Information-theoretic aspects of quantum inseparability of mixed states are investigated in terms of the \ensuremath{\alpha} entropy inequalities and teleportation fidelity. Inseparability of mixed states is defined and a complete characterization of the inseparable 2\ifmmode\times\else\texttimes\fi{}2 systems with maximally disordered subsystems is presented within the Hilbert-Schmidt space formalism. A connection between teleportation and negative conditional \ensuremath{\alpha} entropy is also emphasized. \textcopyright{} 1996 The American Physical Society.
Information-theoretic aspects of quantum inseparability of mixed states are investigated in terms of the \ensuremath{\alpha} entropy inequalities and teleportation fidelity. Inseparability of mixed states is defined and a complete characterization of the inseparable 2\ifmmode\times\else\texttimes\fi{}2 systems with maximally disordered subsystems is presented within the Hilbert-Schmidt space formalism. A connection between teleportation and negative conditional \ensuremath{\alpha} entropy is also emphasized. \textcopyright{} 1996 The American Physical Society.
Abstract This chapter describes entanglement in bipartite systems. We define entanglement for pure states introducing the concept of Schmidt decomposition, and we show that entanglement can be quantified through the von Neumann entropy. We then present dense coding and teleportation, two quantum information protocols that use entanglement as a resource. We present the notions of locality and realism and derive the Clauser-Horne-Shimony-Holt inequality, an extended version of Bell’s inequalities. We then focus on mixed states and we present different techniques to solve the separability problem
The ability to teleport entanglement through maximally entangled mixed states as defined by concurrence and linear entropy is studied. We show how the teleported entanglement depends on the quality of the quantum channel used, as defined through its entanglement and mixedness, as well as the form of the target state to be teleported. We present new results based on the fidelity of the teleported state as well as an experimental setup that is immediately implementable with currently available technology.
It is pointed out that every mixed state statistical operator is, up to a normalization constant, a super state vector in the Hilbert space of linear Hilbert-Schmidt operators acting in the state space of the quantum system. Hence, the well understood Schmidt canonical expansion of ordinary state vectors can be carried over to mixed states. In particular, it can be utilized for evaluating all the twins, i. e., the opposite-subsystem observables the measurement of one of which is, on account of entanglement, ipso facto also a measurement of the other. This is illustrated in full detail in the case of the Horodecki two spin-one-half-particle states with maximally disordered subsystems.
Quantum Information Processing (QIP) exploits the principles of quantum mechanics to perform information storage, communication, and computation in ways that are fundamentally impossible within classical frameworks. This article presents a pedagogical overview of the mathematical foundations of quantum information theory, including qubits, Hilbert spaces, linear operators, quantum measurements, tensor products, density operators, and quantum entanglement. Building upon these concepts, we provide a detailed introduction to quantum teleportation, one of the most remarkable protocols in quantum communication. The discussion covers the no cloning theorem, the original teleportation protocol by Bennett et al., experimental realisations of quantum teleportation, and extensions involving probabilistic and multiqubit teleportation schemes. Particular emphasis is placed on the role of entanglement as a communication resource, together with the study of teleportation channels based on bipartite and multipartite quantum states. Various quantitative measures of entanglement, including concurrence, negativity, entanglement of formation, and relative entropy of entanglement, are reviewed alongside teleportation fidelity as a performance metric. Furthermore, the interplay between Bell nonlocality, mixed state entanglement, and teleportation efficiency is examined, followed by a survey of advanced developments such as controlled teleportation, bidirectional teleportation, cluster state teleportation, and recent advances in the Quantum 2.0 era. This review aims to provide students, researchers, and engineers with a coherent introduction to the theoretical foundations and practical significance of quantum teleportation in emerging quantum technologies.
We report universal statistical properties displayed by ensembles of pure states that naturally emerge in quantum many-body systems. Specifically, two classes of state ensembles are considered: those formed by (i) the temporal trajectory of a quantum state under unitary evolution or (ii) the quantum states of small subsystems obtained by partial, local projective measurements performed on their complements. These cases, respectively, exemplify the phenomena of “Hilbert-space ergodicity” and “deep thermalization.” In both cases, the resultant ensembles are defined by a simple principle: The distributions of pure states have maximum entropy, subject to constraints such as energy conservation, and effective constraints imposed by thermalization. We present and numerically verify quantifiable signatures of this principle by deriving explicit formulas for all statistical moments of the ensembles, proving the necessary and sufficient conditions for such universality under widely accepted assumptions, and describing their measurable consequences in experiments. We further discuss information-theoretic implications of the universality: Our ensembles have maximal information content while being maximally difficult to interrogate, establishing that generic quantum state ensembles that occur in nature hide (scramble) information as strongly as possible. Our results generalize the notions of Hilbert-space ergodicity to time-independent Hamiltonian dynamics and deep thermalization from infinite to finite effective temperature. Our work presents new perspectives to characterize and understand universal behaviors of quantum dynamics using statistical and information-theoretic tools. Published by the American Physical Society 2024
We explore sufficient conditions for inseparability in mixed states with a globally conserved charge, such as a particle number. We argue that even separable states may contain entanglement in fixed charge sectors, as long as the state cannot be separated into charge-conserving components. As a witness of symmetric inseparability we study the number entanglement (NE), $\mathrm{\ensuremath{\Delta}}{S}_{m}$, defined as the entropy change due to a subsystem's charge measurement. Whenever $\mathrm{\ensuremath{\Delta}}{S}_{m}>0$, there exist inseparable charge sectors, having finite (logarithmic) negativity, even when the full state either is separable or has vanishing negativity. We demonstrate that the NE is not only a witness of symmetric inseparability, but also an entanglement monotone. Finally, we study the scaling of $\mathrm{\ensuremath{\Delta}}{S}_{m}$ in thermal one-dimensional systems combining high-temperature expansion and conformal field theory.