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arXiv:2601.15902

Improved cryptographic security in teleportation with q-deformed non-maximal entangled states

Prabal Dasgupta, Debashis Gangopadhyay

quant-phSubmitted Jan 22, 2026• Announced Jan 23, 2026• 0 citations
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Abstract

In this work the machinery of q-deformed algebras are used to enhance cryptographic security during teleportation. We use q-deformed harmonic oscillator states to develop a novel method of teleportation. The deformed states can be expressed in terms of standard oscillator states and the expressions contain certain arbitrary functions of $q$. It is the presence of these arbitrary functions that allows an enhancement of cryptographic security. The specifics are : (a) q-deformed Bell-like states are constructed which reduce to the usual Bell states when the deformation parameter $q\rightarrow 1$. These deformed states form an orthonormal basis for q-deformed entangled bipartite states when certain arbitrary functions of $q$ satisfy a constraint. (b) We discuss the generalisation of the usual teleportation protocol with non-maximally entangled states. This generalisation is then employed to construct two new protocols using q-deformed non-maximally entangled states. These states have additional parameters and these have to be shared for decryption after teleportation. Consequently, the cryptographic security is improved.

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In this work the machinery of q-deformed algebras are used to enhance cryptographic security during teleportation. We use q-deformed harmonic oscillator states to develop a novel method of teleportation. The deformed states can be expressed in terms of standard oscillator states and the expressions contain certain arbitrary functions of qqq. It is the presence of these arbitrary functions that allows an enhancement of cryptographic security. The specifics are :
(a) q-deformed Bell-like states are constructed which reduce to the usual Bell states when the deformation parameter q→1q\rightarrow 1q→1. These deformed states form an orthonormal basis for q-deformed entangled bipartite states when certain arbitrary functions of qqq satisfy a constraint.
(b) We discuss the generalisation of the usual teleportation protocol with non-maximally entangled states. This generalisation is then employed to construct two new protocols using q-deformed non-maximally entangled states. These states have additional parameters and these have to be shared for decryption after teleportation. Consequently, the cryptographic security is improved.
New convenient thumbrules are obtained to test entanglement of wavefunctions for bipartite qubit and qutrit systems. All results are analytic. The new results are: (a) For bipartite qubit systems there exists a matrix AAA for which det⁡A=0\det A = 0detA=0 implies unentanglement while det⁡A≠0\det A \ne 0detA=0 implies entanglement. There is an underlying SU(2) algebra. (2) Teleportation for a general qubit state is possible by using non-maximally entangled bipartite qubit states. This protocol has an additional parameter, viz., det⁡A\det AdetA, which enhances the cryptographic security of the teleportation. (c) For qutrits there is a matrix PPP for which det⁡P=0\det P = 0detP=0 simultaneously with trP=±1{\rm tr}P=\pm 1trP=±1 imply unentanglement. Any departure from these conditions implies entanglement. There exists an underlying SU(3) algebra. (d) Physical interpretation of the underlying algebras are given and plausible experimental scenarios are proposed for the SU(2) case in the context of two entangled electrons. (e) The entanglement entropy in both cases, viz., for qubits and qutrits respectively, are expressed in terms of the determinants and trace of the matrices mentioned above.
Two-qubit quantum teleportation is closely related to quantum computation,so a teleportation protocol in which an arbitrary bipartite quantum state is perfectly teleported probabilistically from sender to receiver is proposed. One of 16 generalized non-maximally entangled Bell states (G states for simplicity) functions as quantum channel. The teleportation can be successfully realized with a certain probability if sender performs generalized Bell state measurements (G measurements) and receiver introduces an auxiliary particle and operates appropriate unitary transformations and single-qubit measurements. The probability of successful teleportation is determined by the smallest one among the coefficients' absolute values of the quantum channel.
Bell states and quantum teleportation play crucial roles in quantum information and computation. However, a comprehensive theoretical study of both topics remains to be carried out. This work aims to investigate key algebraic properties of generalized Bell states and explore the topological features of quantum teleportation. First, the basis theorem and the basis group are introduced to show that the extension of a generalized Bell basis by a unitary matrix still forms an orthonormal basis. Then, a twist operator is defined to establish a connection between a generalized multi-qubit Bell state and a tensor product of two-qubit Bell states. In addition, the Temperley--Lieb algebra, the braid group relations, and the Yang--Baxter equation are employed to provide a topological description of generalized Bell states and quantum teleportation. The results demonstrate that our approach not only offers a clear illustration of relevant quantum information protocols but also reveals the topological nature of quantum entanglement and teleportation.
Quantum secret-sharing is a fundamental technique in quantum communication and plays a crucial role in high-dimensional quantum secret transmission. This paper investigates the teleportation of arbitrary d-dimensional multipartite quantum secrets and proposes both deterministic and probabilistic teleportation protocols. The schemes employ generalized Bell-state measurements, generalized Pauli operators, and auxiliary particles to achieve efficient and secure quantum secret-sharing. The deterministic protocol employs maximally entangled channels to achieve perfect sharing with unit success probability. Moreover, the probabilistic protocol, assisted by auxiliary particles and generalized unitary operations, achieves perfect fidelity quantum secret sharing via non-maximally entangled channels. The protocols are further extended to arbitrary d-dimensional systems, and their robustness under several common quantum noise models is analyzed numerically. Compared with previous schemes, the proposed protocols support arbitrary multipartite entangled states, high-dimensional systems, non-maximally entangled channels, and noise analysis within a unified framework. These results enrich the theory of high-dimensional quantum communication and provide practical approaches for future quantum secret-sharing and secure quantum networks.
We introduce an efficient and versatile quantum teleportation protocol for specific types of n-qubit entangled states. By employing a partially entangled Greenberger-Horne-Zeilinger (GHZ) state as the quantum channel and an optimal Positive Operator-Valued Measure (POVM) based on an improved reciprocal state formulation, we achieve unambiguous state discrimination. The scheme has been generalized to support various entangled state configurations and demonstrates a notable reduction in classical communication costs for these states compared to standard Bell-basis teleportation. Its capacity for integration with conventional protocols is pivotal, enhancing quantum hop-by-hop communication security by allowing strategic choices in quantum channel and teleportation strategy
We consider a generalized quantum teleportation protocol for an unknown qubit using non-maximally entangled state as a shared resource. Without recourse to local filtering or entanglement concentration, using standard Bell-state measurement and classical communication one cannot teleport the state with unit fidelity and unit probability. We show that using non-maximally entangled measurements one can teleport an unknown state with unit fidelity albeit with reduced probability. We also give a generalized protocol for entanglement swapping using non-maximally entangled states. I.