperfect encodings-decodings, making the protocols implementable with presently available quantum technologies.