Entanglement is at the heart of quantum technologies such as quantum information and quantum metrology. Providing larger quantum Fisher information (QFI), entangled systems can be better resources than separable systems in quantum metrology. QFI topic is a very active research area and it has many possible usage areas in quantum information domain. In this study, we review quantum Fisher information research with both from theoritical and application perspective.
Entanglement is at the heart of quantum technologies such as quantum information and quantum metrology. Providing larger quantum Fisher information (QFI), entangled systems can be better resources than separable systems in quantum metrology. QFI topic is a very active research area and it has many possible usage areas in quantum information domain. In this study, we review quantum Fisher information research with both from theoritical and application perspective.
Quantum metrology is one of the hot topics in ultra-cold atoms physics. It is now well established that with the help of entanglement, the measurement sensitivity can be greatly improved with respect to the current generation of interferometers that are using classical sources of particles. Recently, Quantum Fisher information plays an important role in this field. In this paper, a brief introduction on Quantum metrology is presented highlighting the role of the Quantum Fisher information. And then a brief review on the recent developments for i) criteria of multi-particle entanglement and its experimental generation; ii) linear and non-linear atomic interferometers; iii) the effective statistical methods for the analysis of the experimental data.
Studies about Quantum Information Theory continue actively in many research institutions. Very recently, pratical setups of large scale quantum computers are widely studied e.g. quantum repeaters, memories and processors. Entanglement provides us a computational advantage in realization of quantum algorithms. Some ways to quantifiying entanglement were defined. The best formal way to quantify it, is the methods that we call Entanglement Measures or Entanglement Monotones. In this research area, State Ordering Problem is defined and still an open problem especially for multiparticle entangled states. Fisher Information provides a good background for the solution of some actual Information Theory problems. Quantum Fisher Information (QFI) is a value that could be used in situations where phase sensitivity is important and this concept is expected to be the quantum version of the mentioned inftrastructure for Quantum Systems. QFI cannot be defined as an Entaglement Measure or Monotone. In the scope of this thesis, a new optimization technique is proposed for optimizing QFI and thanks to this optimization method, the ordering relation between QFI and entanglement measures is studied. Based on the studies made in the area of quantum state ordering, new and interesting analysis results are found and reported. The main important and interesting result achieved is that for two qubit quantum states, QFI maximized under Local Operation and Classical Communication has an interesting ordering relation with entanglement measures especially with Relative Entropy of Entanglement. Our study is extended for the qubit-qutrit systems and ordering relations and classification results are presented. For some quantum systems, the changes in QFI under decoherence channels are also considered.
Quantum Fisher information (QFI) quantifies the sensitivity of a quantum state to a parameter change and plays a key role in quantum metrology. Meanwhile, quantum coherence is a crucial resource for quantum information processing. However, despite extensive studies on various aspects of quantum metrology, the interplay between the dynamics of the QFI and quantum coherence remains unexplored. Here, we explore the factorization relationship between the QFI and quantum coherence, both theoretically and experimentally. We prepare pure states in qubit and qutrit systems and apply unitary evolution to investigate this relationship. Our results confirm the factorization law, offering strong evidence for this relationship. Furthermore, we establish a lower bound on the variance of the estimated parameter that does not require the final state information. This approach reveals a deep connection between the QFI and quantum coherence, providing insights into quantum parameter estimation. These findings have potential applications in quantum sensing and quantum metrology.
Quantum Fisher information (QFI) has become a fundamental aspect of quantum metrology, connecting the geometry of quantum states to the highest levels of accuracy. In the last ten years, QFI has changed from a purely theoretical concept to a framework that brings together the design of noise-resistant protocols, tests for entanglement in experiments, and benchmarks new quantum platforms. In this Perspective, we examine how QFI is transcending theoretical frameworks to formulate practical solutions for quantum-enhanced sensing in the noisy intermediate-scale quantum (NISQ) era.We emphasize three conceptual borders. First, the interaction between noise and error correction shows that QFI can be both weak and strong, depending on how environmental factors interact with each other. Second, multiparameter estimation and many-body critical phenomena reveal essential trade-offs among measurement incompatibility, entanglement scaling, and decoherence. Third, new experimental platforms, like as photonics, atomic clocks, solid-state qubits, and distributed networks, are increasingly being used with learning-based and random estimation methods that make QFI available on a large scale. We finish by talking about the problems that still need to be solved and the plan for the next ten years. These include making trade-offs between resources in error correction, making sure that critical scaling is strong, and adding QFI to hybrid quantum technologies. We contend that by reconceptualizing QFI as both a theoretical framework and a driver for tangible quantum advantages in sensing, it will be essential in the advancement of quantum technologies.
The quantum Fisher information (QFI) is a fundamental quantity of interest in many areas from quantum metrology to quantum information theory. It can in particular be used as a witness to establish the degree of multiparticle entanglement in quantum many-body systems. In this work, we use polynomials of the density matrix to construct monotonically increasing lower bounds that converge to the QFI. Using randomized measurements we propose a protocol to accurately estimate these lower bounds in state-of-the-art quantum technological platforms. We estimate the number of measurements needed to achieve a given accuracy and confidence level in the bounds, and present two examples of applications of the method in quantum systems made of coupled qubits and collective spins.
The quantum Fisher information (QFI) measures the amount of information that a quantum state carries about an unknown parameter. The (entanglement-assisted) QFI of a quantum channel is defined to be the maximum QFI of the output state assuming an entangled input state over a single probe and an ancilla. Both the channel QFI and the optimal input state could be solved via a semidefinite program (SDP). In quantum metrology, people are interested in calculating the QFI of N identical copies of a quantum channel when N→∞, which we call the asymptotic QFI. It was known that the asymptotic QFI grows either linearly or quadratically with N. Here we obtain a simple criterion that determines whether the scaling is linear or quadratic. In both cases, we found a quantum error correction protocol achieving the asymptotic QFI and an SDP to solve the optimal code. When the asymptotic QFI is quadratic, the Heisenberg limit, a feature once thought unique to unitary quantum channels, is recovered. When the asymptotic QFI is linear, we show it is still in general larger than N times the channel QFI, showing the non-additivity of the channel QFI of general quantum channels.