We investigate whether it is possible to teleport the coherence of an unknown quantum state from Alice to Bob by communicating a smaller number of classical bits in comparison to what is required for teleporting an unknown quantum state. We find that we cannot achieve perfect teleportation of coherence with one bit of classical communication for an arbitrary qubit. However, we find that if the qubit is partially known, i.e., chosen from the equatorial and polar circles of the Bloch sphere, then teleportation of coherence is possible with the transfer of one cbit of information when we have maximally entangled states as a shared resource. In the case of the resource being a nonmaximally entangled state, we can teleport the coherence with a certain probability of success. In a general teleportation protocol for coherence, we derive a compact formula for the final state at Bob's laboratory in terms of the composition of the completely positive maps corresponding to the shared resource state and a joint positive operator-valued measure (POVM) performed by Alice on her qubit and the unknown state. Using this formula, we show that teleportation of the coherence of a partially known state with real matrix elements is perfectly possible with the help of a maximally entangled state as a resource. Furthermore, we explore the teleportation of coherence with Werner states and show that even when Werner states become separable, the amount of teleported coherence is nonzero, implying the possibility of teleportation of coherence without entanglement.
We investigate whether it is possible to teleport the coherence of an unknown quantum state from Alice to Bob by communicating a smaller number of classical bits in comparison to what is required for teleporting an unknown quantum state. We find that we cannot achieve perfect teleportation of coherence with one bit of classical communication for an arbitrary qubit. However, we find that if the qubit is partially known, i.e., chosen from the equatorial and polar circles of the Bloch sphere, then teleportation of coherence is possible with the transfer of one cbit of information when we have maximally entangled states as a shared resource. In the case of the resource being a nonmaximally entangled state, we can teleport the coherence with a certain probability of success. In a general teleportation protocol for coherence, we derive a compact formula for the final state at Bob's laboratory in terms of the composition of the completely positive maps corresponding to the shared resource state and a joint positive operator-valued measure (POVM) performed by Alice on her qubit and the unknown state. Using this formula, we show that teleportation of the coherence of a partially known state with real matrix elements is perfectly possible with the help of a maximally entangled state as a resource. Furthermore, we explore the teleportation of coherence with Werner states and show that even when Werner states become separable, the amount of teleported coherence is nonzero, implying the possibility of teleportation of coherence without entanglement.
We investigate whether it is possible to teleport the coherence of an unknown quantum state from Alice to Bob by communicating a lesser number of classical bits in comparison to what is required for teleporting an unknown quantum state. We find that we cannot achieve perfect teleportation of coherence with one bit of classical communication for an arbitrary qubit. However, we find that if the qubit is partially known, i.e., chosen from the equatorial and polar circles of the Bloch sphere, then teleportation of coherence is possible with the transfer of one cbit of information when we have maximally entangled states as a shared resource. In the case of the resource being a non-maximally entangled state, we can teleport the coherence with a certain probability of success. In a general teleportation protocol for coherence, we derive a compact formula for the final state at Bob's lab in terms of the composition of the completely positive maps corresponding to the shared resource state and joint POVM performed by Alice on her qubit and the unknown state. Using this formula, we show that teleportation of the coherence of a partially known state with real matrix elements is possible perfectly with the help of a maximally entangled state as a resource. Furthermore, we explore the teleportation of coherence with the Werner states and show that even when the Werner states become separable, the amount of teleported coherence is non-zero, implying the possibility of teleportation of coherence without entanglement.
Quantum teleportation is a quintessential quantum communication protocol that enables the transmission of an arbitrary quantum state between two distant parties without physically transmitting the state with the help of shared entanglement and limited classical communication. We show that it is possible to relax the entanglement requirement in quantum teleportation if we have access to a certain strain of superposition of quantum processes. Two types of superposition of quantum processes are generally considered in the literature: superposition of paths identified with quantum maps and superposition of indefinite causal orders of the maps. We find that when superposition of paths is incorporated in the protocol, quantum teleportation with unit fidelity becomes possible with nonzero probability of 1/4 even when the two parties share certain classes of separable states, including pure product states. In contrast, the assistance of superposition of indefinite causal order of quantum maps in teleportation protocol does not enable any quantum advantage for shared pure product states. Furthermore, we show that separable Werner states can also yield quantum advantage in quantum teleportation assisted by the superposition of paths. Finally, we establish that the presence of quantum coherence in the control qubit is both necessary and sufficient to achieve quantum advantage in quantum teleportation assisted with superposition of paths. The results potentially uncover yet another role of quantum superposition, in general, in teleportation versus entanglement.
Quantum teleportation of an unknown quantum state necessitates the transmission of two classical bits of information; however, when the quantum state is partially known, only a single classical bit is required for the teleportation of its quantum coherence. In this study, we explore the teleportation of quantum coherence through noisy channels utilizing merely one classical bit of information. Our findings reveal that, in contrast to noise-free scenarios, the generalized Bell states POVM (GBS-POVM) and non-maximally entangled states may surpass the performance of Bell states POVM (BS-POVM) and maximally entangled states in enabling probabilistic teleportation of quantum coherence. Nevertheless, when assessing the average amount of quantum coherence that can be teleported, maximally entangled states combined with BS-POVM emerges as the optimal choice, regardless of the type of noise encountered. Moreover, we uncover that for bit-phase-flip (BPF) noise, it is feasible to construct a suitable GBS-POVM that completely mitigates this noise. For other types of noise, we demonstrate that enhancing the teleportation of quantum coherence can be accomplished through entangling two consecutive uses of the same noisy channel, i.e., correlated noise. Notably, correlation effects arising from Pauli channels can entirely negate the detrimental impact of Pauli noises on the teleportation process for quantum coherence.
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.
Quantum teleportation provides a way to transfer unknown quantum states from one system to another via an entangled state as a quantum channel without physical transmission of the object itself. The entangled channel, measurement performed by the sender (Alice), and classical information sent to the receiver (Bob) are three key ingredients in the procedure, which need to cooperate with each other. To study the relationship among the three parts, we propose a scheme for perfect teleportation of a qubit through a high-dimensional quantum channel in a pure state with two equal largest Schmidt coefficients. The scheme requires less entanglement of Alice's measurement but more classical bits than the original scheme via a Bell state. The two quantities increase with the entanglement of the quantum channel when its dimension is fixed and thereby can be regard as Alice's necessary capabilities to use the quantum channel. And the two capabilities appear complementary to each other.
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.