Multiparameter estimation with two qubit probes in noisy channels
- URL: http://arxiv.org/abs/2307.13936v1
- Date: Wed, 26 Jul 2023 03:20:48 GMT
- Title: Multiparameter estimation with two qubit probes in noisy channels
- Authors: Lorcan. O. Conlon, Ping Koy Lam and Syed. M. Assad
- Abstract summary: This work compares the performance of single and two qubit probes for estimating several phase rotations simultaneously.
We compute the quantum limits for this simultaneous estimation using collective and individual measurements.
In sufficiently noisy channels, we show that it is possible for single qubit probes to outperform maximally entangled two qubit probes.
- Score: 0.618778092044887
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: This work compares the performance of single and two qubit probes for
estimating several phase rotations simultaneously under the action of different
noisy channels. We compute the quantum limits for this simultaneous estimation
using collective and individual measurements by evaluating the Holevo and
Nagaoka-Hayashi Cram\'er-Rao bounds respectively. Several quantum noise
channels are considered, namely the decohering channel, the amplitude damping
channel and the phase damping channel. For each channel we find the optimal
single and two qubit probes. Where possible we demonstrate an explicit
measurement strategy which saturates the appropriate bound and we investigate
how closely the Holevo bound can be approached through collective measurements
on multiple copies of the same probe. We find that under the action of the
considered channels, two qubit probes show enhanced parameter estimation
capabilities over single qubit probes for almost all non-identity channels,
i.e. the achievable precision with a single qubit probe degrades faster with
increasing exposure to the noisy environment than that of the two qubit probe.
However, in sufficiently noisy channels, we show that it is possible for single
qubit probes to outperform maximally entangled two qubit probes. This work
shows that, in order to reach the ultimate precision limits allowed by quantum
mechanics, entanglement is required in both the state preparation and state
measurement stages. It is hoped the tutorial-style nature of this paper will
make it easily accessible.
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