We analyse the possibility of using the two-qubit output state from the Buzek–Hillery quantum copying machine (not necessarily a universal quantum cloning machine) as a teleportation channel. We show that there is a range of values of the machine parameter ξ for which the two-qubit output state is entangled and violates the Bell-CHSH inequality and for a different range it remains entangled but does not violate the Bell-CHSH inequality. Further, we observe that for certain values of the machine parameter the two-qubit mixed state can be used as a teleportation channel. The use of the output state from the Buzek–Hillery cloning machine as a teleportation channel provides an additional appeal to the cloning machine and motivation for our present work.
We analyse the possibility of using the two-qubit output state from the Buzek–Hillery quantum copying machine (not necessarily a universal quantum cloning machine) as a teleportation channel. We show that there is a range of values of the machine parameter ξ for which the two-qubit output state is entangled and violates the Bell-CHSH inequality and for a different range it remains entangled but does not violate the Bell-CHSH inequality. Further, we observe that for certain values of the machine parameter the two-qubit mixed state can be used as a teleportation channel. The use of the output state from the Buzek–Hillery cloning machine as a teleportation channel provides an additional appeal to the cloning machine and motivation for our present work.
This study investigates the nonlocality characteristics of output states produced by a universal quantum cloning machine, with particular emphasis on the Bell-CHSH inequality violations exhibited by the two-qubit reduced states of cloned outputs. Through systematic analysis, we identify the parameter regimes where these reduced states can effectively serve as quantum channels for teleportation protocols. Our results demonstrate that within specific operational ranges of the cloning machine parameters, the two-qubit reduced states are suitable for quantum teleportation but do not exhibit violations of Bell-CHSH inequalities. Furthermore, we quantitatively characterize the monogamy relations governing Bell-CHSH violations in quantum cloning states across different parameter configurations, revealing fundamental constraints on nonlocality distribution in cloned quantum systems.
The violation of Bell’s inequality in quantum mechanics implies that there exist nonlocality and entanglement. When the density matrix of a composite system cannot be written as a convex combination of the product of the density matrices of its subsystems, we say there exists entanglement. For pure states, the existence of entanglement always leads to the violation of Bell’s inequality. However, in the case of the mixed states, there may be entanglement, but Bell's inequality is not violated and in other words, the nonlocality is not manifested. In addition to Bell's inequality, quantum teleportation is also a manifestation of nonlocality. Quantum teleportation using entangled states is more successful than quantum teleportation with separable states. Therefore, the corresponding fidelity of teleported state with the initial state (in short, the fidelity) of the former is always greater than the fidelity of the latter. In this paper, for Werner's state, we will show that in a range of the related parameter, while the CHSH inequality is violated, the fidelity, which indicates the amount of success of quantum teleportation, is lower than the upper bound of the corresponding fidelity for states that can be simulated with a local hidden variable theory. Meanwhile, we will see that for Gisin's state with hidden nonlocality, filtering, which leads to the appearance of nonlocality and more specifically leads to the violation of the CHSH inequality, also increases the fidelity.
We study the efficiency of two-qubit mixed entangled states as resources for quantum teleportation. We first consider two maximally entangled mixed states, viz., the Werner state\cite{werner}, and a class of states introduced by Munro {\it et al.} \cite{munro}. We show that the Werner state when used as teleportation channel, gives rise to better average teleportation fidelity compared to the latter class of states for any finite value of mixedness. We then introduce a non-maximally entangled mixed state obtained as a convex combination of a two-qubit entangled mixed state and a two-qubit separable mixed state. It is shown that such a teleportation channel can outperform another non-maximally entangled channel, viz., the Werner derivative for a certain range of mixedness. Further, there exists a range of parameter values where the former state satisfies a Bell-CHSH type inequality and still performs better as a teleportation channel compared to the Werner derivative even though the latter violates the inequality.
Due to the axioms of quantum mechanics, perfect cloning of an unknown quantum state is impossible. But since imperfect cloning is still possible, a question arises: ``Is there an optimal quantum cloning machine?'' Buzek and Hillery answered this question and constructed their famous B-H quantum cloning machine. The B-H machine clones the state of an arbitrary single qubit in an optimal manner and hence it is universal. Generalizing this machine for a two-qubit system is straightforward, but during this procedure, except for product states, this machine loses its universality and becomes a state-dependent cloning machine. In this paper, we propose some classes of optimal universal local quantum state cloners for a particular class of two-qubit systems, more precisely, for a class of states with known Schmidt basis. We then extend our machine to the case that the Schmidt basis of the input state is deviated from the local computational basis of the machine. We show that more local quantum coherence existing in the input state corresponds to less fidelity between the input and output states. Also we present two classes of a state-dependent local quantum copying machine. Furthermore, we investigate local broadcasting of two aspects of quantum correlations, i.e., quantum entanglement and quantum discord, defined, respectively, within the entanglement-separability paradigm and from an information-theoretic perspective. The results show that although quantum correlation is, in general, very fragile during the broadcasting procedure, quantum discord is broadcasted more robustly than quantum entanglement.
Bužek and Hillery proposed a universal quantum-copying machine (UQCM) (i.e., transformation) to analyze the possibility of cloning arbitrary states. The UQCM copies quantum-mechanical states with the quality of its output does not depend on the input. We propose a slightly different transformation to analyze a restricted set of input states. We impose the conditions (I) the density matrices of the two output states are the same, and that (II) the distance between input density operator and the output density operators is input state independent. Using Hilbert-Schmidt norm and Bures fidelity, we show that our transformation can achieves the bound of the fidelity.