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Electronics Letters

Qubit state estimation and enhancement by quantum thermal noise

François Chapeau‐Blondeau

Published Sep 25, 2015• 12 citations
Publisher

Abstract

From a qubit in a noisy state affected by an uncontrolled decohering environment represented by a thermal bath at temperature T , estimation of the norm of its Bloch vector is considered, equivalent to estimation of its purity or of its linear entropy. The performance in estimation is assessed by the quantum Fisher information. When the qubit can be prepared with an optimal orientation precisely matched to the thermal noise, the estimation performance always degrades with an increasing temperature of the bath. On the contrary, for a non‐optimal orientation of the qubit, the possibility of an enhancement of the estimation performance with an increasing temperature of the bath is demonstrated. Such behaviour shows that increased decoherence is not necessarily associated with poorer informational performance, and can be compared with stochastic resonance or useful noise effects previously reported in classical (non‐quantum) estimation.

DOI
10.1049/el.2015.2281

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•Jan 30, 2015•1 citation
From a qubit in a noisy state affected by an uncontrolled decohering environment represented by a thermal bath at temperature T , estimation of the norm of its Bloch vector is considered, equivalent to estimation of its purity or of its linear entropy. The performance in estimation is assessed by the quantum Fisher information. When the qubit can be prepared with an optimal orientation precisely matched to the thermal noise, the estimation performance always degrades with an increasing temperature of the bath. On the contrary, for a non‐optimal orientation of the qubit, the possibility of an enhancement of the estimation performance with an increasing temperature of the bath is demonstrated. Such behaviour shows that increased decoherence is not necessarily associated with poorer informational performance, and can be compared with stochastic resonance or useful noise effects previously reported in classical (non‐quantum) estimation.
The task fundamental to quantum communication and coding is considered which consists of detecting between two possible states of a noisy qubit, with a performance assessed by the overall probability of detection error. The detection process operates in the presence of decoherence represented by a quantum thermal noise at an arbitrary temperature. With uneven prior probabilities of the two states, as the noise temperature is increased, non‐monotonic evolutions are reported for the performance, which does not uniformly degrade. Regimes are found where higher noise temperatures are more favourable to detection, with relation to stochastic resonance effects where noise reveals beneficial to information processing.
We exploit the theory of quantum estimation to investigate quantum state estimation in the presence of noise. The quantum Fisher information is used to assess the estimation performance. For the qubit in Bloch representation, general expressions are derived for the quantum score and then for the quantum Fisher information. From this latter expression, it is proved that the Fisher information always increases with the purity of the measured qubit state. An arbitrary quantum noise affecting the qubit is taken into account for its impact on the Fisher information. The task is then specified to estimating the phase of a qubit in a rotation around an arbitrary axis, equivalent to estimating the phase of an arbitrary single-qubit quantum gate. The analysis enables determination of the optimal probing states best resistant to the noise, and proves that they always are pure states but need to be specifically matched to the noise. This optimization is worked out for several noise models important to the qubit. An adaptive scheme and a Bayesian approach are presented to handle phase-dependent solutions.
The fundamental quantum information processing task of estimating the phase of a qubit is considered. Following quantum measurement, the estimation efficiency is evaluated by the classical Fisher information which determines the best performance limiting any estimator and achievable by the maximum likelihood estimator. The estimation process is analyzed in the presence of decoherence represented by essential quantum noises that can affect the qubit and belonging to the broad class of unital quantum noises. Such a class especially contains the bit-flip, the phase-flip, the depolarizing noises, or the whole family of Pauli noises. As the level of noise is increased, we report the possibility of non-standard behaviors where the estimation efficiency does not necessarily deteriorate uniformly, but can experience non-monotonic variations. Regimes are found where higher noise levels prove more favorable to estimation. Such behaviors are related to stochastic resonance effects in signal estimation, shown here feasible for the first time with unital quantum noises. The results provide enhanced appreciation of quantum noise or decoherence, manifesting that it is not always detrimental for quantum information processing.
We investigate the dephasing dynamics of a qubit as an effective mechanism for estimating the temperature of its surrounding environment for different symmetrizes. Our approach is fundamentally quantum, leveraging the qubit's susceptibility to decoherence without necessitating thermal equilibrium with the system under study. We also examine how symmetry properties affect the accuracy of information retrieval and the robustness of quantum information storage in such systems, highlighting their potential advantages in mitigating decoherence effects. The optimization of quantum Fisher information is performed with respect to both the interaction duration and the environmental temperature, focusing on Ohmic-like spectral density environments. Furthermore, we explicitly identify the optimal qubit measurement that attains the quantum Cramer-Rao bound for precision. Our findings reveal that optimal estimation arises from a complex interplay between the qubit's dephasing dynamics and the Ohmic characteristics of the environment with a particular focus on non-Hermitian systems that exhibit enhanced resilience to decoherence. Notably, optimal estimation does not occur when the qubit reaches a stationary state nor under conditions of complete dephasing.
Abstract We address the dephasing dynamics of the quantum Fisher information for the process of quantum thermometry with probes coupled to squeezed thermal baths via the nondemolition interaction. We also calculate the upper bound for the parameter estimation and investigate how the optimal estimation is affected by the initial conditions and decoherence, particularly the squeezing parameters. Moreover, the feasibility of the optimal measurement of the temperature is discussed in detail. Then, the results are generalized for entangled probes and the multi-qubit scenarios for probing the temperature are analysed. Our results show that the squeezing can decrease the number of channel uses for optimal thermometry. Comparing different schemes for multi-qubit estimation, we find that an increase in the number of the qubits, interacting with the channel, does not necessarily vary the precision of estimating the temperature. Besides, we discuss the enhancement of the quantum thermometry using the parallel strategy and starting from the W state.
The unavoidable interaction of a quantum system with its environment usually degrades its coherence and quantumness. The environment and the decoherence process may be described as the interaction with a classical or quantized bath. As a matter of fact, the classical description becomes progressively more reliable as far as the environment has many degrees of freedom, i.e. it becomes complex, or when the interaction between a quantum system and a classical fluctuating field is taken into account. In this thesis, I consider a qubit system coupled to a stochastic classical field and address�the decoherence and non-Markovianity induced by the external noise as well as the spectral characterization of the classical field by quantum-limited measurement on the qubit. I thus analyze the dynamics of quantum correlations between two non-interacting, initially entangled qubits subject to a classical noise generated by a stochastic process. Two relevant classes of noise are taken into account: Gaussian noise, such as the Ornstein-Uhlenbeck process, and non-Gaussian noise, such as the random telgraph noise and the colored noise with 1/f spectrum. I also discuss the evaluation of non-Markovianity of the induced dynamical map and link the presence of revivals of quantum correlations with the information backflow to the system. The precise characterization of the stochastic process generating the classical noise, possibly using minimal resources, is a crucial ingredient for the design of high-precision measurements and reliable communication protocols. To this purpose, I also address the characterization of the spectral parameters of classical noise by quantum probes, e.g. a qubit coupled to the stochastic process generating the noise. By using the tools of quantum estimation theory, I explore the performances of quantum measurements on the qubit and show that it is possible to effectively extract information about the noise.