One of the most prominent features of quantum entanglement is its invariability under local unitary transformations, which implies that the degree of entanglement or nonseparability remains constant during free-space propagation, true for both quantum and classically entangled modes. Here we demonstrate an exception to this rule using a carefully engineered vectorial light field, and we study its nonseparability dynamics upon free-space propagation. We show that the local nonseparability between the spatial and polarization degrees of freedom dramatically decays to zero while preserving the purity of the state and hence the global nonseparability. We show this by numerical simulations and corroborate it experimentally. Our results evince novel properties of classically entangled modes and point to the need for new measures of nonseparability for such vectorial fields, while paving the way for novel applications for customized structured light.
One of the most prominent features of quantum entanglement is its invariability under local unitary transformations, which implies that the degree of entanglement or nonseparability remains constant during free-space propagation, true for both quantum and classically entangled modes. Here we demonstrate an exception to this rule using a carefully engineered vectorial light field, and we study its nonseparability dynamics upon free-space propagation. We show that the local nonseparability between the spatial and polarization degrees of freedom dramatically decays to zero while preserving the purity of the state and hence the global nonseparability. We show this by numerical simulations and corroborate it experimentally. Our results evince novel properties of classically entangled modes and point to the need for new measures of nonseparability for such vectorial fields, while paving the way for novel applications for customized structured light.
It is well known that entanglement is invariant to local unitary transformations, this implies the degree of entanglement or non-separability remains constant during free-space propagation, which is true for both quantum and classically-entangled modes. Here we demonstrate an exception to this rule using a carefully engineered vectorial light field, and study its non-separability dynamics upon free-space propagation. We show that the local non-separability between the spatial and polarisation degrees of freedom dramatically decays to zero, while preserving the purity of the state and hence the global non-separability. We show this by numerical simulations and corroborate it experimentally. Our results evince novel properties of classically-entangled modes, point to the need for new measures of non-separability for such vectorial fields, while paving the way to novel applications for customised structured light.
One of the most prominent features of quantum entanglement is its invariability under local unitary transformations, which implies the degree of entanglement remains constant during free-space propagation. While this is true for quantum and classically--entangled modes, here we demonstrate a novel type of classically-entangled modes that experience an entanglement decay upon free-space propagation. We show this by numerical simulations and corroborate experimentally. Our results evinces novel properties of classically-entangled modes, which pave the way to novel applications.
Nonseparability in classical and quantum states of light gives rise to the notions of classical (local) and quantum (nonlocal) entanglement, usually defined as global features of the fields and states. Here we use concurrence as a measure of this nonseparability and show that it can be spatially resolved, revealing regions of maximum nonseparability and regions with no nonseparability. We use the topical examples of vectorial structured light and its quantum analog, a hybrid spatial mode and polarization entangled states, to test the approach on both local and nonlocal forms of entanglement. Our work has wide reaching implications, for instance, in understanding the spatial dependence of coherence and polarization in vectorial light, as well as in quantum entangled states for imaging, where spatial correlations are vital.
One of the most captivating properties of diffraction-free optical fields is their ability to reconstruct upon propagation in the presence of an obstacle, both classically and in the quantum regime. Here we demonstrate that the local entanglement, or nonseparability, between the spatial and polarization degrees of freedom also experience self-healing. We measured and quantified the degree of nonseparability between the two degrees of freedom when propagating behind various obstructions, which were generated digitally. Experimental results show that even though the degree of nonseparability reduces after the obstruction, it recovers to its maximum value within the classical self-healing distance. To confirm our findings, we performed a Clauser-Horne-Shimony-Holt Bell-like inequality measurement, proving the self-reconstruction of nonseparability. These results indicate that local entanglement between internal degrees of freedom of a photon, can be recovered by suitable choice of the enveloping wave function.
As structured optical fields with spatially inhomogeneous polarization distributions, vector beams have attracted widespread attention for their great applications across multiple fields. The coupling between spatial modes and polarization states in vector beams results in nonseparability analogous to quantum entangled states, referred to as classical entanglement. This concept has garnered considerable scholarly interest, due to its capacity to facilitate quantum-inspired approaches for the characterization of vector optical fields, leading to noteworthy applications such as metrological sensing, communication encryption, and quantum computing. However, most investigations concerning classical entanglement have focused on vector optical fields within the spatial domain, while the classical entanglement characteristics of ultrafast vector beam pulses in the temporal domain remain to be revealed. Here, we investigate the classical local entanglement of ultrafast vector beam pulses in the temporal domain. Through theoretical interpretation and experimental verification, time-varying nonseparability has been demonstrated throughout the pulse duration. The dynamic evolution of spatially vectorial polarization states on femtosecond timescales was measured. The temporal evolution of the classical entanglement and the associated density matrix were analyzed using quantum state tomography. This research provides, to our knowledge, novel perspectives for investigating quantum-classical optical analogies in the temporal domain, advancing deeper fundamental understanding of entanglement.
Complex vectorial light fields, nonseparable in their polarization and spatial degree of freedom, are of relevance in a wide variety of research areas encompassing microscopy, metrology, communication, and topological studies. Controversially, they have been suggested as analogs to quantum entanglement, raising fundamental questions on the relation between nonseparability in classical systems, and entanglement in quantum systems. We perform basis-independent tomography of arbitrary pure vectorial light fields using spatially resolved Stokes projections. Moreover, we propose and demonstrate that concurrence, as a nonseparability witness for any pure vectorial light field, can be extracted from global Stokes projections, without assessing the spatial degree of freedom.