By making use of d-dimensional Hadamard gates and d-dimensional controlled NOT gates, we first construct a five-qudit maximally entangled state, and then use it as the quantum channel to propose a new bidirectional scheme for cloning two different arbitrary unknown single-qudit simultaneously under the assistance from a state preparer and the control of a supervisor. This scheme consists of two stages: quantum teleportation and assisted cloning. To fulfil the purpose, the first stage of this scheme requires bidirectional controlled teleportation via our constructed five-qudit maximally entangled state as quantum channel, where two distant communicators can simultaneously exchange their unknown single-qudit states with unit fidelity and unit probability under the permission of the supervisor.In the second stage,the state preparer disentangles any remaining entangled states by introducing two auxiliary particles, implementing a unitary transformation and two single-particle projective measurements. Subsequently, they transmit a specific number of classical bits to two distinct communicators in order to generate two precise replicas of different unknown states. Subsequently, the above scheme is extended with a certain probability and unit fidelity by replacing the above d-dimensional quantum channel with a five-qudit non-maximally entangled state. Finally, we further analyze the expansion issues of our scheme from the perspectives of positive operator-valued measurement (POVM for short), general quantum channel and the number of state preparers and controllers, and point out that the scheme is secure.
By making use of d-dimensional Hadamard gates and d-dimensional controlled NOT gates, we first construct a five-qudit maximally entangled state, and then use it as the quantum channel to propose a new bidirectional scheme for cloning two different arbitrary unknown single-qudit simultaneously under the assistance from a state preparer and the control of a supervisor. This scheme consists of two stages: quantum teleportation and assisted cloning. To fulfil the purpose, the first stage of this scheme requires bidirectional controlled teleportation via our constructed five-qudit maximally entangled state as quantum channel, where two distant communicators can simultaneously exchange their unknown single-qudit states with unit fidelity and unit probability under the permission of the supervisor.In the second stage,the state preparer disentangles any remaining entangled states by introducing two auxiliary particles, implementing a unitary transformation and two single-particle projective measurements. Subsequently, they transmit a specific number of classical bits to two distinct communicators in order to generate two precise replicas of different unknown states. Subsequently, the above scheme is extended with a certain probability and unit fidelity by replacing the above d-dimensional quantum channel with a five-qudit non-maximally entangled state. Finally, we further analyze the expansion issues of our scheme from the perspectives of positive operator-valued measurement (POVM for short), general quantum channel and the number of state preparers and controllers, and point out that the scheme is secure.
Abstract The purpose of this article is to further investigate the assisted cloning of a d-dimensional arbitrary unknown state by utilizing quantum teleportation (QT) and remote state preparation (RST) techniques. We first propose a scheme for cloning an arbitrary unknown single-qudit state with assistance from a state preparer. In this scheme, the maximally and non-maximally bipartite d-dimensional states are used as quantum channels, respectively. In the first stage of scheme requires usual QT and in the second stage, the state preparer disentangles the left over entangled states by introducing one auxiliary qudit and performing a generalized CNOT, a single-qudit positive operator-valued measurement (POVM) and a single-qudit projective measurement process and conveys some classical messages to different parties so that a copy is produced probabilistically with the unit fidelity.Then by replacing the maximally or non-maximally bipartite d-dimensional entangled channel with a sequence of maximally or non-maximally bipartite d-dimensional entangled states as quantum channel, we can extend the above scheme to the case of cloning a d-dimensional arbitrary unknown m-qudit state with the unit fidelity and a certain probability in the help of the state preparer. PACS numbers 03.67.Hk, 03.67.-a, 03.65.Bz
Abstract The purpose of this article is to explore a scheme for controlled double-direction cyclic (DDC) assisted cloning of arbitrary unknown single-qubit states. We first present a construction method for a 13-qubit entangled quantum state using Hadamard gates and controlled-NOT gates, and subsequently generalize it to a ( 4 n + 1 ) -qubit entangled quantum state. Using the 13-qubit entangled state we constructed as a quantum channel, we propose a novel theoretical scheme for achieving five-party controlled DDC-assisted cloning. The first stage of the scheme involves a controlled DDC quantum teleportation, where each of the three communicators can simultaneously teleport two distinct unknown single-qubit states to the other two, under the supervisor’s control. This process ensures that controlled cyclic quantum communication occurs synchronously in both clockwise and anticlockwise directions. In the second stage of the scheme, with the help of special multi-qubit projective measurements from the state preparer, perfect copies or orthogonal complement copies of the two original unknown single-qubit states can be simultaneously created at each sender’s location. Furthermore, the above presented five-party scheme for controlled DDC-assisted cloning can be extended to scenarios with ( n + 1 ) (n > 3) parties by using the ( 4 n + 1 ) -qubit maximally entangled state as the quantum channel. Moreover, we have provided the mathematical expressions for the general analysis of both the sender’s operations and the receiver’s transformations in each scheme. The study shows that the intrinsic efficiency, security, feasibility, and control power of our scheme are good.
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).
Utilizing Hadamard gates and controlled not gates, maximally entangled states of four, five and six qubits are generated. Then, we propose respectively controlled and assisted cloning schemes of unknown two-, three- and four-qubit states via these constructed states as quantum channels. Each of the three schemes includes two stages: controlled teleportation and assisted cloning. The controlled teleportation stage of our schemes all require a single-qubit [Formula: see text]-basis measurement by controller, and need different GHZ-state measurements by senders of three schemes to complete the transmission process of their respective quantum states. In the assisted cloning stage of our schemes, after the state preparers of three schemes perform respectively appropriate GHZ-state measurements, at the senders’ locations, perfect replicas and orthogonal complementary copies of unknown states will be produced through appropriate local quantum operations. Compared with usual assisted cloning schemes, every suggested plan is extremely efficient in terms of quantum resources, as it only requires a small number of GHZ-state measurements, significantly decreasing the need for quantum operations and classical resources. Through discussion, we conclude that our schemes are safe and can be extended to assisted cloning of unknown multi-qubit GHZ-state with multiple controllers.
Abstract The purpose of this article is to explore how to transmit low-dimensional unknown single-particle states in a multi-output manner through a high-dimensional entangled state as a quantum channel under the control of a supervisor. First, we construct a set of complete orthogonal non-symmetric bases in ( d × f ) -dimensional Hilbert space and a ( 2 N + 1 ) -qudit maximally entangled state in d -dimensional Hilbert space, taking a set of ( 3 × 2 ) -dimensional non-symmetric bases and a 3-dimensional 5-qutrit entangled state as their special cases, respectively. We then propose a controlled teleportation scheme, where by using the 3-dimensional 5-qutrit maximally entangled state as a quantum channel and employing the ( 3 × 2 ) -dimensional non-symmetric basis measurement, two 2-dimensional single-qubit states are simultaneously teleported through quantum teleportation technology under the control of a supervisor. Subsequently, the above maximally entangled quantum channel is replaced by a 3-dimensional 5-qutrit non-maximally entangled state, and two unknown single-qubit states are teleported, under the control of a supervisor, in such a way that they can be probabilistically reconstructed by introducing auxiliary qubits and performing appropriate operations. The success probabilities of the above two schemes are given, and the analysis shows that the scheme based on a non-maximally entangled channel is a generalization of the previous scheme. In addition, the above schemes can be extended from the following two perspectives: (a) the quantum channels can be extended from 3-dimensional to arbitrary d -dimensional; (b) the transmitted quantum information can be extended from 2-dimensional to any f -dimensional through d -dimensional entangled quantum channels ( f < d ).
We first propose a novel protocol to realize quantum cloning of an arbitrary unknown shared state with assistance offered by a state preparer. The initial phase of this protocol involves the utilization of quantum teleportation (QT), enabling the transfer of quantum information from an arbitrary number of senders to another arbitrary number of receivers through a maximally entangled GHZ-type state serving as a network channel, without centralizing the information at any specific location. In the second stage of this protocol, the state preparer performs a special single-qubit projective measurement and multiple Z-basis measurements and then communicates a number of classical bits corresponding to measurement results, the perfect copy or orthogonal-complementing copy of an unknown shared state can be produced at senders hands. Then, using a non-maximally entangled GHZ-type state instead of the aforementioned quantum channel, we extend the proposed protocol from three perspectives: projective measurement, positive operator-value measurement (POVM), and a single generalized Bell-state measurement. Our schemes can relay quantum information over a network without requiring fully trusted central or intermediate nodes, and none of participants can fully access the information.