Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1807.02690

Quantum Fisher information matrix for unitary processes: closed relation for $SU(2)$

Mohammad Javad Shemshadi·Seyed Javad Akhtarshenas
View original source ↗Read source document ↗Export metadata ↓

Abstract

Quantum Fisher information plays a central role in the field of quantum metrology. In this paper we study the problem of quantum Fisher information of unitary processes. Associated to each parameter $θ_i$ of unitary process $U(\boldsymbolθ)$, there exists a unique Hermitian matrix $M_{θ_i}=i(U^\dagger\partial_{θ_i} U)$. Except for some simple cases, such as when the parameter under estimation is an overall multiplicative factor in the Hamiltonian, calculation of these matrices is not an easy task to treat even for estimating a single parameter of qubit systems. Using the Bloch vector $\boldsymbol{m}_{θ_i}$, corresponding to each matrix $M_{θ_i}$, we find a closed relation for the quantum Fisher information matrix of the $SU(2)$ processes for an arbitrary number of estimation parameters and an arbitrary initial state. We extend our results and present an explicit relation for each vector $\boldsymbol{m}_{θ_i}$ for a general Hamiltonian with arbitrary parametrization. We illustrate our results by obtaining the quantum Fisher information matrix of the so-called angle-axis parameters of a general $SU(2)$ process. Using a linear transformation between two different parameter spaces of a unitary process, we provide a way to move from quantum Fisher information of a unitary process in a given parametrization to the one of the other parametrization. Knowing this linear transformation enables one to calculate the quantum Fisher information of a composite unitary process, i.e. a unitary process resulted from successive action of some simple unitary processes. We apply this method for a spin-half system and obtain the quantum Fisher matrix of the coset parameters in terms of the one of the angle-axis parameters.

Explore related subjects

quant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Mohammad Javad Shemshadi, Seyed Javad Akhtarshenas. 2018-11-14. Quantum Fisher information matrix for unitary processes: closed relation for $SU(2)$. https://doi.org/10.1007/s11128-018-2108-2

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quantum Authenticated Key Expansion with Key Recycling

Data privacy and authentication are two main security requirements for remote access and cloud services. While QKD has been explored to address data privacy concerns, oftentimes its use is separate from the client authentication protocol despite implicitly providing authentication. Here, we present a quantum authentication key expansion (QAKE) protocol that (1) integrates both authentication and key expansion within a single protocol, and (2) provides key recycling property - allowing all authentication keys to be reused. We analyse the security of the protocol in a QAKE framework adapted from a classical authentication key exchange (AKE) framework, providing separate security conditions for authentication and data privacy. We experimentally implemented the protocol with appropriate post-selection. Additional results on the security of pseudorandom basis generation in QAKE and decoy state BB84 are provided.

quant-ph↗
arXiv2026

Entanglement as Difference: Reduction-induced Minimal Partial Entropy Difference

Bipartite mixed-state quantum entanglement (QE) and its measures play a crucial role in both theoretical research and practical quantum applications. Its internal structure is far more complex and less well understood compared with bipartite pure-state QE. Some existing measures involve inherently intractable global optimizations, while others are only applicable to highly limited-dimensional quantum systems. Here based on the inherent feature that bipartite QE systems nonseparable necessarily implies that local reduced density matrix differs from its \textquotedblleft native\textquotedblright density matrix, we propose a more physical and intuitive measure termed Reduction-induced Minimal Partial Entropy Difference to quantify arbitrary bipartite mixed-state QE. Partial Von Neumann Entropy is only a pure-state special case of this method. This measure offers intrinsic structural %perspective insights into bipartite QE characterization, thereby establishing itself as a valuable complementary measure. Its intuitive and clear physical picture, combined with relatively low computational complexity and wide applicability, facilitates exploring its potential quantum information applications, hence its conceptual framework and line of thought deserve to be further developed to describe and quantify multipartite QE in the future.

quant-ph↗
arXiv2026

Non-local mass superpositions and optical clock interferometry in atomic ensemble quantum networks

Quantum networks are emerging as powerful platforms for sensing, communication, and fundamental tests of physics. We propose a programmable quantum sensing network based on entangled atomic ensembles, where optical clock qubits realize mass superpositions arising via mass-energy equivalence, as in atom and atom-clock interferometry. Our approach uniquely combines scalability to large atom numbers with minimal control requirements, relying only on collective addressing of internal atomic states. This enables the creation of both non-local and local superpositions with spatial separations beyond those achievable in conventional matter-wave interferometry with single atoms. Starting from Bell-type seed states distributed via photonic channels, collective operations within atomic ensembles coherently build many-body mass superpositions sensitive to gravitational redshift. The resulting architecture implements a non-local Ramsey interferometer, where gravitationally induced phase shifts are imprinted on non-local entangled states and are read out through local measurements at the network nodes. Beyond extending the spatial reach of mass superpositions, our scheme establishes a scalable, programmable platform to probe the interface of quantum mechanics and gravity, and offers a new experimental pathway to test atom and atom-clock interferometer proposals, e.g. for probing gravitational dephasing, in a network-based quantum laboratory.

quant-ph↗