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.
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.
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.
For discrimination between two signaling states of a qubit, the optimal detector minimizing the probability of error is applied to the situation where detection has to be performed from a noisy qubit affected by an arbitrary quantum noise separately characterized. With no noise, any pair of orthogonal pure quantum states is optimal for signaling as it enables error-free detection. In the presence of noise, detection errors are in general inevitable, and the pairs of signaling states best resistant to such noise are investigated. With an arbitrary quantum noise, modeled as a channel affecting the qubit, and when minimum-error detection is performed from the output, a characterization of the optimal input signaling pairs and of their best detection performance is obtained through a simple maximization of a quadratic scalar criterion in three constrained real variables. This general characterization enables to establish that such optimal signaling pairs are always made of two orthogonal pure quantum states, but that they must be specifically selected to match the noise properties and prior probabilities. The maximization is explicitly solved for several generic quantum noise processes relevant to the qubit, such as the squeezed generalized amplitude damping noise which describes interaction with a thermal bath representing a decohering environment and which includes as special cases both the generalized and the regular amplitude damping noise processes, and such as general Pauli noise processes which include for instance the bit-flip noise and the depolarizing noise. Also, examined is the situation of one imposed (pure or mixed) signaling state, for which the other associated signaling state optimal for noisy detection is determined as a pure state, yet not necessarily orthogonal.
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.
Quantum phenomena such as superposition and entanglement imbue quantum systems with information processing power in excess of their classical counterparts. These properties of quantum states are, however, highly fragile. As we enter the era of noisy intermediate-scale quantum (NISQ) devices, this vulnerability to noise is a major hurdle to the experimental realisation of quantum technologies. In this thesis we explore the role of noise in quantum information processing from two different perspectives. In Part I we consider noise from the perspective of quantum error correcting codes. Error correcting codes are often analysed with respect to simplified toy models of noise, such as iid depolarising noise. We consider generalising these techniques for analysing codes under more realistic noise models, including features such as biased or correlated errors. We also consider designing customised codes which not only take into account and exploit features of the underlying physical noise. Considering such tailored codes will be of particular importance for NISQ applications in which finite-size effects can be significant. In Part II we apply tools from information theory to study the finite-resource effects which arise in the trade-offs between resource costs and error rates for certain quantum information processing tasks. We start by considering classical communication over quantum channels, providing a refined analysis of the trade-off between communication rate and error in the regime of a finite number of channel uses. We then extend these techniques to the problem of resource interconversion in theories such as quantum entanglement and quantum thermodynamics, studying finite-size effects which arise in resource-error trade-offs. By studying this effect in detail, we also show how detrimental finite-size effects in devices such as thermal engines may be greatly suppressed by carefully engineering the underlying resource interconversion processes.
We analyze quantum state preservation in open quantum systems using quantum error-correcting (QEC) codes explicitly embedded in microscopic system-bath models. Rather than assuming abstract quantum channels, we consider multi-qubit registers coupled to bosonic thermal environments, derive a second-order master equation for the reduced dynamics, and use it to benchmark the five-qubit, Steane, and toric codes under local and collective noise. We compute state fidelities as functions of system-bath coupling strength, bath temperatures, and the number of correction cycles. In the low-temperature regime, repeated error correction with the five-qubit code significantly suppresses decoherence and relaxation for weak-to-moderate couplings. In the high-temperature regime, thermal excitations reduce the effectiveness of all codes, although within the parameter range studied, the five-qubit code still yields the highest fidelities among the three codes. For two-qubit Werner states, we identify a critical evolution time associated with an early-time crossover, before which the overhead of QEC does not compensate for the noise-induced degradation; this critical time increases with entanglement, reflecting the greater fragility of strongly entangled states. Overall, our results provide a microscopic master-equation-based framework for benchmarking QEC performance in realistic open-system environments and for assessing code behavior in near-term noisy quantum architectures.
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.