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Civil War Book Review

Stochastic resonance in Gaussian quantum channels

Cosmo Lupo, Stefano Mancini, Mark M. Wilde

Published Feb 1, 2013• 5 citations
OpenAlex

Abstract

We determine conditions for the presence of stochastic resonance in a lossy bosonic channel with a nonlinear, threshold decoding. The stochastic resonance effect occurs if and only if the detection threshold is outside of a 'forbidden interval'. We show that it takes place in different settings: when transmitting classical messages through a lossy bosonic channel, when transmitting over an entanglement-assisted lossy bosonic channel and when discriminating channels with different loss parameters. Moreover, we consider a setting in which stochastic resonance occurs in the transmission of a qubit over a lossy bosonic channel with a particular encoding and decoding. In all cases, we assume the addition of Gaussian noise to the signal and show that it does not matter who, between sender and receiver, introduces such a noise. Remarkably, different results are obtained when considering a setting for private communication. In this case, the symmetry between sender and receiver is broken and the 'forbidden interval' may vanish, leading to the occurrence of stochastic resonance effects for any value of the detection threshold. © 2013 IOP Publishing Ltd.

Related papers

Stochastic resonance in Gaussian quantum channels

Cosmo Lupo, Stefano Mancini, Mark M. Wilde

We determine conditions for the presence of stochastic resonance in a lossy bosonic channel with a nonlinear, threshold decoding. The stochastic resonance effect occurs if and only if the detection threshold is outside of a 'forbidden interval'. We show that it takes place in different settings: when transmitting classical messages through a lossy bosonic channel, when transmitting over an entanglement-assisted lossy bosonic channel and when discriminating channels with different loss parameters. Moreover, we consider a setting in which stochastic resonance occurs in the transmission of a qubit over a lossy bosonic channel with a particular encoding and decoding. In all cases, we assume the addition of Gaussian noise to the signal and show that it does not matter who, between sender and receiver, introduces such a noise. Remarkably, different results are obtained when considering a setting for private communication. In this case, the symmetry between sender and receiver is broken and the 'forbidden interval' may vanish, leading to the occurrence of stochastic resonance effects for any value of the detection threshold.

arXiv:1109.4147•Journal of Physics A Mathematical and Theoretical•Jan 10, 2013•4 citations

Quantum forbidden-interval theorems for stochastic resonance

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Civil War Book Review•Dec 2, 2009•20 citations

Can classical noise enhance quantum transmission?

Mark M. Wilde

A modified quantum teleportation protocol broadens the scope of the classical forbidden-interval theorems for stochastic resonance. The fidelity measures performance of quantum communication. The sender encodes the two classical bits for quantum teleportation as weak bipolar subthreshold signals and sends them over a noisy classical channel. Two forbidden-interval theorems provide a necessary and sufficient condition for the occurrence of the nonmonotone stochastic resonance effect in the fidelity of quantum teleportation. The condition is that the noise mean must fall outside a forbidden interval related to the detection threshold and signal value. An optimal amount of classical noise benefits quantum communication when the sender transmits weak signals, the receiver detects with a high threshold and the noise mean lies outside the forbidden interval. Theorems and simulations demonstrate that both finite-variance and infinite-variance noise benefit the fidelity of quantum teleportation. © 2009 IOP Publishing Ltd.

Civil War Book Review•Nov 20, 2009•3 citations

Can classical noise enhance quantum transmission?

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A modified quantum teleportation protocol broadens the scope of the classical forbidden-interval theorems for stochastic resonance. The fidelity measures performance of quantum communication. The sender encodes the two classical bits for quantum teleportation as weak bipolar subthreshold signals and sends them over a noisy classical channel. Two forbidden-interval theorems provide a necessary and sufficient condition for the occurrence of the nonmonotone stochastic resonance effect in the fidelity of quantum teleportation. The condition is that the noise mean must fall outside a forbidden interval related to the detection threshold and signal value. An optimal amount of classical noise benefits quantum communication when the sender transmits weak signals, the receiver detects with a high threshold and the noise mean lies outside the forbidden interval. Theorems and simulations demonstrate that both finite-variance and infinite-variance noise benefit the fidelity of quantum teleportation.

arXiv:0801.0096•Journal of Physics A Mathematical and Theoretical•Jul 21, 2009•3 citations

Quantum forbidden-interval theorems for stochastic resonance

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arXiv:0801.3141•Journal of Physics A Mathematical and Theoretical•Oct 28, 2009•17 citations

Data Transmission over a Bosonic Channel under Classical Noise

Janis Nötzel

Compound channels model situations where a sender and receiver both have only partial information about the stationary channel they are transmitting over. They can be used to analyse the robustness of a communication system. With this work we provide a coding theorem for a class of practically relevant quantum compound channel models, where we consider the system uncertainty as due to a stationary but unknown jamming signal. Namely, we give an explicit formula for the case of the lossy Bosonic channel in the presence of a semi-classical attack utilizing the injection of coherent states into the transmission line. Mathematically, this is modelled by letting transmitter and jammer access the two different ports of a beam-splitter, and the receiver observe one of the output ports. While the transmitter can modulate their input, the jammer must transmit a constant (but unknown) sequence of states. We conjecture a new quantum entropy power inequality and show its relation to the capacity under study.

IEEE International Symposium on Information Theory (ISIT)•Jul 7, 2024•3 citations
We determine conditions for the presence of stochastic resonance in a lossy bosonic channel with a nonlinear, threshold decoding. The stochastic resonance effect occurs if and only if the detection threshold is outside of a 'forbidden interval'. We show that it takes place in different settings: when transmitting classical messages through a lossy bosonic channel, when transmitting over an entanglement-assisted lossy bosonic channel and when discriminating channels with different loss parameters. Moreover, we consider a setting in which stochastic resonance occurs in the transmission of a qubit over a lossy bosonic channel with a particular encoding and decoding. In all cases, we assume the addition of Gaussian noise to the signal and show that it does not matter who, between sender and receiver, introduces such a noise. Remarkably, different results are obtained when considering a setting for private communication. In this case, the symmetry between sender and receiver is broken and the 'forbidden interval' may vanish, leading to the occurrence of stochastic resonance effects for any value of the detection threshold. © 2013 IOP Publishing Ltd.
We determine conditions for the presence of stochastic resonance in a lossy bosonic channel with a nonlinear, threshold decoding. The stochastic resonance effect occurs if and only if the detection threshold is outside of a 'forbidden interval'. We show that it takes place in different settings: when transmitting classical messages through a lossy bosonic channel, when transmitting over an entanglement-assisted lossy bosonic channel and when discriminating channels with different loss parameters. Moreover, we consider a setting in which stochastic resonance occurs in the transmission of a qubit over a lossy bosonic channel with a particular encoding and decoding. In all cases, we assume the addition of Gaussian noise to the signal and show that it does not matter who, between sender and receiver, introduces such a noise. Remarkably, different results are obtained when considering a setting for private communication. In this case, the symmetry between sender and receiver is broken and the 'forbidden interval' may vanish, leading to the occurrence of stochastic resonance effects for any value of the detection threshold.
We extend the classical forbidden-interval theorems for a stochastic-resonance noise benefit in a nonlinear system to a quantum-optical communication model and a continuous-variable quantum key distribution model. Each quantum forbidden-interval theorem gives a necessary and sufficient condition that determines whether stochastic resonance occurs in quantum communication of classical messages. The quantum theorems apply to any quantum noise source that has finite variance or that comes from the family of infinite-variance alpha-stable probability densities. Simulations show the predicted noise benefits for the basic quantum communication model and the continuous-variable quantum key distribution model. © 2009 IOP Publishing Ltd.
A modified quantum teleportation protocol broadens the scope of the classical forbidden-interval theorems for stochastic resonance. The fidelity measures performance of quantum communication. The sender encodes the two classical bits for quantum teleportation as weak bipolar subthreshold signals and sends them over a noisy classical channel. Two forbidden-interval theorems provide a necessary and sufficient condition for the occurrence of the nonmonotone stochastic resonance effect in the fidelity of quantum teleportation. The condition is that the noise mean must fall outside a forbidden interval related to the detection threshold and signal value. An optimal amount of classical noise benefits quantum communication when the sender transmits weak signals, the receiver detects with a high threshold and the noise mean lies outside the forbidden interval. Theorems and simulations demonstrate that both finite-variance and infinite-variance noise benefit the fidelity of quantum teleportation. © 2009 IOP Publishing Ltd.
A modified quantum teleportation protocol broadens the scope of the classical forbidden-interval theorems for stochastic resonance. The fidelity measures performance of quantum communication. The sender encodes the two classical bits for quantum teleportation as weak bipolar subthreshold signals and sends them over a noisy classical channel. Two forbidden-interval theorems provide a necessary and sufficient condition for the occurrence of the nonmonotone stochastic resonance effect in the fidelity of quantum teleportation. The condition is that the noise mean must fall outside a forbidden interval related to the detection threshold and signal value. An optimal amount of classical noise benefits quantum communication when the sender transmits weak signals, the receiver detects with a high threshold and the noise mean lies outside the forbidden interval. Theorems and simulations demonstrate that both finite-variance and infinite-variance noise benefit the fidelity of quantum teleportation.
We extend the classical forbidden-interval theorems for a stochastic-resonance noise benefit in a nonlinear system to a quantum-optical communication model and a continuous-variable quantum key distribution model. Each quantum forbidden-interval theorem gives a necessary and sufficient condition that determines whether stochastic resonance occurs in quantum communication of classical messages. The quantum theorems apply to any quantum noise source that has finite variance or that comes from the family of infinite-variance alpha-stable probability densities. Simulations show the predicted noise benefits for the basic quantum communication model and the continuous-variable quantum key distribution model.
Compound channels model situations where a sender and receiver both have only partial information about the stationary channel they are transmitting over. They can be used to analyse the robustness of a communication system. With this work we provide a coding theorem for a class of practically relevant quantum compound channel models, where we consider the system uncertainty as due to a stationary but unknown jamming signal. Namely, we give an explicit formula for the case of the lossy Bosonic channel in the presence of a semi-classical attack utilizing the injection of coherent states into the transmission line. Mathematically, this is modelled by letting transmitter and jammer access the two different ports of a beam-splitter, and the receiver observe one of the output ports. While the transmitter can modulate their input, the jammer must transmit a constant (but unknown) sequence of states. We conjecture a new quantum entropy power inequality and show its relation to the capacity under study.