The role of localizable concurrence in quantum teleportation protocols

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.

Comment on “Quantum key agreement protocol”

The first two-party Quantum Key Agreement (QKA) protocol, based on quantum teleportation, was proposed by Zhou et al. (Electron. Lett. 40(18) (2004) 1149). In this protocol, to obtain the key bit string, one of the parties uses a device to obtain the inner product of two quantum states, one being unknown, and the other one performs Bell measurement. However, in this paper, we show that it is not possible to obtain a device that would output the inner product of two qubits even when only one of the qubits is unknown. This is so because the existence of such a device would imply perfectly distinguishing among four different states in a two-dimensional vector space. This is not permissible in quantum mechanics. Furthermore, we argue that the existence of such a device would also imply a violation of the “No Signaling Theorem” as well.

Public-key quantum signature based on phase shift operation

A public-key quantum signature (QS) scheme is proposed, in which the phase shift is the private key and the quantum state after the phase shift operation is the public key. The signatory uses the private key to encode the quantum state, and uses the Bell measurement to generate the signature. The receiver performs the unitary operation according to the signature, and then compares the quantum state with the public key to verify the signature. Our scheme does not need a trusted arbitrator, and the signature can be verified by the receiver publicly. Compared to the existing arbitrated QS scheme, our scheme will be more practical.

Improvement of a multi-layer quantum secret sharing based on GHZ state and Bell measurement

Recently, a novel Multi-layer Quantum Secret Sharing (MQSS) scheme based on GHZ state and generalized Bell measurement is presented in [X.-J. Wang, L.-X. An, X.-T. Yu and Z.-C. Zhang, Phys. Lett. A 381(38) (2017) 3282.]. The novelty of the MQSS scheme is that a quantum secret can be shared by up to [Formula: see text] parties at the [Formula: see text]th layer. In this paper, we show that the MQSS scheme can be significantly simplified and improved. The improved MQSS scheme is much easier to implement in practice and more efficient. In our improved scheme, the parties of the [Formula: see text]th layer need not put their particles together to carry out the generalized Bell measurement, which is needed to share the secret to the next layer in the original scheme. Instead, each party only has to carry out local operations.