Abstract Quantum multiparameter estimation involves estimating multiple parameters simultaneously and can be more precise than estimating them individually. Our interest here is to determine fundamental quantum limits to the achievable multiparameter estimation precision in the presence of noise. We first present a lower bound to the estimation error covariance for a noisy initial probe state evolving through a noiseless quantum channel. We then present a lower bound to the estimation error covariance in the most general form for a noisy initial probe state evolving through a noisy quantum channel. We show conditions and accordingly measurements to attain these estimation precision limits for noisy systems. We see that the Heisenberg precision scaling of 1/N can be achieved with a probe comprising N particles even in the presence of noise. In fact, some noise in the initial probe state or the quantum channel can serve as a feature rather than a bug, since the estimation precision scaling achievable in the presence of noise in the initial state or the channel in some situations is impossible in the absence of noise in the initial state or the channel. However, a lot of noise harms the quantum advantage achievable with N parallel resources, and allows for a best precision scaling of ${\bf{1}}/\sqrt{{\boldsymbol{N}}}$ 1 / N . Moreover, the Heisenberg precision limit can be beaten with noise in the channel, and we present a super-Heisenberg precision limit with scaling of 1/N2 for optimal amount of noise in the channel, characterized by one-particle evolution operators. Furthermore, using γ-particle evolution operators for the noisy channel, where γ > 1, the best precision scaling attainable is 1/N2γ, which is otherwise known to be only possible using 2γ-particle evolution operators for a noiseless channel.Abstract Quantum multiparameter estimation involves estimating multiple parameters simultaneously and can be more precise than estimating them individually. Our interest here is to determine fundamental quantum limits to the achievable multiparameter estimation precision in the presence of noise. We first present a lower bound to the estimation error covariance for a noisy initial probe state evolving through a noiseless quantum channel. We then present a lower bound to the estimation error covariance in the most general form for a noisy initial probe state evolving through a noisy quantum channel. We show conditions and accordingly measurements to attain these estimation precision limits for noisy systems. We see that the Heisenberg precision scaling of 1/N can be achieved with a probe comprising N particles even in the presence of noise. In fact, some noise in the initial probe state or the quantum channel can serve as a feature rather than a bug, since the estimation precision scaling achievable in the presence of noise in the initial state or the channel in some situations is impossible in the absence of noise in the initial state or the channel. However, a lot of noise harms the quantum advantage achievable with N parallel resources, and allows for a best precision scaling of $${\bf{1}}/\sqrt{{\boldsymbol{N}}}$$ 1 / N . Moreover, the Heisenberg precision limit can be beaten with noise in the channel, and we present a super-Heisenberg precision limit with scaling of 1/N2 for optimal amount of noise in the channel, characterized by one-particle evolution operators. Furthermore, using γ-particle evolution operators for the noisy channel, where γ > 1, the best precision scaling attainable is 1/N2γ, which is otherwise known to be only possible using 2γ-particle evolution operators for a noiseless channel.

arXiv:1805.07902Scientific ReportsJan 31, 20199 citations

The uncertainty of quantum channels in terms of variance

Yuan Sun, Nan Li

Quantum Information ProcessingJan 1, 202126 citations

Quantum illumination strategy for parameter estimation

L. Davidovich, R. L. de Matos Filho

Establishing the limits of precision in the estimation of parameters for noisy quantum channels probed by qubits is important for many areas of quantum information, such as quantum sensing, computation, and communication. Here we consider the estimation of parameters characterizing a general class of noisy Pauli channels. We show that two entangled qubits, such that only one of them probes the channel, may lead, under an entangling measurement, to strong enhancement of the precision in the estimation, as compared to the precision corresponding to sending the pair, entangled or not, through the channel. We prove that entanglement plays an essential role, as does the entangling detection procedure, consisting in projecting the final state onto a Bell-state basis. We also prove that quantum advantage is obtained only when the output state, after interaction with the sample, is not entangled anymore. This behavior has striking similarities with quantum illumination, where initial entanglement of probe and ancilla beams, followed by an entangling measurement, lead to enhancement of the sensitivity of photodetection, even after the output beams are disentangled. Similarities and differences with ghost imaging are also discussed.Establishing the limits of precision in the estimation of parameters for noisy quantum channels probed by qubits is important for many areas of quantum information, such as quantum sensing, computation, and communication. Here we consider the estimation of parameters characterizing a general class of noisy Pauli channels. We show that two entangled qubits, such that only one of them probes the channel, may lead, under an entangling measurement, to strong enhancement of the precision in the estimation, as compared to the precision corresponding to sending the pair, entangled or not, through the channel. We prove that entanglement plays an essential role, as does the entangling detection procedure, consisting in projecting the final state onto a Bell-state basis. We also prove that quantum advantage is obtained only when the output state, after interaction with the sample, is not entangled anymore. This behavior has striking similarities with quantum illumination, where initial entanglement of probe and ancilla beams, followed by an entangling measurement, lead to enhancement of the sensitivity of photodetection, even after the output beams are disentangled. Similarities and differences with ghost imaging are also discussed.

Physical Review AOct 19, 20231 citation

Quantum Capacity of Noisy Quantum Channel

Masanori Ohya, Noboru Watanabe

Springer eBooksJan 1, 199734 citations

{\bf{1}}/\sqrt{{\boldsymbol{N}}}

1 / N . Moreover, the Heisenberg precision limit can be beaten with noise in the channel, and we present a super-Heisenberg precision limit with scaling of 1/N2 for optimal amount of noise in the channel, characterized by one-particle evolution operators. Furthermore, using γ-particle evolution operators for the noisy channel, where γ > 1, the best precision scaling attainable is 1/N2γ, which is otherwise known to be only possible using 2γ-particle evolution operators for a noiseless channel.