Quantum coherence is the key resource in quantum technologies, including faster computing, secure communication, and advanced sensing. Its quantification and detection are, therefore, paramount within the context of quantum information processing. Having certain prior knowledge of the observables may enhance the efficiency of coherence detection. In this work, we posit that the trace of the observables is a known quantity. Our investigation confirms that this assumption indeed extends the scope of coherence-detection capabilities. Utilizing this prior knowledge of the trace of the observables, we establish a series of coherence-detection criteria. We investigate the detection capabilities of these coherence criteria from diverse perspectives and ultimately ascertain the existence of four distinct and inequivalent criteria. These findings contribute to the deepening of our understanding of coherence-detection methodologies, thereby potentially opening new avenues for advancements in quantum technologies.
Quantum coherence is the key resource in quantum technologies, including faster computing, secure communication, and advanced sensing. Its quantification and detection are, therefore, paramount within the context of quantum information processing. Having certain prior knowledge of the observables may enhance the efficiency of coherence detection. In this work, we posit that the trace of the observables is a known quantity. Our investigation confirms that this assumption indeed extends the scope of coherence-detection capabilities. Utilizing this prior knowledge of the trace of the observables, we establish a series of coherence-detection criteria. We investigate the detection capabilities of these coherence criteria from diverse perspectives and ultimately ascertain the existence of four distinct and inequivalent criteria. These findings contribute to the deepening of our understanding of coherence-detection methodologies, thereby potentially opening new avenues for advancements in quantum technologies.
Quantum coherence is a fundamental feature that enables the distinctive advantages of quantum systems, including enhanced computational power and secure communication. The rapid evolution of quantum technologies has highlighted the importance of understanding how coherence affects information processing and system stability. This study aims to decode the role of quantum coherence in improving computational efficiency, error rates, and system resilience, providing critical insights into the operational stability of quantum systems. The research employs a qualitative literature review, synthesizing data from various studies to identify patterns and key insights into the impact of quantum coherence. The review focuses on a diverse range of quantum platforms, including superconducting qubits, trapped ions, and quantum communication systems, to assess the influence of coherence on their operational capacities. Data collection involved a systematic selection of over 80 peer-reviewed articles, which were analyzed using thematic coding to explore the relationships among coherence, error rates, and system stability. The findings reveal that coherence significantly enhances the fidelity and depth of quantum operations, thereby improving computational accuracy and communication security. However, maintaining coherence across different quantum systems remains a challenge due to environmental decoherence. The study suggests that continued research into error-correction techniques, material innovations, and environmental shielding is crucial to advancing quantum technologies. In conclusion, quantum coherence remains a pivotal element for achieving scalable and fault-tolerant quantum systems. Future research should focus on developing coherence-preserving technologies and exploring hybrid quantum-classical approaches to bridge the gap between theoretical potential and practical deployment.
Quantum information science aims to harness different kinds of quantum resources to accomplish specific information-processing tasks. These resources also play an increasingly important role in addressing fundamental questions concerning quantum phases and dynamics. Therefore, developing powerful and practical methods for identifying and detecting quantum resources is of great significance, with applications ranging from benchmarking quantum devices to understanding the fundamental structure of quantum theory. In this work, we propose witness expansion, a unified framework for constructing nonlinear criteria for detecting quantum resources that are associated with a well-defined group of free unitaries. These criteria apply to both pure and mixed quantum states and are based on polynomial functions of the target state, which can be estimated experimentally using multiple copies of the state and evaluated analytically in certain physical models. We show how several well-known resource-detection quantities naturally emerge from our framework, including the l2 norm of coherence, partial-transpose moments for entanglement, stabilizer entropy for nonstabilizerness (quantum magic), and fermionic antiflatness for fermionic non-Gaussianity. Beyond recovering these existing structures, our framework also yields new criteria for detecting qubit and qudit magic states, substantially enhancing witness-based detection capabilities. In addition, it gives, to the best of our knowledge, the first analytical criterion for detecting mixed-state fermionic non-Gaussianity with respect to the convex hull of pure fermionic Gaussian states that remains nontrivial for arbitrary numbers of qubits, demonstrating the broad applicability and conceptual unifying power of the framework.
Entanglement detection is essential in quantum information science and quantum many-body physics. It has been proved that entanglement exists almost surely for a random quantum state, while the realizations of effective entanglement criteria usually consume exponentially many resources with regard to system size or qubit number, and efficient criteria often perform poorly without prior knowledge. This fact implies a fundamental limitation might exist in the detectability of entanglement. In this work, we formalize this limitation as a fundamental trade-off between the efficiency and effectiveness of entanglement criteria via a systematic method to evaluate the detection capability of entanglement criteria theoretically. For a system coupled to an environment, we prove that any entanglement criterion needs exponentially many observables to detect the entanglement effectively when restricted to single-copy operations. Otherwise, the detection capability of the criterion will decay double exponentially. Furthermore, if multicopy joint measurements are allowed, the effectiveness of entanglement detection can be exponentially improved, which implies a quantum advantage in entanglement detection problems. Our results may shed light on why quantum phenomena are difficult to observe in large noisy systems.
Quantum coherence, present whenever a quantum system exists in a superposition of multiple classically distinct states, marks one of the fundamental departures from classical physics.Quantum coherence has recently been investigated rigorously within a resource-theoretic formalism.However, the finer-grained notion of multilevel coherence, which explicitly takes into account the number of superposed classical states, has remained relatively unexplored.A comprehensive analysis of multilevel coherence, which acts as the singleparty analogue to multipartite entanglement, is essential for understanding natural quantum processes as well as for gauging the performance of quantum technologies.Here, we develop the theoretical and experimental groundwork for characterizing and quantifying multilevel coherence.We prove that nontrivial levels of purity are required for multilevel coherence, as there is a ball of states around the maximally mixed state that do not exhibit multilevel coherence in any basis.We provide a simple, necessary, and sufficient analytical criterion to verify the presence of multilevel coherence, which leads to a complete classification of multilevel coherence for three-level systems.We present the robustness of multilevel coherence, a bona fide quantifier, which we show to be numerically computable via semidefinite programming and experimentally accessible via multilevel coherence witnesses, which we introduce and characterize.We further verify and lower bound the robustness of multilevel coherence by performing a semi-device-independent phase discrimination task, which is implemented experimentally with four-level quantum probes in a photonic setup.Our results contribute to understanding the operational relevance of genuine multilevel coherence, also by demonstrating the key role it plays in enhanced phase discrimination-a primitive for quantum communication and metrology-and suggest new ways to reliably and effectively test the quantum behavior of physical systems.
The detection and characterization of quantum coherence is of fundamental importance both in the foundations of quantum theory as well as for the rapidly developing field of quantum technologies, where coherence has been linked to quantum advantage. Typical approaches for detecting coherence employ {\it coherence witnesses} -- observable quantities whose expectation value can be used to certify the presence of coherence. By design, coherence witnesses are only able to detect coherence for some, but not all, possible states of a quantum system. In this work we construct protocols capable of detecting the presence of coherence in an {\it unknown} pure quantum state ∣ψ⟩. Having access to m copies of an unknown pure state ∣ψ⟩ we show that the sample complexity of any experimental procedure for detecting coherence with constant probability of success ≥2/3 is Θ(c(∣ψ⟩)−1), where c(∣ψ⟩) is the geometric measure of coherence of ∣ψ⟩. However, assuming access to the unitary Uψ which prepares the unknown state ∣ψ⟩, and its inverse Uψ†, we devise a coherence detecting protocol that employs amplitude-amplification {\it a la} Grover, and uses a quadratically smaller number O(c(∣ψ⟩)−1/2) of samples. Furthermore, by augmenting amplitude amplification with phase estimation we obtain an experimental estimation of upper bounds on the geometric measure of coherence within additive error ε with a sample complexity that scales as O(1/ε) as compared to the O(1/ε2) sample complexity of Monte Carlo estimation methods. The average number of samples needed in our amplitude estimation protocol provides a new operational interpretation for the geometric measure of coherence. Finally, we also derive bounds on the amount of noise our protocols are able to tolerate.
Quantum communication and quantum sensing, which leverage the unique characteristics of quantum systems, enable information-theoretically secure communication and high-precision measurement of physical quantities. However, they both face numerous challenges on the path to practical application. Artificial intelligence (AI), as a major technological advancement in current scientific landscape, offers powerful data processing and analytical capabilities, providing new ideas and methods for optimizing and enhancing quantum communication and sensing systems. In quantum communication, AI techniques have greatly improved the performance and security of quantum key distribution, quantum memory, and quantum networks through parameter optimization, real-time feedback control, and attack detection. In quantum sensing, quantum sensing technology enables ultra-high sensitivity detection of physical quantities such as time and magnetic fields. The introduction of AI has opened up new avenues for achieving high-precision and high-sensitivity quantum measurements. With AI, sensor performance is optimized, and measurement accuracy is further enhanced through data analysis. This paper also analyzes the current challenges in using AI to empower quantum communication and sensing systems, such as implementing efficient algorithm deployment and system feedback control under limited computational resources, and addressing complex task environments, dynamically changing scenarios, and multi-task coordination requirements. Finally, this paper discusses and envisions future development prospects in this field.