Entanglement of quantum systems refers to the situation where two or more systems interact and the state of the whole system cannot be seen as a superposition of states of the single systems. This feature of quantum dynamics is crucial in many algorithms of quantum communication and quantum information processing and it is a resource for many fascinating applications. Moreover entanglement, as a feature of quantum mechanics, has stimulated in-depth investigation on the value of quantum mechanics itself as a physical theory.
Entanglement of quantum systems refers to the situation where two or more systems interact and the state of the whole system cannot be seen as a superposition of states of the single systems. This feature of quantum dynamics is crucial in many algorithms of quantum communication and quantum information processing and it is a resource for many fascinating applications. Moreover entanglement, as a feature of quantum mechanics, has stimulated in-depth investigation on the value of quantum mechanics itself as a physical theory.
Entanglement of quantum systems refers to the situation where two or more systems interact and the state of the whole system cannot be seen as a superposition of states of the single systems. This chapter is devoted to the definition of entanglement both for pure states and mixed states. It also discusses methods to detect entanglement. The chapter is devoted to the study of the dynamics of entanglement. It is also devoted to the problem of local equivalence between states, i.e., how to determine when, given two states, it is possible to evolve from one to the other by transformations which act on systems separately.
In this chapter, we study the properties of quantum entanglement, and more generally the way correlations can appear in quantum mechanics. Quantum entanglement is an important notion that we have already discussed, for instance in the context of the Von Neumann chain or of the Schrödinger cat, but here we give more details on its properties. In classical physics, the notion of correlation is well known. It hinges on the calculation of probabilities and on linear averages over a number of possibilities. A distribution gives the probability of having the first system in a some given state and the second in another state. If this distribution is not a product, the two systems are correlated. If it is a product, they are uncorrelated; measuring the properties of one system does not bring any information on the other. This is in particular the case if the state of each of the two systems is perfectly defined (which also defines the state of the whole system perfectly well). The notion of correlation between sub-systems therefore stems from the multiplicity of possible states of the whole system; fluctuations of this state are necessary to give its full meaning to the classical notion of correlation. In quantum mechanics, the situation is different: as we have seen (in particular in Chapter 4), even a physical system that is perfectly defined by a given state vector already contains fluctuations.
Quantum entanglement is amongst the strangest ideas of quantum mechanics and is being considered as an asset for revolutionary advances in quantum computing technologies. It arises due to the interaction between two quantum particles, which makes their quantum states independently ambiguous. The observation of one particle instantly affects the state of the other across significant spatial divides. Entangled particles exist in predetermined states even before observation but remain ambiguous until a practical measurement. This chapter surveys the underlying principles of quantum entanglement and its conceptual applications in quantum information processing. It further investigates the historical evolution and fundamentals of quantum theory to explain the role of quantum entanglement in the field of quantum computing. The discussion does not conclude at this point but briefly touches upon cutting-edge technologies like quantum teleportation, explaining the transmission of quantum states across large distances devoid of the physical transmission of matter. Though initially seen as science fiction, research has now begun on its practical applications towards enabling secure quantum communication.
QUANTUM ENTANGLEMENT: THEORY, APPLICATIONS AND EMERGING TECHNOLOGIES provides a comprehensive introduction to one of the most fascinating and fundamental phenomena of quantum mechanics. The book explains the theoretical foundations of quantum entanglement, including quantum states, superposition, measurement, non-local correlations, Bell’s theorem, and the principles underlying entangled systems. It further examines important applications of entanglement in quantum computing, quantum communication, quantum cryptography, quantum teleportation, quantum sensing, and information processing. Special attention is given to emerging technologies and current research directions that are shaping the development of next-generation quantum systems. By connecting fundamental concepts with practical applications, the book helps readers understand both the scientific significance and technological potential of quantum entanglement. It is intended as a useful reference for students, researchers, educators, and readers interested in quantum science, information technology, and emerging quantum technologies.
Quantum entangled states play very important roles in quantum information processing,such as quantum teleportation,dense coding,error correction,cryptography,and computation.The theory of entanglement mainly concerns the characterization of quantum entanglement and the classification of quantum states,as well as its applications in quantum information processing.We present some basic concepts and results,including:the relationship between locality and reality in quantum mechanics and Bell inequalities,and that between Bell inequalities and the separability of quantum states;the definition of separability for pure and mixed quantum states,and some separability criteria such as the positive map approach,positive partial transpose,reduction criterion,realignment,entanglement witnesses,and the covariance matrix approach and local uncertainty relations;some entanglement measures such as the entanglement of formation,concurrence,relative entropy,negativity,tangle,entanglement of assistance,and their estimation;the change in entanglement when the physical system evolves or undergoes interaction with the environment.
Entanglement is one of the most striking features of quantum mechanics, and yet it is not specifically quantum.More specific to quantum mechanics is the connection between entanglement and thermodynamics, which leads to an identification between entropies and measures of pure state entanglement.Here we search for the roots of this connection, investigating the relation between entanglement and thermodynamics in the framework of general probabilistic theories.We first address the question whether an entangled state can be transformed into another by means of local operations and classical communication.Under two operational requirements, we prove a general version of the Lo-Popescu theorem, which lies at the foundations of the theory of pure-state entanglement.We then consider a resource theory of purity where free operations are random reversible transformations, modelling the scenario where an agent has limited control over the dynamics of a closed system.Our key result is a duality between the resource theory of entanglement and the resource theory of purity, valid for every physical theory where all processes arise from pure states and reversible interactions at the fundamental level.As an application of the main result, we establish a one-to-one correspondence between entropies and measures of pure bipartite entanglement.The correspondence is then used to define entanglement measures in the general probabilistic framework.Finally, we show a duality between the task of information erasure and the task of entanglement generation, whereby the existence of entropy sinks (systems that can absorb arbitrary amounts of information) becomes equivalent to the existence of entanglement sources (correlated systems from which arbitrary amounts of entanglement can be extracted).