Quantum teleportation with a two-qubit state can be suitably characterized in terms of maximal fidelity and fidelity deviation---the former is the maximal value of the average fidelity achievable within the standard protocol and local unitary operations and the latter is the standard deviation of fidelity over all input states. In this paper, we consider the problem of characterizing two-qubit states that are optimal for quantum teleportation for a given value of some state property. The optimal states are defined as those states that, for a given value of the state property under consideration, achieve the largest maximal fidelity and also exhibit zero fidelity deviation. We provide a complete characterization of optimal states for a given linear entropy, maximum mean value of the Bell--Clauser-Horne-Shimony-Holt (CHSH) observable, and concurrence, respectively. We find that for a given linear entropy or Bell-CHSH violation the largest maximal fidelity states are optimal, but for a given concurrence the optimal states form a strict subset of the largest maximal fidelity states.
Quantum teleportation with a two-qubit state can be suitably characterized in terms of maximal fidelity and fidelity deviation---the former is the maximal value of the average fidelity achievable within the standard protocol and local unitary operations and the latter is the standard deviation of fidelity over all input states. In this paper, we consider the problem of characterizing two-qubit states that are optimal for quantum teleportation for a given value of some state property. The optimal states are defined as those states that, for a given value of the state property under consideration, achieve the largest maximal fidelity and also exhibit zero fidelity deviation. We provide a complete characterization of optimal states for a given linear entropy, maximum mean value of the Bell--Clauser-Horne-Shimony-Holt (CHSH) observable, and concurrence, respectively. We find that for a given linear entropy or Bell-CHSH violation the largest maximal fidelity states are optimal, but for a given concurrence the optimal states form a strict subset of the largest maximal fidelity states.
Abstract Quantum teleportation with an arbitrary two-qubit state can be appropriately characterized in terms of maximal fidelity and fidelity deviation. The former quantifies optimality of the process and is defined as the maximal average fidelity achievable within the standard protocol and local unitary strategies, whereas the latter, defined as the standard deviation of fidelity over all input states, is a measure of fidelity fluctuations. The maximal fidelity for a two-qubit state is known and is given by a simple formula that can be exactly computed, but no such formula is known for the fidelity deviation. In this paper, we derive an exact computable formula for the fidelity deviation in optimal quantum teleportation with an arbitrary state of two qubits. From this formula, we obtain the dispersion-free condition, also known as the universality condition: the condition that all input states are teleported equally well and provide a necessary and sufficient condition for a state to be both useful (maximal fidelity larger than the classical bound) and universal (zero fidelity deviation). We also show that for any given maximal fidelity, larger than the classical bound, there always exist dispersion-free or universal states and argue that such states are the most desirable ones within the set of useful states. We illustrate these results with well-known families of two-qubit states: pure entangled states, Bell-diagonal states, and subsets of X states.
We consider a scenario where a party, say, Alice prepares a pure two-qubit (either maximally entangled or nonmaximally entangled) state and sends one half of this state to another distant party, say, Bob through a qubit (either unital or nonunital) channel. Finally, the shared state is used as a teleportation channel. In this scenario, we focus on characterizing the set of qubit channels with respect to the final state's efficacy as a resource of quantum teleportation (QT) in terms of maximal average fidelity and fidelity deviation (fluctuation in fidelity values over the input states). Importantly, we point out the existence of a subset of qubit channels for which the final state becomes useful for universal QT (having maximal average fidelity strictly greater than the classical bound and having zero fidelity deviation) when the initially prepared state is either useful for universal QT (i.e., for a maximally entangled state) or not useful for universal QT (i.e., for a subset of nonmaximally entangled pure states). Interestingly, in the latter case, we show that nonunital channels (dissipative interactions) are more effective than unital channels (nondissipative interactions) in producing useful states for universal QT from nonmaximally entangled pure states.
Quantum steering, which lies between Bell nonlocality and entanglement, is a characteristic quantum correlation. Its application in quantum information tasks is worth pursuing. In this paper, we investigate the application of quantum steering as resource of quantum teleportation. It is found that two-qubit states violating the three-setting linear steering inequality are always useful for teleportation. Some steerable states which obey the Bell--Clauser-Horne-Shimony-Holt (CHSH) inequality could be used for teleportation. Two-qubit states that are optimal for quantum teleportation for a fixed amount of steering are present. The optimal states achieve the maximal average fidelity and also exhibit zero fidelity deviation.
Achieving near-unity fidelity of Quantum Teleportation (QT) in a noisy environment is an essential requirement for its real-world applications. Towards this goal, we devise a distinctive protocol based on the timing of the sender Alice's Bell-basis measurement, synchronous with the suitably engineered structure of noise in the receiver Bob's wing, without requiring any knowledge or manipulation of Alice's local noise. For this purpose, to finally obtain the teleported states by performing the required unitary operations, Bob has to retain his qubits for only two particular Bell-basis outcomes communicated by Alice, whose corresponding reduced states have no dependence on the noise parameters in Alice's wing. Such postselection is crucial for enhancing the fidelity of the teleported state towards its ideal limit, while ensuring its full independence of Alice's noise. We formulate the specifics of our protocol in terms of a generic two-level quantum system, subjected to a general non-Markovian spin-boson model for dephasing noise. The proposed scheme is illustrated by using any pure maximally/non-maximally entangled state as well as a Werner-type mixed state as resource. In particular, using resource states having small values of entanglement measure, we show that the high fidelity of QT is achievable in the presence of noise. Further, using our scheme, considering even the local regime of Werner states, wherein the Bell-CHSH inequalities are not violated, we show that the QT fidelity in the presence of noise can be appreciably high.
Abstract We analyze the performance of quantum teleportation in terms of average fidelity and fidelity deviation. The average fidelity is defined as the average value of the fidelities over all possible input states and the fidelity deviation is their standard deviation, which is referred to as a concept of fluctuation or universality. In the analysis, we find the condition to optimize both measures under a noisy quantum channel—we here consider the so-called Werner channel. To characterize our results, we introduce a 2D space defined by the aforementioned measures, in which the performance of the teleportation is represented as a point with the channel noise parameter. Through further analysis, we specify some regions drawn for different channel conditions, establishing the connection to the dissimilar contributions of the entanglement to the teleportation and the Bell inequality violation.
In this work, we consider the following teleportation protocol: There is an arbitrary two-qubit resource state, shared between two spatially separated parties, Alice and Bob. Applying local unitary operators, they transform the resource state into the canonical form. To teleport an unknown qubit, Alice now measures her qubits in the Bell basis. Then, the measurement outcome is communicated by Alice to Bob via noisy classical channel(s). Finally, after receiving the classical message, Bob applies the necessary unitary operator to his qubit. Under this protocol, we find the exact formulae of teleportation fidelity and its deviation. We further find conditions for non-classical fidelity within this protocol. If the classical communication is noiseless in the above protocol then there are resource states which can lead to zero fidelity deviation. However, we show that such states may not lead to zero fidelity deviation when the classical communication is noisy in the same protocol. We also explore the opposite case, i.e., the states, which cannot lead to zero fidelity deviation in the above protocol when the classical communication is noiseless, may lead to zero fidelity deviation when the classical communication is noisy in the same protocol without compromising the non-classical fidelity. Moreover, we exhibit scenarios within the present protocol, where the fidelity deviation increases if the entanglement of the resource state is increased.