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arXiv:2307.04413 · International Journal of Quantum Information

Quantum Zeno effect: A qutrit controlled by a qubit

Komal Kumari, Garima Rajpoot, Sudhir R. Jain

Published Jan 27, 2024• 1 citation
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Abstract

For a three-level system monitored by an ancilla, we show that the quantum Zeno effect can be employed to control quantum jump for error correction. Further, we show that we can realize cNOT gate, and effect dense coding and teleportation using a three-level system with an ancilla. We believe that this work paves the way to generalize the control of a qudit.

DOI
10.1142/s0219749924500060

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For a three-level system monitored by an ancilla, we show that the quantum Zeno effect can be employed to control quantum jump for error correction. Further, we show that we can realize cNOT gate, and effect dense coding and teleportation using a three-level system with an ancilla. We believe that this work paves the way to generalize the control of a qudit.
In Nature, 570, 200 (2019), Minev and co-authors’ experiment shows how to deterministically “catch and reverse a quantum jump mid-flight” in a continuously-observed Rabi-stimulated qubit. Its interpretation is in debate (La Recherche, 555, 40, (2020)). We show that the quantum Zeno effect (QZE) of continuous measurement —by use of photon emission from a 3rd high-rate monitored ancilla level— can be described by an action-angle canonical transformation of the original Hamiltonian dynamical system (HDS) theory of QZE. Then energy whose mean value yields the well-known resonant Rabi harmonic dynamics is actually defined by large-amplitude high-frequency oscillations of the internal as well as of the overall phase of the two-level system. By making use of their standard deviation, we show that the separatrix crossing of the HDS trajectory yields the quantized action nh where n = 1, 2, 3 .... Therefore, the jump dynamics observed in Minev et al. experiment belongs to a series of discrete quantum jumps: it corresponds in this experiment to n = 3.
In principle the Zeno effect controlled-sign gate of Franson et al (2004 Phys. Rev. A 70 062302) is a deterministic two-qubit optical gate. However, when realistic values of photon loss are considered its fidelity is significantly reduced. Here we consider the use of measurement based quantum processing techniques to enhance the operation of the Zeno gate. With the help of quantum teleportation, we show that it is possible to achieve a Zeno CNOT gate (GC-Zeno gate) that gives (near) unit fidelity and moderate probability of success of 0.8 with a two-photon to one-photon absorption ratio κ = 10 4 . We include some mode-mismatch effects and estimate the bounds on the mode overlap and κ for which fault tolerant operation would be possible.
The protection of the coherence of open quantum systems against the influence of their environment is a very topical issue. A scheme is proposed here which protects a general quantum system from the action of a set of arbitrary uncontrolled unitary evolutions. This method draws its inspiration from ideas of standard error correction (ancilla adding, coding and decoding) and the quantum Zeno effect. A demonstration of our method on a simple atomic system---namely, a rubidium isotope---is proposed.
Quantum information processing has become a promising research area. In quantum information processing qubits and qutrits will be used instead of bits. A qubit is a two level quantum system and a qutrit is a three level quantum system. Zeeman levels of spin-1 electron or nucleus can be considered as qutrit states. In this study, first, two and three qutrit SWAP logic gates are developed. For two qutrit states, there exist different types of CNOT quantum logic gates. The relationships between these different types of CNOT gates are obtained in this study.
We show how the quantum Zeno effect can be exploited to control quantum many-body dynamics for quantum information and computation purposes. In particular, we consider a one dimensional array of three level systems interacting via a nearest-neighbour interaction. By encoding the qubit on two levels and using simple projective frequent measurements yielding the quantum Zeno effect, we demonstrate how to implement a well defined quantum register, quantum state transfer on demand, universal two-qubit gates and two-qubit parity measurements. Thus, we argue that the main ingredients for universal quantum computation can be achieved in a spin chain with an always-on and constant many-body Hamiltonian. We also show some possible modifications of the initially assumed dynamics in order to create maximally entangled qubit pairs and single qubit gates.