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Quantum Information and Computation

Asymmetric quantum teleclonging of multiqubit states

Limei Chen, Y.-X. Chen

Published Nov 1, 2007• 7 citations
Publisher

Abstract

A scheme of 1$\rightarrow$2 optimal universal asymmetric quantum telecloning for pure multiqubit states is proposed. We first investigate the telecloning of arbitrary 2-qubit states and then extend it to the case of multiqubit system. We discuss the scheme in terms of the quantum channels and fidelities of clones, as well as the entanglement of states in the telecloning.

DOI
10.26421/qic7.8-2

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A scheme of 1→\rightarrow→2 optimal universal asymmetric quantum telecloning for pure multiqubit states is proposed. We first investigate the telecloning of arbitrary 2-qubit states and then extend it to the case of multiqubit system. We discuss the scheme in terms of the quantum channels and fidelities of clones, as well as the entanglement of states in the telecloning.
We propose a scheme of 1$\to2optimaluniversalasymmetricquantumtelecloningofpuremultiqubitstates.Inparticular,wefirstinvestigatetheasymmetrictelecloningofarbitrary2−qubitstatesandthenextendittothecaseofmultiqubitsystem.Manyfiguresofmeritforthetelecloningprocessarechecked,includingtheentanglementofthequantumchannelandfidelitiesoftheclones.Ourschemecanbeusedforthe12 optimal universal asymmetric quantum telecloning of pure multiqubit states. In particular, we first investigate the asymmetric telecloning of arbitrary 2-qubit states and then extend it to the case of multiqubit system. Many figures of merit for the telecloning process are checked, including the entanglement of the quantum channel and fidelities of the clones. Our scheme can be used for the 12optimaluniversalasymmetricquantumtelecloningofpuremultiqubitstates.Inparticular,wefirstinvestigatetheasymmetrictelecloningofarbitrary2−qubitstatesandthenextendittothecaseofmultiqubitsystem.Manyfiguresofmeritforthetelecloningprocessarechecked,includingtheentanglementofthequantumchannelandfidelitiesoftheclones.Ourschemecanbeusedforthe1\to$4 universal telecloning of mixed multiqubit states.
We study the process of quantum telecloning of d -dimensional pure quantum states using partially entangled pure states as quantum channel. This process efficiently mixes optimal universal symmetric cloning with quantum teleportation. It is shown that it is possible to implement universal symmetric telecloning in a probabilistic way using unambiguous state discrimination and quantum state separation schemes. It is also shown that other strategies, such as minimum error discrimination, lead to a decrease in the fidelity of the copies and that certain partially entangled pure states with maximal Schmidt rank lead to an average telecloning fidelity which is always above the optimal fidelity of measuring and preparation of quantum states. We also discuss the case of partially entangled pure states with non-maximal Schmidt rank. The results presented here are valid for arbitrary numbers of copies of a single-input qudit state of any dimension.
A scheme combining three processes of quantum teleportation, optimal universal quantum flipping and optimal universal quantum cloning for universal teleflipping and telecloning of arbitrary qubit is proposed. When a particular four-particle entangled state shared by the sender and three spatially separated receivers is used as quantum information channel, after the sender's Bell measurement, class ical communication and each receiver's local unitary operation, one receiver can get one orthogonal complementing state of the original unknown state with the o ptimal fidelity of 2/3, the other two receivers can respectively get one copy of the original unknown state with the optimal fidelity of 5/6. This scheme implem ents the universal quantum teleflipping and telecloning simultaneously with corr esponding optimal fidelity by using the reduced entanglement. The key to realizi ng this scheme is the construction of the particular four-particle entangled sta te shared by the sender and three receivers used as quantum information channel. The entanglement structure of the special four-particle entangled state is anal yzed.
We propose a generalization of quantum teleportation: the so-called many-to-many quantum communication of the information of a d-level system from N spatially separated senders to M>NM>NM>N receivers situated at different locations. We extend the concept of asymmetric telecloning from qubits to d-dimensional systems. We investigate the broadcasting of entanglement by using local $\stackrel{\ensuremath{\rightarrow}}{1}2$ optimal universal asymmetric Pauli machines and show that the maximal fidelities of the two final entangled states are obtained when symmetric machines are applied. Cloning of entanglement is studied using a nonlocal optimal universal asymmetric cloning machine and we show that the symmetric machine optimally copies the entanglement. The ``many-to-many'' teleportation scheme is applied in order to distribute entanglement shared between two observers to two pairs of spatially separated observers.
Due to the no-cloning theorem, generating perfect quantum clones of an arbitrary unknown quantum state is not possible, however approximate quantum clones can be constructed. Quantum telecloning is a protocol that originates from a combination of quantum teleportation and quantum cloning. Here we present 1 → 2 and 1 → 3 quantum telecloning circuits, with and without ancilla, that are theoretically optimal (meaning the clones have the highest fidelity allowed by quantum mechanics), universal (meaning the clone fidelity is independent of the state being cloned), and symmetric (meaning the clones all have the same fidelity). We implement these circuits on gate model IBMQ and Quantinuum NISQ hardware and quantify the clone fidelities using parallel single qubit state tomography. Quantum telecloning using mid-circuit measurement with classical feed-forward control (i.e. real time if statements) is demonstrated on the Quantinuum H1-2 device. Two alternative implementations of quantum telecloning, deferred measurement and post selection, are demonstrated on ibmq_montreal, where mid-circuit measurements with real time if statements are not available. Our results show that NISQ devices can achieve near-optimal quantum telecloning fidelity; for example the Quantinuum H1-2 device running the telecloning circuits without ancilla achieved a mean clone fidelity of 0.824 with standard deviation of 0.024 for two clone circuits and 0.765 with standard deviation of 0.022 for three clone circuits. The theoretical fidelity limits are 0.83ˉ0.8\bar 30.83ˉ for two clones and 0.7ˉ0.\bar 70.7ˉ for three clones. This demonstrates the viability of performing experimental analysis of quantum information networks and quantum cryptography protocols on NISQ computers.
We propose a scheme to implement the optimal symmetric 1 → 2 universal quantum telecloning through cavity-assisted interaction. In our scheme, an arbitrary single atomic state can be telecloned to two single atomic states. And three atoms are trapped in three spatially separated cavities respectively. With a particular multiparticle entangled state acting as a quantum information channel and the trapped single atom acting as a quantum network node for its long-lived internal state, quantum information can be telecloned among nodes and can stored in the nodes.