Using quantum channels to transmit classical information has been proven to be advantageous in several scenarios. These channels have been assumed to be memoryless, meaning that consecutive transmissions of information are uncorrelated. However, as shown experimentally, such correlations do exist, and thereby retain memory of previous information. This memory complicates the protection of entangled-information transmission from decoherence. We have recently addressed these fundamental questions by developing a generalized master equation for multipartite entangled systems coupled to finite-temperature baths and subject to arbitrary external perturbations whose role is to provide dynamical protection from decay and decoherence. Here we explore and extend the foregoing strategy to quantum optical communication schemes wherein polarization-entangled photons traverse a bit-flip channel with temporal and spatial memory, such that the two channels experience cross-decoherence. We introduce a novel approach to the protection of the entangled information from decoherence in such schemes. It is based on selectively modulating the photon polarizations in each channel. We show that by applying selective modulation, one can independently control the symmetry and spatial memory attributes of the channel. We then explore the effects of these attributes on the channel capacity. Remarkably, we show that there is a nontrivial interplay between the effects of asymmetry and memory on the channel capacity.
Using quantum channels to transmit classical information has been proven to be advantageous in several scenarios. These channels have been assumed to be memoryless, meaning that consecutive transmissions of information are uncorrelated. However, as shown experimentally, such correlations do exist, and thereby retain memory of previous information. This memory complicates the protection of entangled-information transmission from decoherence. We have recently addressed these fundamental questions by developing a generalized master equation for multipartite entangled systems coupled to finite-temperature baths and subject to arbitrary external perturbations whose role is to provide dynamical protection from decay and decoherence. Here we explore and extend the foregoing strategy to quantum optical communication schemes wherein polarization-entangled photons traverse a bit-flip channel with temporal and spatial memory, such that the two channels experience cross-decoherence. We introduce a novel approach to the protection of the entangled information from decoherence in such schemes. It is based on selectively modulating the photon polarizations in each channel. We show that by applying selective modulation, one can independently control the symmetry and spatial memory attributes of the channel. We then explore the effects of these attributes on the channel capacity. Remarkably, we show that there is a nontrivial interplay between the effects of asymmetry and memory on the channel capacity.
Quantum communication is at the heart of the quantum information theory. We study two types of quantum communication protocols over noisy transmission channels, i.e. super dense coding and cryptography protocols. In the first part of this thesis, for various scenarios, it is discussed how the super dense coding capacity is influenced by noisy quantum channels. The case of memoryless channels as well as those channels with memory which are modelled by uncorrelated and correlated noise, respectively, are considered. Explicitly Pauli channels over arbitrary dimensions are treated and the super dense coding capacity for some resource states is derived. For the qubit depolarizing channel, when noise is uncorrelated, the super dense coding capacity with respect to the input state is also optimized. This illustrates a threshold value of the noise parameter below which the super dense coding capacity is optimized by a maximally entangled initial state, while above the threshold value the super dense coding capacity is optimized by a product state. For Pauli channels, with correlated noise, the case of non unitary encoding is studied and the super dense coding capacity is derived. The first part of this thesis is concluded with an example for multipartite super dense coding.
In the second part of the thesis, the problem of optimal eavesdropping on noisy states in quantum key distribution is investigated. The case of the six state protocol, when the signal states are mixed with white noise, is considered. This situation may arise either when Alice deliberately adds noise to the signal states before they leave her lab, or, in a realistic scenario when the eavesdropper (referred to as Eve) is not assumed to replace the noisy quantum channel by a noiseless one. For individual attacks, we find Eve's optimal mutual information with Alice as a function of the quantum bit error rate. Finally, the results illustrate that adding noise on the quantum level can make quantum key distribution more robust against eavesdropping.
The maximum rates for information transmission through noisy quantum channels has primarily been developed for memoryless channels, where the noise on each transmitted state is treated as independent. Many real-world communication channels experience noise which is modeled better by errors that are correlated between separate channel uses. In this Brief Report, upper bounds on the classical information capacities of a class of quantum memory channels are derived. The class of channels consists of indecomposable quantum memory channels, a generalization of classical indecomposable finite-state channels.
We study non Markovian quantum systems for communication of quantum information. The quantum capacities of an exactly solvable spin-star system are analytically determined.Our results show that they strongly depend on the bath frequencies and system-bath coupling.The Ising spin-bath becomes noisy as the bath temperature is increased decreasing its capacity to transmit information.For random couplings and bath frequencies, recurrences of coherence are small in amplitude and rapidly die out. However, full periodic recurrences occur for equal coupling and frequencies. For small number of bath spins, the capacities are higher at low temperature.We also study two time-correlated non-unital channels for the transmission of classical and quantum information, provided limited or unlimited entanglement is shared prior to the communication.The noise over two successive uses of the channel is assumed to be time-correlated Markov noise.For amplitude-damping channel, the capacities exhibit strong dependence on channel memory.They decrease as the channel noise increases and reduce to zero when noise is maximum. However, our results show that the capacities are always non-zero, in the presence of channel memory.This is similar to the superactivation phenomenon. For perfect memory channel, the capacities acquire maximum value.Finally, we determine the entanglement-assisted classical capacity of generalized amplitude-damping channel. Our results show that depending on the channel noise and system-reservoir coupling, there exists a memory threshold.Below this threshold, the capacity decreases as channel memory increases.However, the capacity increases with memory beyond this threshold and is maximum for perfect memory channels.
The amount of coherent quantum information that can be reliably transmitted down the memory Pauli channels with Markovian correlated noise is investigated. Two methods for evaluating the quantum capacity of the memory Pauli channels are proposed to try to trace the memory effect on the transmissions of quantum information. We show that the evaluation of quantum capacity can be reduced to the calculation of the initial memory state of each successive transmission. Furthermore, we derive quantum capacities of the memory phase flip channel, bit flip channel and bit-phase flip channel. Also, a lower bound of the quantum capacity of the memory depolarizing channel is obtained. An increase of the degree of memory of the channels has a positive effect on the increase of their quantum capacities.
Any physical process can be represented as a quantum channel mapping an initial state to a final state. Hence it can be characterized from the point of view of communication theory, i.e., in terms of its ability to transfer information. Quantum information provides a theoretical framework and the proper mathematical tools to accomplish this. In this context the notion of codes and communication capacities have been introduced by generalizing them from the classical Shannon theory of information transmission and error correction. The underlying assumption of this approach is to consider the channel not as acting on a single system, but on sequences of systems, which, when properly initialized allow one to overcome the noisy effects induced by the physical process under consideration. While most of the work produced so far has been focused on the case in which a given channel transformation acts identically and independently on the various elements of the sequence (memoryless configuration in jargon), correlated error models appear to be a more realistic way to approach the problem. A slightly different, yet conceptually related, notion of correlated errors applies to a single quantum system which evolves continuously in time under the influence of an external disturbance which acts on it in a non-Markovian fashion. This leads to the study of memory effects in quantum channels: a fertile ground where interesting novel phenomena emerge at the intersection of quantum information theory and other branches of physics. A survey is taken of the field of quantum channels theory while also embracing these specific and complex settings.
Successful implementation of several quantum information and communication protocols require distributing entangled pairs of quantum bits in reliable manner [1, 2]. While there exists a substantial amount of recent theoretical and experimental activities dealing with non-Markovian quantum dynamics, experimental application and verification of the usefulness of memory-effects for quantum information tasks is still missing. Here we combine these two aspects and show experimentally that a recently introduced concept of nonlocal memory effects [3] allows to protect and distribute polarization entangled pairs of photons in efficient manner within optical fibers. The introduced scheme is based on correlating the environments, i.e. frequencies of the polarization entangled photons, before their physical distribution. When comparing to the case without nonlocal memory effects, we demonstrate a 12-fold improvement in the channel, or fiber length, for preserving the highly-entangled initial polarization states of photons against dephasing.