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Physical Review A

Probabilistic ancilla-free phase-covariant telecloning of qudits with the optimal fidelity

Xin-Wen Wang, Guojian Yang

Published Jun 26, 2009• 26 citations
Publisher

Abstract

We study the ancilla-free $1\ensuremath{\rightarrow}2$ phase-covariant telecloning for qudits. We show that the fidelity of the two clones can probabilistically reach that of the clones in the optimal $1\ensuremath{\rightarrow}2$ phase-covariant cloning (involving an ancilla). More interestingly, that can realize the above nonlocal cloning tasks are suitable nonmaximally entangled states rather than the maximally entangled states.

DOI
10.1103/physreva.79.064306

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We derive the optimal $N\ensuremath{\rightarrow}M$ phase-covariant quantum cloning for equatorial states in dimension ddd with M=kd+NM=kd+NM=kd+N, kkk integer. The cloning maps are optimal for both global and single-qudit fidelity. The map is achieved by an ``economical'' cloning machine, which works without ancilla.
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.
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 study the 1→ N faithful telecloning of two linear-independent states of a one-qubit system. Based on the analysis of the probabilistic cloning machine, we construct a multiparticle entangled state, and present a telecloning scheme under local operations and classical communication (LOCC). The success probability is greater than half of the optimal probability of the probabilistic cloning machine. Specifically, we show how to prepare the three-particle entangled state needed by 1→2 telecloning under LOCC using the Greenberger-Horne-Zeilinger state as a resource. All the operations in 1→2 telecloning are within the reach of current technology.