Relevance of rank for a mixed state quantum teleportation resource

Abstract

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.

Bounds on mixedness and entanglement of quantum teleportation resources

“…In the present work, we obtain rank dependent upper bounds on measures of mixedness, above which the states of respective ranks become useless for quantum teleportation. In our previous work [7], we observed that mixedness and entanglement of a mixed state resource independently influence teleportation. For a state with a fixed value of mixedness, the state being entangled is only necessary for it to be a resource for quantum teleportation, but not sufficient.…”

“…where r is the rank of the state, which varies from 2 to 4. In our previous work [7], based on the analysis of a class of maximally entangled mixed states of 2 × 2 bipartite system given in [12], we observed that for a given value of linear entropy, there exists a rank dependent upper bound on the optimal teleportation fidelity and the upper bound increases with increase in the rank. This is equivalent to stating that for a given value of optimal telportation fidelity, there exists a rank dependent upper bound on linear entropy and the upper bound increases with rank.…”

“…Maximally entangled pure states give maximum optimal teleportation fidelity of unity. On the other hand, for mixed states, success of teleportation depends, in addition to strength of entanglement, on mixedness of the state [5][6][7]. It was shown in [6] that, for mixed entangled states, there is an upper bound on mixedness above which the state is useless for quantum teleportation.…”

The effect of quantum memory on quantum speed limit time

“…Quantum speed limit time is one among them. Quantum speed limit as a measure of non-Markovianity, and its connection with the hierarchy of quantum correlations of composite quantum system [28,29] are discussed in [30,31]. Even though quantum speed limit time seems to identify the information backflow due to the non-Markovianity, in [30] it is shown that there exists no simple connection between non-Markovianity and speed limit time.…”

Hierarchy in loss of nonlocal correlations of two-qubit states in noisy environments

“…Gisin shows [8] if the fidelity of the given state is greater than F lhv (Gisin bound) then the state is non local in the sense, it is incompatible with local hidden variable description. In our previous work [9] on two qubit maximally entangled mixed states, we observed that entangled states, states that can be used for quantum teleportaion, states that violate Bell-CHSH inequality and states that do not admit local hidden variable description is the hi-erarchy in which order of nonlocal correlations increases In this work, we investigate whether the hierarchy in the order of nonlcoal correlations exhibited by two qubit quantum states would preserve itself in the presence of noisy environment. For that we study the decoherence of a pure maximally entangled Bell state, maximally entangled mixed Werner state and a class of states belonging to maximally entangled mixed states due to amplitude damping channel.…”