Abstract
High-dimensional entangled states are promising candidates for increasing the security and encoding capacity of quantum systems. While it is possible to witness and set bounds for the entanglement, precisely quantifying the dimensionality and purity in a fast and accurate manner remains an open challenge. Here, we report an approach that simultaneously returns the dimensionality and purity of high-dimensional entangled states by simple projective measurements. We show that the outcome of a conditional measurement returns a visibility that scales monotonically with state dimensionality and purity, allowing for quantitative measurements for general photonic quantum systems. We illustrate our method using two separate bases, the orbital angular momentum and pixels bases, and quantify the state dimensionality by a variety of definitions over a wide range of noise levels, highlighting its usefulness in practical situations. Importantly, the number of measurements needed in our approach scale linearly with dimensions, reducing data acquisition time significantly. Our technique provides a simple, fast and direct measurement approach.
Highlights
High-dimensional entangled states are promising candidates for increasing the security and encoding capacity of quantum systems
Through the precise control of highdimensional photonic states[2], i.e., time–energy, transverse momentum, spatial degrees of freedom or all of them simultaneously[3], the potential benefits of high-dimensional state encoding are taking centre stage. Recent developments in this direction have displayed the feasibility of quantum information processing that is robustness against optimal quantum cloning machines[4,5], environmental noise[6] and improved information rates[7], demonstrating a significant advantage in comparison to traditional qubit encoding
The purity of the quantum system, and the entanglement between photon pairs, is reduced due to noise introduced by the source, the environment and/or the detection system, very often in the form of white noise produced by background photons, high dark counts in single-photon detectors and unwanted multiphoton events[20]
Summary
High-dimensional entangled states are promising candidates for increasing the security and encoding capacity of quantum systems. Through the precise control of highdimensional photonic states[2], i.e., time–energy, transverse momentum, spatial degrees of freedom or all of them simultaneously[3], the potential benefits of high-dimensional state encoding are taking centre stage Recent developments in this direction have displayed the feasibility of quantum information processing that is robustness against optimal quantum cloning machines[4,5], environmental noise[6] and improved information rates[7], demonstrating a significant advantage in comparison to traditional qubit encoding. Many techniques have been developed to witness, bound and attempt to quantify high-dimensional quantum states These include approximating the density matrix via quantum state tomography (QST) with multiple qubit state projections[8], using mutually unbiased bases[9,10] to probe the states or incorporating self-guided approaches[11,12], and testing non-local bi-photon correlations by generalised Bell tests in higher dimensions[13,14,15]. Our quantitative technique is simple, robust and scales favourably (linearly) with dimension, making it ideal for practical implementations of quantum protocols with general highdimensional photonic quantum entangled states, even under undesired noise conditions
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