Quantifying Quantum Coherence, New Detection Methods and Robustness Bounds.

Researchers demonstrate novel methods for detecting and quantifying quantum coherence, a fundamental property of mechanics. They establish a coherence criterion using partial transposition and a nonlinear detection strategy that outperforms standard techniques, particularly for certain coherent states. A refined lower bound for coherence robustness, based on witness operators, is also presented.

Quantum coherence, a fundamental property dictating the superposition of quantum states, underpins many processes crucial to emerging technologies such as quantum computing and sensing. Accurately detecting and quantifying this coherence remains a significant challenge, requiring methods that move beyond complete state characterisation. Researchers at Hainan Normal University, Yiding Wang and Tinggui Zhang, address this need in their article, “Notes on detection and measurement of quantum coherence”, by proposing novel criteria and strategies for coherence assessment. Their work details a partial transposition-based coherence criterion, a coherent nonlinear detection strategy utilising witnesses – operators used to identify quantum states with specific properties – and a refined lower bound for coherence robustness, a measure of a state’s resistance to decoherence, offering improvements over existing methods and potentially facilitating advancements in quantum technologies.

Quantum state characterisation receives advancement through refined coherence detection methods, moving beyond the comprehensive, yet resource-intensive, technique of full state tomography. Researchers now establish a coherence criterion predicated on partial transposition, a mathematical operation that rearranges the elements of a density matrix, offering a more efficient assessment of quantum coherence. This approach demonstrates the limitations of standard ‘witness-based’ detection, which frequently fails to identify coherence in certain quantum states. The newly proposed nonlinear detection strategy successfully identifies coherence in these previously elusive instances, and crucially, detection success increases with the number of state copies utilised. This highlights the benefit of employing multiple, identical copies of a quantum state to enhance signal reliability and overcome the inherent limitations of analysing single states.

Addressing the computational complexity of determining coherence robustness for arbitrary quantum states, researchers introduce a novel lower bound calculated using the ‘witness operator’, a Hermitian operator used to verify the presence of a quantum state. Comparative analysis demonstrates this newly developed lower bound outperforms currently established limits, offering a more accurate and potentially useful metric for assessing the resilience of quantum coherence. This ability to accurately detect, quantify, and assess the robustness of coherence proves crucial for the development and optimisation of quantum devices and protocols, opening new avenues for progress in quantum technologies.

Characterisation of ‘multipartite entanglement’, a phenomenon where multiple quantum particles are linked together, utilises ‘Bell-like inequalities’, mathematical expressions that define limits imposed by classical physics. Investigations focus on ‘Greenberger-Horne-Zeilinger (GHZ)’ and ‘W states’, specific examples of multipartite entangled states. Experiments successfully demonstrate violation of these Bell-like inequalities, confirming the presence of GHZ entanglement even when ‘decoherence’, the loss of quantum information due to interaction with the environment, is introduced. The degree of violation diminishes with increasing noise levels, a predictable consequence of environmental interaction.

The ability to discriminate between different entangled states proves crucial for implementing specific quantum protocols that rely on particular entanglement structures. Investigations reveal the feasibility of detecting GHZ states when qubits, the fundamental units of quantum information, traverse a noisy quantum channel. Results indicate that entanglement detection remains viable even under these conditions, demonstrating the potential for long-distance quantum communication and networking. Experiments employ a series of measurements designed to test these principles, confirming the persistence of entanglement despite environmental interference.

Researchers establish that entanglement persists even with noise, as the degree of violation of Bell-like inequalities diminishes, but does not disappear, with increasing noise levels. This resilience is crucial for practical quantum technologies, suggesting that quantum systems are more robust than previously thought and can function effectively even in imperfect environments.