The distribution of entangled quantum systems among the nodes of a network is a key task at the basis of the development of quantum technologies, e.g., quantum communication, quantum computation, etc. Many efforts have been devoted to identify strategies, based on pre- and post-processing operations or decoherence-free subspaces, to prevent the deterioration of such exotic correlations. However, all these approaches loose their usefulness when the noise level affecting the system surpasses a certain minimal threshold that leads to an entanglement-breaking dynamics. Here we attack this problem in the context of discrete- and continuous-time description of the system dynamics, providing some explicit examples in the context of qubit channels.
The distribution of entangled quantum systems among the nodes of a network is a key task at the basis of the development of quantum technologies, e.g., quantum communication, quantum computation, etc. Many efforts have been devoted to identify strategies, based on pre- and post-processing operations or decoherence-free subspaces, to prevent the deterioration of such exotic correlations. However, all these approaches loose their usefulness when the noise level affecting the system surpasses a certain minimal threshold that leads to an entanglement-breaking dynamics. Here we attack this problem in the context of discrete- and continuous-time description of the system dynamics, providing some explicit examples in the context of qubit channels.
The temporal evolution of entanglement between a noisy system and an ancillary system is analyzed in the context of continuous-time open quantum system dynamics. Focusing on a couple of analytically solvable models for qubit systems, we study how Markovian and non-Markovian characteristics influence the problem, discussing in particular their associated entanglement-breaking regimes. These performances are compared with those one could achieve when the environment of the system is forced to return to its input configuration via periodic instantaneous resetting procedures.
One of the greatest challenges in the fields of quantum information processing and quantum technologies is the detailed coherent control over each and every constituent of quantum systems with an ever increasing number of particles. Within this endeavor, harnessing of many-body entanglement against the detrimental effects of the environment is a major pressing issue. Besides being an important concept from a fundamental standpoint, entanglement has been recognized as a crucial resource for quantum speed-ups or performance enhancements over classical methods. Understanding and controlling many-body entanglement in open systems may have strong implications in quantum computing, quantum simulations of many-body systems, secure quantum communication or cryptography, quantum metrology, our understanding of the quantum-to-classical transition, and other important questions of quantum foundations.In this paper we present an overview of recent theoretical and experimental efforts to underpin the dynamics of entanglement under the influence of noise. Entanglement is thus taken as a dynamic quantity on its own, and we survey how it evolves due to the unavoidable interaction of the entangled system with its surroundings. We analyze several scenarios, corresponding to different families of states and environments, which render a very rich diversity of dynamical behaviors.In contrast to single-particle quantities, like populations and coherences, which typically vanish only asymptotically in time, entanglement may disappear at a finite time. In addition, important classes of entanglement display an exponential decay with the number of particles when subject to local noise, which poses yet another threat to the already-challenging scaling of quantum technologies. Other classes, however, turn out to be extremely robust against local noise. Theoretical results and recent experiments regarding the difference between local and global decoherence are summarized. Control and robustness-enhancement techniques, scaling laws, statistical and geometrical aspects of multipartite-entanglement decay are also reviewed; all in order to give a broad picture of entanglement dynamics in open quantum systems addressed to both theorists and experimentalists inside and outside the field of quantum information.
This review consolidates theoretical and experimental progress on quantum entanglement within open systems, with a particular focus on research conducted in Kenya between 2021 and 2022. It critically synthesises local efforts to model decoherence in noisy environments, offering a unified framework that bridges Markovian and non-Markovian dynamics. The work further identifies key challenges in maintaining entanglement under realistic conditions, thereby providing a foundational reference for future experimental quantum information initiatives in the region. The mathematical description of open quantum systems is examined through the Lindblad master equation and Kraus operator formalism, classifying decoherence into dephasing, dissipation, and collective noise. Striking phenomena such as entanglement sudden death, sudden birth, and revivals are explored, alongside experimental validation on trapped-ion and photonic qubit platforms. A thematic analysis addresses non-Markovian memory effects, which can delay entanglement loss through coherence backflow, and evaluates protection strategies including dynamical decoupling, decoherence-free subspaces, and quantum error correction. The suitability of entanglement measures such as concurrence and negativity for assessing these strategies is discussed. A conspicuous research gap is the near absence of experimental quantum laboratories in East Africa; Kenya lacks infrastructure for trapped-ion or superconducting qubit experiments. This deficit motivates the development of low-cost entangled photon sources based on spontaneous parametric down-conversion using continuous-wave diode lasers, which could support fundamental decoherence studies and proof-of-principle demonstrations of entanglement-based quantum key distribution. Underexplored areas include entanglement in biological systems, hybrid quantum-classical networks, and resource-efficient error mitigation techniques. Theoretically, Kenyan physicists are well positioned to develop open-system models incorporating local environmental conditions, bridging the gap between theoretical elegance and experimental feasibility in resource-constrained settings.
The work is devoted to the study of the problems of using the technology of quantum distribution of secret keys, namely the problems of using and forming new secret keys, based on the generation of quantum keys and the distribution of new keys in networks of complex topologies. In secure communication systems, information is transmitted over public networks, and thus is available to a potential attacker for carrying out various types of attacks. A potential attacker is able to store encrypted data transmitted over network channels, and attempt to decrypt it later, when technical means and attacks on information protection algorithms will allow, in an acceptable time, to carry out decryption. This is the basic principle of "Store now, decrypt later", which is one of the problems of information protection systems. For block ciphers, there is a parameter - the key load, which limits the amount of information that one key can process using the data protection algorithm. NIST recommends a time frame for using secret keys, calculated in years. In the field of information security, there are more significant restrictions on the key load, related to the number of blocks that can be processed by one key, caused by attacks on block ciphers. With these restrictions, there is a need to regularly change the secret key used, and search for options for generating and delivering keys between two network nodes that organize a secure information transmission channel. Changing the secret key to a new key, independent of the previous one, allows you to protect the transfer of confidential information when the key used is compromised. The technology of creating a quantum computer allows you to effectively attack known algorithms for generating secret keys based on the factorization of large numbers or the complexity of calculating a discrete logarithm. The quantum Shor algorithm [5, 6] allows you to solve these problems in polynomial time, so it is necessary to look for alternative solutions to the problem of regular changes in the network channel of the secret key in a pair of nodes. It is important to take into account the need to ensure the quality of Perfect forward secrecy, when the master key is compromised, all subsequent secret keys must not be compromised. To achieve this property of modern encryption algorithms, there is a periodic update of master keys. To prevent the accumulation of information, to successfully carry out attacks by the attacker and to comply with the load requirement on the secret key, it is necessary to solve the problem of regular changes of the secret, and regular generation/delivery of keys to network nodes. Given the urgent needs that are intensively developing today in the secure and high-speed transmission of information, and no less, the rapid growth of technical capabilities, there is a need to develop options in advance that will ensure the security of information during transmission. Regular change, in geographically dispersed data protection systems, of common secret keys, in the case of ensuring the independence of secret keys, allows successfully solving the task.
One of the greatest challenges in the fields of quantum information processing and quantum technologies is the detailed coherent control over each and every constituent of quantum systems with an ever increasing number of particles. Within this endeavor, harnessing of many-body entanglement against the detrimental effects of the environment is a major pressing issue. Besides being an important concept from a fundamental standpoint, entanglement has been recognized as a crucial resource for quantum speed-ups or performance enhancements over classical methods. Understanding and controlling many-body entanglement in open systems may have strong implications in quantum computing, quantum simulations of many-body systems, secure quantum communication or cryptography, quantum metrology, our understanding of the quantum-to-classical transition, and other important questions of quantum foundations. In this paper we present an overview of recent theoretical and experimental efforts to underpin the dynamics of entanglement under the influence of noise. Entanglement is thus taken as a dynamic quantity on its own, and we survey how it evolves due to the unavoidable interaction of the entangled system with its surroundings. We analyze several scenarios, corresponding to different families of states and environments, which render a very rich diversity of dynamical behaviors. In contrast to single-particle quantities, like populations and coherences, which typically vanish only asymptotically in time, entanglement may disappear at a finite time. In addition, important classes of entanglement display an exponential decay with the number of particles when subject to local noise, which poses yet another threat to the already-challenging scaling of quantum technologies. Other classes, however, turn out to be extremely robust against local noise. Theoretical results and recent experiments regarding the difference between local and global decoherence are summarized. Control and robustness- enhancement techniques, scaling laws, statistical and geometrical aspects of multipartite-entanglement decay are also reviewed; all in order to give a broad picture of entanglement dynamics in open quantum systems addressed to both theorists and experimentalists inside and outside the field of quantum information.