Quantum State Representation and Polarization Dynamics

Quantum state representation provides the mathematical framework for describing and manipulating the complete information of a quantum system, whether through state vectors, density matrices or more geometrical constructions. In parallel, polarisation dynamics examines how the orientation and coherence of light’s electric field evolve under propagation, interaction with materials and quantum operations. At its core, the density matrix captures both pure and mixed states, while tools such as the Bloch sphere and Majorana stellar representation furnish intuitive visualisations of two-level and higher-spin systems. For polarisation, classical descriptions via Stokes parameters extend naturally to the quantum domain, giving rise to non-classical features such as entanglement of polarisation modes, squeezed polarisation states and quantum channels modelled by Mueller matrices. Understanding these representations and dynamics is essential for diverse applications, including quantum communication, high-precision metrology and the development of novel optical sensors. Recent advances have deepened our grasp of how engineered quantum states of light can be tailored to probe fundamental physics and drive emerging technologies.

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Extending geometric methods to non-standard degrees of freedom, a recent study introduced a Majorana stellar representation for twisted photons, mapping their orbital angular momentum and polarisation onto discrete constellations on a curved phase space. This approach not only generalises Bloch-sphere techniques but also reveals new trajectories for state evolution and quantumness measures in structured light fields.

Investigations into the extremal polarisation properties of quantum states have employed multipole expansions of the density matrix to derive extremal states on the Poincaré sphere. By analysing the cumulative distribution of multipoles, these works identify highly polarised and maximally non-classical states, demonstrating how SU(2) coherent states and their anticoherent counterparts define the boundaries between classical and quantum polarisation regimes.

A comprehensive theoretical framework has been developed to connect classical polarimetry with quantum channel theory, constructing sets of quantum operations that correspond to arbitrary Mueller matrices. This formulation clarifies how depolarising and non-depolarising processes act on quantum states of light, and suggests new quantum-enhanced strategies for material characterisation, pushing classical polarimetry beyond its traditional limits.

Quantum State Representation and Polarization Dynamics publication trend

The graph below shows the total number of articles in quantum state representation and polarization dynamics across all publications each year (not limited to Nature Index journals).

Technical terms

Quantum state: A complete description of a system in Hilbert space, represented by a state vector or density matrix.

Density matrix: Operator capturing both pure and mixed quantum states, enabling statistical predictions of measurements.

Majorana stellar representation: Geometric mapping of a spin or polarisation state onto constellations of points on a sphere.

Stokes parameters: Quartet of real values describing the polarisation state of light through intensity and coherence measurements.

Mueller matrix: 4×4 real matrix that transforms input Stokes parameters into output parameters in polarimetric analysis.

References

1. Majorana stellar representation of twisted photons. Physical Review Research (2023).
2. Stars of the quantum Universe: extremal constellations on the Poincaré sphere. Physica Scripta (2015).
3. Quantum theory of polarimetry: From quantum operations to Mueller matrices. Physical Review Research (2020).