Mixed entangled states are generic resource for quantum teleportation. Optimal teleportation fidelity measures the success of quantum teleportation. The relevance of rank in the teleportation process is investigated by constructing three new maximally entangled mixed states (MEMS) of different ranks. Linear entropy, concurrence, optimal teleportation fidelity and Bell function are obtained for each of these states analytically. It is found that mixed states with higher rank are better resource for teleportation. In order to achieve a fixed value of optimal teleportation fidelity, we find that low rank states must have high concurrence. Further, for each of ranks 2, 3 and 4, we numerically generate 30000 maximally entangled mixed states. The analysis of these states reveals the existence of a rank dependent upper bound on optimal teleportation fidelity for a fixed purity. In order to achieve a fixed optimal teleportation fidelity, we find MEMS exhibit a rank dependent lower bound on concurrence. MEMS are classified in terms of their degree of nonlocality. The results are found to be same with logarithmic negativity used as a measure of entanglement.
Quantum coherence and quantum entanglement are two different manifestations of the superposition principle. In this paper, we show that the right choice of basis to be used to estimate coherence is the separable basis. The quantum coherence estimated using the Bell basis does not represent the coherence in the system, since there is a coherence in the system due to the choice of the basis states. We first compute the entanglement and quantum coherence in the two-qubit mixed states prepared using the Bell states and one of the states from the computational basis. The quantum coherence is estimated using the [Formula: see text]-norm of coherence, the entanglement is measured using the concurrence and the mixedness is measured using the linear entropy. Then we estimate these quantities in the Bell basis and establish that coherence should be measured only in separable basis, whereas entanglement and mixedness can be measured in any basis. We then calculate the teleportation fidelity of these mixed states and find the regions where the states have a fidelity greater than the classical teleportation fidelity. We also examine the violation of the Bell-CHSH inequality to verify the quantum nonlocal correlations in the system. The estimation of the above-mentioned quantum correlations, teleportation fidelity and the verification of Bell-CHSH inequality is also done for bipartite states obtained from the tripartite systems by the tracing out of one of their qubits. We find that for some of these states’ teleportation is possible even when the Bell-CHSH inequality is not violated, signifying that nonlocality is not a necessary condition for quantum teleportation.
We study the entanglement dynamics of
n=2,3,4-qubit Bell- and GHZ-type states under an amplitude-damping channel (ADC). We quantify multipartite entanglement using the genuine multipartite concurrence (GMC) and evaluate its utility through the optimal teleportation fidelity. For
2-qubit states, we analyze the standard (Bennett) teleportation protocol. For
3- and
4-qubit states, we study controlled quantum teleportation (CQT) with one and two \emph{controllers}, respectively. Entanglement sudden death (ESD) denotes the abrupt, finite-time disappearance of entanglement caused by decoherence in contrast to asymptotic decay. To counteract ESD, we apply local NOT (
σ^x) operations on
m of the
n qubits (
m≤n) and derive analytic formulae, revealing that a single-NOT operation often suffices to alter ESD into asymptotic decay when handling GMC. In contrast, teleportation fidelity can decay more rapidly for single-NOT flipped states, whereas flipping all qubits is more useful for preserving teleportation fidelity in certain regimes, highlighting that the amount of entanglement alone does not guarantee teleportation utility. Remarkably, in the case of GHZ-type states, ADC-evolved mixed biseparable states can be exploited successfully in the CQT protocol. Further, using the GHZ-symmetric parametrization, we map the 2- and 3-qubit ADC-evolved mixed states onto a
(x,y) plane, revealing their SLOCC (Stochastic Local Operations and Classical Communication) entanglement classes. We also explicitly check the Bell-CHSH nonlocality hierarchy in the 2-qubit teleportation alongside localizable-entanglement diagnostics for 3-qubit CQT. Our results clarify the distinct roles of global versus localizable bipartite correlations and suggest simple, experimentally accessible unitary controls for preserving useful quantum resources in noisy channels.