Noisy Classical Channel Research Articles

Optimal teleportation fidelity and its deviation in noisy scenarios

In this work, we study quantum teleportation, a fundamental protocol of quantum physics. In particular, we present a mathematical methodology to study the combined effects of noisy resource state and noisy classical communication on teleportation fidelity and its deviation. We describe a teleportation protocol where an arbitrary two-qubit state in canonical form is used as a resource. Thereafter, to teleport an unknown qubit, Alice measures her qubits in Bell basis and conveys the measurement outcome to Bob via noisy classical channel(s). We derive the exact formulae of optimal teleportation fidelity and corresponding fidelity deviation where the resource state and the classical communication, both can be noisy. To provide the proof of optimality, we provide a systematic method. We further find conditions for non-classical fidelity and dispersion-free teleportation for our teleportation protocol. In this way, we identify noisy environments where it is possible to achieve dispersion-free teleportation without compromising non-classical fidelity. We also demonstrate scenarios where the increase of entanglement in the resource state, may degrade the quality of teleportation — a counter-intuitive instance. Finally, we discuss about the minimum classical communication cost required to achieve non-classical fidelity for our protocol. Here we mainly focus on a possible way to optimize the classical communication cost.

Certifying the classical simulation cost of a quantum channel

A fundamental objective in quantum information science is to determine the cost in classical resources of simulating a particular quantum system. The classical simulation cost is quantified by the signaling dimension which specifies the minimum amount of classical communication needed to perfectly simulate a channel's input-output correlations when unlimited shared randomness is held between encoder and decoder. This paper provides a collection of device-independent tests that place lower and upper bounds on the signaling dimension of a channel. Among them, a single family of tests is shown to determine when a noisy classical channel can be simulated using an amount of communication strictly less than either its input or its output alphabet size. In addition, a family of eight signaling dimension witnesses is presented that completely characterize when any four-outcome measurement channel, such as a Bell measurement, can be simulated using one communication bit and shared randomness. Finally, we bound the signaling dimension for all partial replacer channels in $d$ dimensions. The bounds are found to be tight for the special case of the erasure channel.

Activation of entanglement in teleportation

We study the activation of entanglement in teleportation protocols. To this end, we present a derivation of the average fidelity of the teleportation process with a noisy classical channel for qudits. In our work, we do not make any assumptions about the entangled states shared by communicating parties. Our result allows us to specify the minimum amount of classical information required to beat the classical limit when the protocol is based on the Bell measurements. We also compare the average fidelity of teleportation obtained using a noisy and perfect classical channel with restricted capacity. The most important insight into the intricacies of quantum information theory that we gain is that, although entanglement is obviously a necessary resource for efficient teleportation, it requires a certain threshold amount of classical communication to be more useful than classical communication. Another interesting finding is that the amount of classical communication required to activate entanglement for teleportation purposes depends on the dimension d of the system being teleported but is not monotonic, reaching a maximum for d = 4.

Optimal entanglement-assisted one-shot classical communication

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 sent via a single use of the channel. Prevedel et al. (PRL 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. We completely 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 from the given classical channel and to prove the limit of such protocols. As an example, we show that the Prevedel et al. protocol is optimal for two-qubit entanglement. We also prove some simple upper bounds on the improvement that can be obtained from quantum and no-signaling correlations.

Entanglement-Enhanced Classical Communication Over a Noisy Classical Channel

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.

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.

Capacity of the noisy quantum channel

An upper limit is given to the amount of quantum information that can be transmitted reliably down a noisy, decoherent quantum channel using the high-probability states of quantum sources. A class of quantum error-correcting codes is presented that allows the information transmitted to attain this limit. The result is a quantum analog of Shannon's bound and code for the noisy classical channel [C. E. Shannon and W. Weaver, The Mathematical Theory of Communication (University of Illinois Press, Chicago, 1948)].