Quantum channels and memory effects

Abstract

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

Interferometric quantum cascade systems

“…In the collisional model approach [37][38][39][40][41][42][43] to open quantum systems dynamics the environment is represented as a large many-body quantum system whose constituents (quantum information carriers or carriers in the following) interact with the system of interest via an ordered sequence of impulsive unitary transformations (collisional events). This yields a, time-discrete, stroboscopic evolution which can then be turned into a continuous time dynamics by properly sending to infinite the number of collisions and to zero the time interval among them while keeping constant their product.…”

Harnessing non-Markovian quantum memory by environmental coupling

“…In the conventional study, one usually considers the quantum system being coupled to a single environment [1,4,5]. However, in several realistic scenarios the system may be simultaneously influenced by many environments [45][46][47][48][49].…”

“…The degree of a non-Markovian evolution, the socalled non-Markovianity, can be quantified by different measures based on dynamical features of the system capable to grasp the memory effects of the environment on the system evolution [28][29][30][31][32][33][34][35]. So far, many factors that can trigger and modify the non-Markovian dynamics have been found, as strong system-environment coupling, structured reservoirs, low temperatures, and initial system-environment correlations [1,[4][5][6][36][37][38][39][40]. Apart from these mechanisms, some other peculiar conditions such as classical environments [41,42] and environmental initial correlations [43,44] have also been predicted and experimentally demonstrated [42,44] enabling emergence of non-Markovianity.…”

“…In the theory of open quantum systems, the non-Markovian dynamics is one of main concerns being linked to the preservation of quantum memory stored in a quantum system [1,4,5]. It arises in many realistic situations [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23], and also proves useful in quantum information processing such as quantum state engineering, quantum channel capacity and quantum control [4,[24][25][26][27][28]. The degree of a non-Markovian evolution, the socalled non-Markovianity, can be quantified by different measures based on dynamical features of the system capable to grasp the memory effects of the environment on the system evolution [28][29][30][31][32][33][34][35].…”

Additive Classical Capacity of Quantum Channels Assisted by Noisy Entanglement

“…Classical information theory [1,2] says that a channel is essentially characterized by a single quantity-the (classical) channel capacity, i.e., its maximum (classical) information transmission rate. However, quantum channels [3] can transmit information beyond the classical. Formally, a (memoryless) quantum channel is a time-invariant completely positive trace preserving (CPTP) linear map between quantum states.…”