Consider two remote laboratories: Alice holds an unknown input |ξ⟩ and a private single-qubit unitary UA, while Bob holds |η⟩ and UB. We present an exact local-operations-and-classical-communication protocol that produces UB|ξ⟩ at Alice’s site and UA|η⟩ at Bob’s site only after the controller labels are released. A five-qubit channel first relocates the input states; operation delivery then uses a five-particle channel of local dimension d, a 2d-outcome nonsymmetric qubit–qudit measurement, and label-dependent inverse maps. We give the qutrit case explicitly and one correction formula for arbitrary d. A dual-layer construction lets Charlie authorize both directions, while David and Fiona authorize one direction each. In the ideal lossless model, all admissible branches have recovery maps and their probabilities sum to unity. The basic qutrit protocol uses ten entangled carriers and 13 fixed-length classical bits; the dual-layer protocol uses fourteen carriers and 19 bits. Thus, dimensional flexibility and direction-selective control are obtained at increased resource-protection and signaling costs. This is an exact theoretical remote-operation construction, not an experimentally mature or composably secure communication protocol.
Consider two remote laboratories: Alice holds an unknown input |ξ⟩ and a private single-qubit unitary UA, while Bob holds |η⟩ and UB. We present an exact local-operations-and-classical-communication protocol that produces UB|ξ⟩ at Alice’s site and UA|η⟩ at Bob’s site only after the controller labels are released. A five-qubit channel first relocates the input states; operation delivery then uses a five-particle channel of local dimension d, a 2d-outcome nonsymmetric qubit–qudit measurement, and label-dependent inverse maps. We give the qutrit case explicitly and one correction formula for arbitrary d. A dual-layer construction lets Charlie authorize both directions, while David and Fiona authorize one direction each. In the ideal lossless model, all admissible branches have recovery maps and their probabilities sum to unity. The basic qutrit protocol uses ten entangled carriers and 13 fixed-length classical bits; the dual-layer protocol uses fourteen carriers and 19 bits. Thus, dimensional flexibility and direction-selective control are obtained at increased resource-protection and signaling costs. This is an exact theoretical remote-operation construction, not an experimentally mature or composably secure communication protocol.
We study the remote implementation of a unitary transformation on the state of a qubit. We show the existence of nontrivial protocols (i.e., using less resources than bidirectional state teleportation) that allow the perfect remote implementation of certain continuous sets of quantum operations. We prove that, up to a local change of basis, only two subsets exist that can be implemented remotely with a nontrivial protocol: Arbitrary rotations around a fixed direction $\stackrel{\ensuremath{\rightarrow}}{n}$ and a $\ensuremath{\pi}$ rotation about an arbitrary direction lying in a plane orthogonal to $\stackrel{\ensuremath{\rightarrow}}{n}.$ The former operations effectively constitute the teleportation of arbitrary angles. The overall classical information and distributed entanglement cost required for the remote implementation depends on whether it is known, a priori, in which of the two teleportable subsets the transformation belongs. If it is known, the optimal protocol consumes one e-bit of entanglement and one c-bit in each direction. If it is not known in which subset the transformation belongs, two e-bits of entanglement need to be consumed and the classical channel becomes asymmetric with two c-bits being conveyed from Alice to Bob but only one from Bob to Alice.
We propose a protocol for the remote implementation of an arbitrary two-qubit unitary operation using pre-shared entanglement. In our protocol, Bob possesses an unknown two-qubit state, while Alice implements the required operations using calibrated black-box devices. Alice does not need to know the parameters of these operations, and Bob's unknown state never leaves his laboratory. The protocol is based on the Euler decomposition of single-qubit unitary operations and the Cartan decomposition of two-qubit unitary operations. First, we construct protocols for the remote implementation of the single-qubit operation U=Rz(γ)Rx(β)Rz(α) using pre-shared Bell states. We then construct a protocol for the two-qubit operation Rzz(θ) using a single pre-shared Bell state and extend it to Rxx(θ) and Ryy(θ) through local unitary transformations. These elementary protocols are finally combined to implement an arbitrary two-qubit unitary operation. A third party, Charlie, determines the required decomposition and provides Alice with the corresponding black-box devices before the protocol begins. Thus, neither Alice nor Bob requires the classical description of the unitary operation.
This study investigates controlled bidirectional transmission of two low-dimensional unknown single-particle quantum states through high-dimensional entangled channels. Initially, complete orthogonal non-symmetric bases in [Formula: see text]-dimensional Hilbert space and five-particle maximally entangled states in d-dimensional Hilbert space are constructed, with [Formula: see text]-dimensional non-symmetric bases and 3-dimensional 5-qutrit entangled states serving as specific instances. We then propose a controlled bidirectional teleportation (CBT) protocol wherein a 3-dimensional 5-qutrit maximally entangled channel enables simultaneous exchange of two 2-dimensional single-qubit states under supervisor authorization, implemented via non-symmetric basis measurements. Subsequent replacement of the maximally entangled channel with a 3-dimensional 5-qutrit non-maximally entangled state facilitates probabilistic reconstruction of the original states through auxiliary particle introduction and appropriate unitary operations, still under supervisory control. The success probabilities are analytically derived, demonstrating that the non-maximally entangled protocol generalizes the former scheme. Furthermore, these protocols admit dual extensions: (i) quantum channel dimensionality scalable from 3-dimensional to arbitrary d dimensions; (ii) transmitted state dimensionality extendable from 2-dimensional to arbitrary f-dimensional Hilbert space (f < d).
Abstract In this paper, we develop a quantum communication protocol for the simultaneous preparation of a two-qubit and a three-qubit state at the positions of two different parties situated spatially apart. For one party, Alice, it is a remote state preparation of a known two-qubit state while for the other party, Bob, it is a joint remote state preparation with the help of a third party, Eve. The protocol is executed in a hybrid form bi-directionally in the presence of two controllers, Charlie and David. There is a hierarchy in the process through different levels of control under which the actions by Alice and Bob are performed. There is a need for a ten-qubit entangled channel connecting the five parties. The generation of this channel through a circuit is discussed. The protocol is executed on the IBM Quantum platform. We also study the effect of noise on our protocol. Here, amplitude-damping, bit-flip and phase-flip noisy environments are considered and the corresponding variations of fidelity are theoretically and numerically analyzed.
We propose two multi-layer controlled multi-output remote state preparation (RSP) schemes for arbitrary single-qubit and single-qudit states. Twelve-particle entangled channels are constructed in two-dimensional and d-dimensional Hilbert spaces, and a hierarchical authorization mechanism is introduced to enable controllers with different permission levels to jointly and selectively regulate the reconstruction of quantum states at multiple receivers. First, based on a twelve-qubit maximally entangled channel, we design a deterministic three-layer controlled multi-output RSP protocol in which one sender assists three receivers in preparing their respective target single-qubit states. In this protocol, the controllers are assigned high-, medium-, and low-level permissions. Under different multi-layer control conditions, the three receivers can reconstruct their respective original single-qubit states by performing appropriate local unitary operations. The results show that the protocol achieves unit success probability, exhibits good universality and provides a structured basis for extension to larger multi-user settings, and enforces hierarchical access control by preventing unauthorized receivers from deterministically reconstructing the target states. Subsequently, we replace the maximally entangled channel with a non-maximally entangled twelve-qubit state. After the sender performs two specific three-qubit projective measurements, the receivers can probabilistically reconstruct their respective target states under the same three-layer control structure by introducing auxiliary qubits, applying controlled-U gates, and measuring the auxiliary systems. Finally, by employing positive operator-valued measurements, the above scheme is generalized from qubit systems to arbitrary d-dimensional qudit systems, providing a theoretical basis for exploring larger multi-user quantum communication settings with hierarchical authorization.
Abstract This paper proposes a hierarchical controlled bidirectional hybrid quantum information transmission (HCBHQIT) protocol for arbitrary two-qubit states based on a special ten-qubit entangled state. The protocol implements a hierarchical control mechanism where high-level agent Alice can complete quantum teleportation of any unknown two-qubit state to Bob with only one controller Charlie’s assistance, while low-level agent Bob requires collaborative control from both Charlie and an additional controller David to remotely prepare arbitrary known two-qubit states at Alice’s location (with Alice remaining completely unaware of the state). We comprehensively analyze protocol implementation in noisy environments, particularly examining fidelity degradation under various noise conditions, and calculate the intrinsic efficiency through comparative evaluations. The scheme innovatively integrates multi-level control architecture with bidirectional hybrid communication technology over a shared quantum channel, with detailed discussions for both ideal and noisy scenarios. Demonstrated to maintain practical value across multiple application scenarios, this protocol advances controllable quantum communication systems through its hierarchical access management and dual-directional information transfer capabilities.