Teleporting an unknown qubit state is a paradigmatic quantum information processing task revealing the advantage of quantum communication protocols over their classical counterpart. For a teleportation protocol using a Bell state as quantum channel, the resource has been identified to be the concurrence. However, for mixed multipartite states the lack of computable entanglement measures has made the identification of the quantum resource responsible for this advantage more challenging. Here, by building on previous results showing that localizable concurrence is the necessary resource for controlled quantum teleportation, we show that any teleportation protocol using an arbitrary multipartite state, that includes a Bell measurement, requires a nonvanishing localizable concurrence between two of its parties to perform better than the classical protocol. By first analyzing Greenberger–Horne–Zeilinger (GHZ) channel and GHZ measurement teleportation protocol, in the presence of GHZ-symmetric-preserving noise, we compare different multipartite entanglement measures with the fidelity of teleportation, and we find that the protocol performs better than the classical protocol when all multipartite entanglement measures vanish, except for the localizable concurrence. Finally, we extend our proof to an arbitrary teleportation protocol with an arbitrary multipartite entangled channel.
Teleporting an unknown qubit state is a paradigmatic quantum information processing task revealing the advantage of quantum communication protocols over their classical counterpart. For a teleportation protocol using a Bell state as quantum channel, the resource has been identified to be the concurrence. However, for mixed multipartite states the lack of computable entanglement measures has made the identification of the quantum resource responsible for this advantage more challenging. Here, by building on previous results showing that localizable concurrence is the necessary resource for controlled quantum teleportation, we show that any teleportation protocol using an arbitrary multipartite state, that includes a Bell measurement, requires a nonvanishing localizable concurrence between two of its parties to perform better than the classical protocol. By first analyzing Greenberger–Horne–Zeilinger (GHZ) channel and GHZ measurement teleportation protocol, in the presence of GHZ-symmetric-preserving noise, we compare different multipartite entanglement measures with the fidelity of teleportation, and we find that the protocol performs better than the classical protocol when all multipartite entanglement measures vanish, except for the localizable concurrence. Finally, we extend our proof to an arbitrary teleportation protocol with an arbitrary multipartite entangled channel.
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.
Quantum teleportation is a cornerstone protocol for future quantum networks and distributed quantum com- puting. However, scaling teleportation to an arbitrary N- qubit state using conventional methods, which require N separate Bell pairs, presents a significant challenge in terms of both quantum and classical resource overhead. This paper introduces a novel and resource-efficient protocol for tele- porting an arbitrary N-qubit state using a single, pre-shared (N+1)-qubit Greenberger-Horne-Zeilinger (GHZ) state. Our approach reduces the required entangled channel qubits and classical communication bits from O(2N) to N+1, offering a substantial improvement in communication efficiency. The protocol mechanism involves a sequence of local and non-local CNOT gates performed by the sender (Alice), followed by local measurements on her N+1 qubits. The N+1 classical measurement outcomes are then transmitted to the receiver (Bob), who recovers the original quantum state by applying a specific corrective unitary transformation U-f, followed by a set of conditional Pauli gates. We provide a high-level proof of the protocol’s correctness and show that the corrective trans- formation U-f can be implemented efficiently using only local operations on the receiver’s side. Recognizing the practical difficulty of implementing non-local quantum gates between spatially separated nodes, we also propose a modified scheme to enhance near-term feasibility. This practical approach re- locates the non-local operations to a co-located preparation phase, thereby trading the formidable challenge of non-local interactions for a high-fidelity quantum memory requirement. This work analyzes the critical trade-offs between communication efficiency and operational complexity, presenting a vi- able alternative for designing scalable and resource-optimized quantum communication systems.
In distributed quantum computing, quantum networks provide a potential infrastructure for long-range quantum information processing. Controlled quantum teleportation (CQT) is a key practically relevant protocol that can connect two parties on a network and enables a third party, the controller to allow or abort the secure teleportation of an arbitrary single-qubit state between the two parties. We investigate the robustness of a three-qubit GHZ resource under bit-flip, phase-flip, depolarizing, and amplitude-damping noise. Using the Kraus-operator formalism, we characterize the noisy resource through multipartite quantum discord, genuine multipartite concurrence (GMC), localizable entanglement (LE), and CQT fidelity. We also outline a proof-of-concept photonic implementation for preparing the three-qubit GHZ resource and realizing the CQT protocol, which could enable experimental investigation of the effects of noise. Our results show that bit-flip and amplitude-damping noise generally preserve useful mutipartite quantum correlations over broader noise parameter ranges. Interestingly, multipartite discord exhibits freezing under bit-flip noise over a finite parameter regime. Moreover, discord can persist beyond the sudden death of genuine multipartite entanglement, revealing the distinct robustness of nonclassical correlations. We further demonstrate that CQT fidelity which characterizes the performance of CQT can exceed the classical threshold even after GMC vanishes, while LE more closely reflects the operational usefulness of the noisy resource. These findings highlight the complementary roles of quantum correlations and entanglement in assessing the resilience of GHZ-based protocols.
Quantum teleportation in the presence of noisy channels acting on a bipartite resource state is considered. We consider a family of generalized noisy channels that continuously connect the amplitude damping and the dephasing channels, encompassing a wide family of in-between scenarios, to delve into the relation between the teleportation success and the amount of three- and four-partite entanglement (distributed among the qubits of the resource state and those representing local environments) generated during the evolution. Our analysis reveals that for a fixed entanglement of the resource state, the channels that better protect the teleportation fidelity against the detrimental effects of noise are those that generate higher amounts of (Greenberger-Horne-Zeilinger--type) multipartite entanglement. This suggests that the dynamically induced multipartite correlations may serve as an additional resource for teleportation and provides insight into the characterization of processes and of the type of induced entanglement according to their ability to assist the protocol.
Ideal Controlled quantum teleportation, discovered theoretically by Karlsson and Bourennane, is a weird paradigm of nonlocal transplantation of probability-amplitudes of an arbitrary unknown generic information-qubit possessed by a sender (Alice) on a qubit preserved by a distantly located receiver (Bob) under control or cooperation by a third party (Charlie) via maximally entangled Greenberger-Horne-Zeilinger (GHZ) state employed as the quantum channel with local operation and classical communication. The GHZ state is a fragile quantum resource and extremely sensitive to inevitable noisy environment causing decoherence. It fuels, therefore, an imperatively pressing demand to strategize a scheme for noise-resistant control quantum teleportation. We revisit the ideal control quantum teleportation but with a noisy Greenberger-Horne-Zeilinger State in which each intertwining qubit suffers with differing noises and inequivalent levels, namely, bit-flip, amplitude-flip and phase-flip, i.e., asymmetric noise ambience. The controlling power, introduced by Li and Ghose, is invoked to assess the performance of the afore-described noisy strategy. It is seen that differing levels of noises breaks the classical bound of controlling power and, thereby, demonstrating the loosening authority of controller. Our findings suggest that to which extent of asymmetric noise ambience noisy control quantum teleportation is noise-tolerant.
Abstract The superposition principle provides us the opportunity to unfold many surprising facts. One such fact leads to the generation of entanglement which may allow one to teleport an unknown quantum state from one location to another. We try to understand the role of superposition in the process of quantum teleportation, as a question of potentially fundamental importance. We consider, within the scenario of quantum teleportation, a set-up where the sender and the receiver are in a superposed situation of using a maximally entangled state and not using any entangled state in the teleportation protocol, controlled by a qubit. We address two distinct protocols: in the first case, the sender and the receiver do nothing when they do not have the authority to use entanglement, while in the second case, they still use classical communication even if they do not use entanglement. After accomplishing the protocols, we operate a Hadamard gate on the control qubit, measure the control qubit’s state, and consider the outcome corresponding to a particular state of the control. We compare the protocol’s fidelity with the maximum fidelity achievable through classical resources only. In particular, we provide conditions to achieve nonclassical fidelity in teleportation, in the presence of the control qubit. To explore if there is any quantum advantage (advantage of superposition present in the control qubit), we compare the fidelities of the control qubit-based protocols with the fidelity achieved in a situation where the two parties are in a classical mixture of using and not using the maximally entangled state. We observe that there exists a wide range of parameters defining the initial state of the control qubit for which our protocols provide quantum advantage. To analyse the role of superposition quantitatively, we discuss whether the amount of quantum advantage can be expressed in terms of quantum coherence present in the state of the control qubit.