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arXiv:2606.17251

Post-Selection Probability and Fidelity of Bidirectional Teleportation

Ning Sun, Lei Feng, Pengfei Zhang

quant-phcond-mat.quant-gasSubmitted Jun 15, 2026• Announced Jun 17, 2026• 0 citations
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Abstract

Understanding the scrambling of quantum information is central to many areas of quantum physics, including quantum thermalization, entanglement growth, and quantum information processing. Insights from these studies have, in turn, inspired the development of novel quantum protocols and algorithms. Recently, a bidirectional teleportation protocol was proposed to implement a digital SWAP operation between qubits by leveraging chaotic Hamiltonian evolution combined with measurement and post-selection. In this work, we provide a comprehensive study of two central quantities that characterize the protocol, the post-selection probability and the fidelity, taking into account possible errors in time-reversed dynamics. We show that these quantities can be expressed in terms of standard diagnostics in quantum dynamics, including the Loschmidt echo and its subsystem variant. The results unveil (1) the initial-state dependence of the fidelity and (2) the stability of the post-selection probability in integrable models. Our findings offer practical guidance for the implementation of the protocol on realistic quantum devices.

Comments
7 pages, 4 figures

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Understanding the scrambling of quantum information is central to many areas of quantum physics, including quantum thermalization, entanglement growth, and quantum information processing. Insights from these studies have, in turn, inspired the development of novel quantum protocols and algorithms. Recently, a bidirectional teleportation protocol was proposed to implement a digital SWAP operation between qubits by leveraging chaotic Hamiltonian evolution combined with measurement and post-selection. In this work, we provide a comprehensive study of two central quantities that characterize the protocol, the post-selection probability and the fidelity, taking into account possible errors in time-reversed dynamics. We show that these quantities can be expressed in terms of standard diagnostics in quantum dynamics, including the Loschmidt echo and its subsystem variant. The results unveil (1) the initial-state dependence of the fidelity and (2) the stability of the post-selection probability in integrable models. Our findings offer practical guidance for the implementation of the protocol on realistic quantum devices.
Quantum teleportation is a fundamental protocol in quantum information science, whose performance is conventionally evaluated under the assumption of ideal Bell-state measurements. In realistic implementations, however, joint measurements are often imperfect and can deviate from maximally entangled bases due to coherent errors in entangling operations. In this work, we analytically show how the entanglement of joint measurements determines teleportation performance, and we propose a strategy to overcome the limitations imposed by partially entangled joint measurements to recover the unit teleportation fidelity with a nonzero success probability. This is achieved by optimizing a reversing operation on the teleported state to compensate for the known coherent deformation of the Bell-state measurement. We then derive an exact equation revealing a quantitative relation between measurement entanglement, channel entanglement, and the success probability to realize the unit-fidelity two-qubit teleportation. We illustrate our results using elegant joint measurements and realistic coherent error models arising from imperfect entangling operations in quantum systems. Our work provides fundamental insight into the role of measurement entanglement in quantum teleportation and offers a practical framework for achieving faithful teleportation without requiring substantial modifications to existing hardware.
We show that quantum information scrambling can enable a generic SWAP gate between collective degrees of freedom in systems without universal local control. Our protocol combines the Hayden-Preskill recovery scheme, associated with the black hole information paradox, with quantum teleportation and runs them in parallel and in opposite directions, enabling bidirectional exchange of quantum states through global interactions alone. This approach cleanly distinguishes the roles of information spreading, entanglement, and chaos for enabling both coherent state transfer and recovery. We propose an experimental realization using the Dicke model, which can be realized in cavity-QED and trapped-ion platforms, highlighting the utility of holography in designing practical quantum gates.
A bidirectional quantum teleportation protocol is introduced over a quantum network consisting of more than four members sharing a coherent entangled state, where it is implemented in a perfect or noisy environment. The results show that the amplitude of the coherent state and the decoherence parameter play important roles in maximizing or minimizing this probability. At fixed values of the amplitude and decoherence parameters, the success of probability increases as the number of users increases. The fidelity of the teleported coherent state depends on the type of encoded information, whether entangled/partial or classical information, namely, it depends on the weight parameter. The stable behavior of the fidelity is displayed when users teleport classical information.
In this contribution, we reformulated the bidirectional teleportation protocol suggested in Ref. 7, by means of Bloch vectors as well as the local operations are represented by using Pauli operators. Analytical and numerical calculations for the teleported state and Fisher information are introduced. It is shown that both quantities depend on the initial state settings of the teleported qubits and their triggers. The Fidelities and the Fisher information of the bidirectionally teleported states are maximized when the qubit and its trigger are polarized in the same direction. The minimum values are predicted if both initial qubits have different polarization or nonzero phase. The maximum values of the Fidelity and the quantum Fisher information are the same, but they are predicted at different polarization angles. We display that the multi-parameter form is much better than the single parameter form, where it satisfies the bounds of classical, entangled systems and the uncertainty principle.
Abstract In this suggested version of the bidirectional teleportation protocol, it is assumed that the used quantum channel passes through an amplitude damping channel. Therefore, some of its quantum correlations (entanglement) are lost and, consequently, its efficiency to implement this protocol decreases. The weak and the reversal measurements are used to recover the losses of these correlations, where the negativity, as a measure of entanglement is improved. In this context, we discussed the effect of the noisy strength on the fidelities of the bidirectional teleported states between the users. It is shown that, by applying the weak and the reversal measurements (WRM) on the initial quantum channel between the users, the fidelities of the teleported states are improved. Moreover, we showed that, the upper bounds of the teleported states depend on the initial states of the triggers and the strengths of WRM. It is worth noting that the WRM improves the quantum correlations of the shared channel and, hence, the fidelity of the teleported state if the initial fidelity of the teleported state is larger than 0.5.
We suggest a new technique for bidirectional quantum teleportation (BQT) that combines coherent-state encoding with discrete-time quantum walks to allow two users to communicate quantum information simultaneously. Our method enables Alice and Bob to simultaneously teleport quantum states to one another within a single protocol, as compared to unidirectional teleportation, which only transmits quantum states in one direction. To allow for a qubit-like representation and fidelity analysis using Bloch vector formalism, the quantum information is encoded using non-orthogonal coherent states that are converted into an orthonormal basis of even and odd Schrödinger cat states. Four different quantum walk steps, each acting on a three-part quantum system made up of position and coin spaces, drive the teleportation process. We use density matrix overlaps in the even-odd basis to derive closed-form formulas for teleportation fidelity in both directions analytically. Using the SeQUeNCe discrete-event simulator, we simulate large-scale quantum network settings with realistic limitations, including photon loss, memory decoherence, entanglement swapping degradation, and various channel capacities in order to evaluate the potential of our approach. We evaluate quantum memory utilization, throughput, and end-to-end fidelity in various network topologies and scenarios. Our findings demonstrate that BQT allows symmetric communication with strong fidelity, particularly in high-capacity and large-scale network situations, but requires a greater resource overhead than unidirectional protocols. The hybrid framework developed in this study offers a scalable and analytically simple solution for next-generation quantum communication systems by combining discrete-time quantum evolution with continuous-variable state encoding.