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Physica Scripta

On the one-classical-bit quantum teleportation

Muhammad Taufiqi, Agus Purwanto, Bintoro Anang Subagyo

Published Nov 21, 2024• 8 citations
Publisher

Abstract

Abstract This study re-evaluates Parakh’s one-classical-bit quantum teleportation protocol, in which the proposed protocol replaces the traditional two-classical-bit requirement with a reset procedure, resulting in only one classical bit. However, if the input (to-be-teleported) state is unknown, the reset procedure cannot always work effectively, thereby limiting the protocol’s performance. This study modifies the protocol by adding simple CNOT operations, which ensures that the reset procedure always works properly even when the input state is unknown. We also compute the upper bound of the teleportation success probability and the classical bit resource cost inequality using the one-classical-bit protocol. Finally, we simulate the protocol in Qiskit and discuss the results.

DOI
10.1088/1402-4896/ad94b7

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Abstract This study re-evaluates Parakh’s one-classical-bit quantum teleportation protocol, in which the proposed protocol replaces the traditional two-classical-bit requirement with a reset procedure, resulting in only one classical bit. However, if the input (to-be-teleported) state is unknown, the reset procedure cannot always work effectively, thereby limiting the protocol’s performance. This study modifies the protocol by adding simple CNOT operations, which ensures that the reset procedure always works properly even when the input state is unknown. We also compute the upper bound of the teleportation success probability and the classical bit resource cost inequality using the one-classical-bit protocol. Finally, we simulate the protocol in Qiskit and discuss the results.
We proposed an N-qubit GHZ-like state quantum teleportation protocol using a two-qubit entangled quantum channel state assisted with only one classical bit. In this protocol, we use CNOT gates and a reset procedure, assuming the sender has many copies of the state that will be teleported. The CNOT gates can reduce the number of N-qubit to only one qubit, while the reset procedure may reduce the number of classical bits required to only one classical bit. Lastly, we show that the teleportation success probability depends on the state of the N-qubit state’s coefficients and is generally more than one-half.
Quantum teleportation allows one to transmit an arbitrary qubit from point A to point B using a pair of (pre-shared) entangled qubits and classical bits of information. The conventional protocol for teleportation uses two bits of classical information and assumes that the sender has access to only one copy of the arbitrary qubit to be sent. Here, we ask whether we can do better than two bits of classical information if the sender has access to multiple copies of the qubit to be teleported. We place no restrictions on the qubit states. Consequently, we propose a modified quantum teleportation protocol that allows Alice to reset the state of the entangled pair to its initial state using only local operations. As a result, the proposed teleportation protocol requires the transmission of only one classical bit with a probability greater than one-half. This has implications for efficient quantum communications and the security of quantum cryptographic protocols based on quantum 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.
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.