4 research outputs found
Can Classical Noise Enhance Quantum Transmission?
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.Comment: 11 pages, 3 figures, replaced with published version that includes
new section on imperfect entanglement and references to J. J. Ting's earlier
wor
Stochastic resonance in Gaussian quantum channels
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.Comment: 17 pages, 6 figures. Manuscript improved in many ways. New results on
private communication adde
Quantum Forbidden-Interval Theorems for Stochastic Resonance
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
noise benefits for the basic quantum communication model and the
continuous-variable quantum key distribution model.Comment: 13 pages, 2 figure
Applications of Forbidden Interval Theorems in Stochastic Resonance
Abstract Forbidden interval theorems state whether a stochastic-resonance noise benefit occurs based on whether the average noise value falls outside or inside an interval of parameter values. Such theorems act as a type of screening device for mutual-information noise benefits in the detection of subthreshold signals. Their proof structure reduces the search for a noise benefit to the often simple task of showing that a zero limit exists. This chapter presents the basic forbidden interval theorem for threshold neurons and four applications of increasing complexity. The first application shows that small amounts of electrical noise can help a carbon nanotube detect faint electrical signals. The second application extends the basic forbidden interval theorem to quantum communication through the judicious use of squeezed light. The third application extends the theorems to noise benefits in standard models of spiking retinas. The fourth application extends the noise benefits in retinal and other neuron models to Levy noise that generalizes Brownian motion and allows for jump and impulsive noise processes. 1 Forbidden Interval Theorems for Stochastic Resonance Stochastic resonance (SR) occurs in a nonlinear system when noise benefits the system [3, 17, 33]. The noise benefit can take the form of an increase in mutual information or a signal-to-noise ratio or correlation or a decrease in an error measure. But when will such a noise benefit occur? Forbidden interval theorems answer that SR question for several nonlinear systems. The theorems act as a type of SR screening device because they can give sufficient or necessary conditions for an SR noise benefit. We here restrict noise benefit