Quantum Zeno Effect applied to amplitude damping on a general pointer basis

Abstract

Developing protocols for preserving information in quantum systems is a central quest for implementing realistic quantum computation. However, many of the most promising approaches to this problem rely on hypotheses that may not reflect practical physical scenarios, like knowing the exact dynamics of the qubit-environment system or being able to store an informational qubit in multiple physical qubits. Here, we step away from these usual assumptions and analyze the probability of successfully storing a classical bit of information on a physical qubit during a single computational step, both for the case in which the qubit evolves freely and also when it is subject to a sequence of repeated measurements. The setup consists of a qubit coupled to a heat bath at finite temperature, whose dynamics is given by a generalized amplitude damping channel in a pointer basis that does not necessarily coincide with the computational basis of the qubit. We first show that requiring the dynamics to be Markovian implies an exponential decay of the pointer basis' populations. Then, we obtain the success probability as function of time and angle \(\theta_0\) between the initial state of the qubit and the ground state of the pointer basis. Finally, we calculate these probabilities for the Zeno effective dynamics and show that they are never larger than those for the free evolution, implying that a repeated measurements protocol cannot improve the probability of a successful storage in our model. This last result indicates that to perform realistic quantum computation, when information is being continuously lost to the environment, the information must be somehow driven back into the system, highlighting this as the core feature of any technique that aims at reducing noise in open quantum systems.