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arXiv:2001.09430 · Physical Review A

Counterfactual logic gates

Zheng-Hong Li, Xiaofei Ji, Saeed Asiri, Luojia Wang, M. Al-Amri

Published Aug 10, 2020• 10 citations

Abstract

We present how basic logic gates including nand, nor, and xor gates can be implemented counterfactually. The two inputs (Bob and Charlie) and the output (Alice) of the proposed counterfactual logic gate are not within the same station but rather separated in three different locations. We show that there is no need to prearrange entanglement for the gate, and, more importantly, there are no real physical particles traveling among Alice, Bob, and Charlie during the information processing. Bob and Charlie only need to independently control the blocking and unblocking of the transmission channels that connect them to Alice. In this way, they can completely determine the state of a real photon at Alice's end, thereby leading to implemention of a counterfactual logic gate. The functionality of a particular counterfactual logic gate is determined only by an appropriate design of Alice's optical device. Furthermore, by utilizing the proposed counterfactual logic gates, we demonstrate how to counterfactually prepare the Greenberger-Horne-Zeilinger state and W state with three remote quantum objects, which are in superposition states of blocking and unblocking the transmission channel.

DOI: 10.1103/physreva.102.022606

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We show that an unknown quantum state can be transferred with neither quantum nor classical particle traveling in the transmission channel. Our protocol does not require prearranged entangled photon pairs and Bell measurements. By utilizing quantum Zeno effect and counterfactuality, we can entangle and disentangle a photon and an atom by nonlocal interaction. It is shown that quantum information is completely transferred from an atom to photon due to controllable disentanglement processes. There is no need to cross-check the result via classical channels.

We show that two unknown quantum states, either pure or mixed, can be bidirectionally ``teleported'' counterfactually. In the process of information exchange, there is no physical particle traveling between two communicators. Unlike conventional quantum teleportation, our protocol requires neither prearranged entangled pairs nor Bell measurements. We entangle and disentangle a photon and an atom through multiple measurements in a special sequence. These multiple measurements can smoothly but reversibly control system evolution. The total effect of multiple measurements can be considered as a unitary time evolution operator. Therefore, our protocol can be regarded as a counterfactual quantum swap gate. Based on our approach, all known conventional quantum gates can be counterfactualized.

By encoding the digital input of a classical logic gate on the Hamiltonian of a quantum system and driving the logic operation by preparing it in the same nonstationary state whatever the input, NOR and NAND classical logic gates are designed with a minimum of three quantum states. The outputs of one gate are obtained either by measuring the distance between the $\ensuremath{\rho}(t)$ periodic quantum trajectory and the output target state ${\ensuremath{\rho}}_{b}$, or by measuring the secular frequency of the $\ensuremath{\rho}(t)$ almost periodic trajectory in the ${\ensuremath{\rho}}_{b}$ direction. A comparison of the stability to noise between the two approaches demonstrates that the frequency approach is more immune to random fluctuations in the Hamiltonian than a distance control approach, opening the way to determine the logic output using a tunneling current passing through the gate.

Quantum teleportation circumvents the uncertainty principle using dual channels: a quantum one consisting of previously-shared entanglement, and a classical one, together allowing the disembodied transport of an unknown quantum state over distance. It has recently been shown that a classical bit can be counterfactually communicated between two parties in empty space, “Alice” and “Bob”. Here, by using our “dual” version of the chained quantum Zeno effect to achieve a counterfactual CNOT gate, we propose a protocol for transporting an unknown qubit counterfactually, that is without any physical particles travelling between Alice and Bob—no classical channel and no previously-shared entanglement.