Wavefronts for single and multiple photons are derived and combined with quantum hyper-entanglement, multiphoton entanglement, and network properties. Each node of the network will transmit at least one signal and one ancilla photon in a hyper-entangled state. Parameters used for hyper-entanglement will include photon polarization, energy-time, orbital angular momentum (OAM), radial quantum number, etc. as well as up to 12 parameters characterizing the wavefront properties. These parameters arise from using Lie algebra techniques to solve the paraxial wave equation. Eigenfunctions of operators associated with each 2D paraxial wave equation will be determined each being a function of up to six parameters. The resulting wavefronts will be shown in some cases to be propagation invariant and have the self-healing property. The free parameters of the derived wavefront will offer a programmable wavefront that will permit better imaging around obstacles and reduced propagation loss. Unlike the results found in the literature the free parameters will permit photonic trajectories to be programmed for better performance. Parabolic trajectories, i.e. ones with quadratic terms will emerge as well as those with cubic or higher degree terms. This will further facilitate imaging around obstacles. The same wavefront or combinations of wavefronts can be applied to multiple signal photons to combine hyper-entanglement with multiphoton entanglement offering additional performance improvements. Wavefront engineering can be applied to a single ancilla or multiple ancilla photons. Enhanced superdense coding will be considered. Measures of effectiveness (MOEs) such as the SNR, measurement time, resolution measures, and Holevo bound will be derived or provided.
Wavefronts for single and multiple photons are derived and combined with quantum hyper-entanglement, multiphoton entanglement, and network properties. Each node of the network will transmit at least one signal and one ancilla photon in a hyper-entangled state. Parameters used for hyper-entanglement will include photon polarization, energy-time, orbital angular momentum (OAM), radial quantum number, etc. as well as up to 12 parameters characterizing the wavefront properties. These parameters arise from using Lie algebra techniques to solve the paraxial wave equation. Eigenfunctions of operators associated with each 2D paraxial wave equation will be determined each being a function of up to six parameters. The resulting wavefronts will be shown in some cases to be propagation invariant and have the self-healing property. The free parameters of the derived wavefront will offer a programmable wavefront that will permit better imaging around obstacles and reduced propagation loss. Unlike the results found in the literature the free parameters will permit photonic trajectories to be programmed for better performance. Parabolic trajectories, i.e. ones with quadratic terms will emerge as well as those with cubic or higher degree terms. This will further facilitate imaging around obstacles. The same wavefront or combinations of wavefronts can be applied to multiple signal photons to combine hyper-entanglement with multiphoton entanglement offering additional performance improvements. Wavefront engineering can be applied to a single ancilla or multiple ancilla photons. Enhanced superdense coding will be considered. Measures of effectiveness (MOEs) such as the SNR, measurement time, resolution measures, and Holevo bound will be derived or provided.
New results have been derived for wavefronts for single and multiple photons and combined with quantum hyperentanglement, multiphoton entanglement, and network properties. These new results arise from use of Lie algebra techniques for disentanglement of certain operators related to propagation. The new results include closed form exact expressions for functions related to the disentanglement process. These expressions permit many different solutions to the disentanglement process. These new expressions offer much higher order programmable self-accelerating curves to be created. This in turn facilitates more effective quantum-based sensing and communication around corners and other obstacles, with reduced loss. This approach significantly increases the information that can be communicated or stored when using a recently derived extension of superdense coding. The resulting wavefronts are shown to reduce diffraction and have the self-healing property, i.e. automatically reobtain their original form when initially damaged by turbulence. Each node of the network will transmit at least one signal and one ancilla photon in a hyper-entangled state. Parameters used for hyper-entanglement will include photon polarization, energy-time, orbital angular momentum, radial quantum number, etc. as well as up to 12 parameters characterizing the wavefront properties. Eigenfunctions of operators associated with each 2D paraxial wave equation will be determined each being a function of up to six parameters. The same wavefront or combinations of wavefronts can be applied to multiple photons to combine hyper-entanglement with multiphoton entanglement offering additional improvements. Measures of effectiveness such as the signal-to-noise ratio (SNR), measurement time, resolution measures, and Holevo bound are considered.
Quantum hyper-entanglement, multi-photon entanglement and quantum networks are combined to develop enhanced sensing capabilities. Quantum hyper-entanglement refers to entanglement in more than one degree of freedom, e.g. polarization, energy-time, orbital angular momentum (OAM), and frequency. Multi-photon entanglement involves entanglement typically between more than two photons, whereas hyper-entanglement is generally described as occurring between two photons referred to as the signal and ancilla photon. Multi-photon states representing an increasing hierarchy of robustness are discussed. These include N00N states, M&N states and linear combinations of M&N states. A M&N state, the (N, 1) states is shown to be very useful. A method of constructing M&N states using Shrodinger kitten states is considered. Multi-photon entanglement and hyper-entanglement are combined for enhanced sensing. This combined approach permits improvement in measures of effectiveness (MOEs) like SNR, signal to interference ratio (SIR), time-on-target (TOT), Holevo bound, and system range. The combined approach yields significant improvements in resolution both by permitting an effective reduction in wavelength used for measurement as well as decreasing the related Cramer Rao lower bound. This in turn permits sensors based on these concepts to have enhanced parameter estimation capabilities. These parameters can include range, bearing and elevation. Additional enhancements are found by combining the multi-photon hyper-entangled states with the idea of a quantum network. Quantum networks are a collection of nodes that may have quantum memory. This approach can significantly reduce loss; offer noise and interference resistance; decrease measurement error; and reduce size, weight, power and costs (SWAPC) for the overall system.
Quantum systems combining various forms of quantum entanglement, quantum networks and wavefront design via Lie optics are discussed. The forms of entanglement include multiphoton entanglement and hyperentanglement, with an emphasis on hybrid states born of combining these two forms of entanglement. Lie optics refers to the use of Lie algebra techniques in optics. Improvements born of combining these techniques are discussed in terms of various measures of effectiveness (MOE) including: signal-to-noise ratio (SNR); signal-to-interference ratio (SIR); quantum Cramer Rao lower bound (QCRLB); classical Cramer Rao lower bound (CCRLB); measurement time (MT); quantum Chernoff bound; sensing range; communications range; phase and angular resolution; size, weight, power and costs (SWAPC); various measures associated with information content of signals; superdense coding; and the Holevo bound. Quantum networks coupled with hyperentanglement increase the likelihood that samples are statistically independent improving both classical and quantum estimation results. This can reduce both estimation uncertainty and measurement time. Quantum networks also offer opportunities for additional processing of signals exploiting signal processing, information fusion, adaptive optics and other techniques. Wavefronts designed using Lie optics offer additional advantages in terms of reduced diffraction, the ability to design self-accelerating curves to enhance sensing and communications, and improved MOE values in all categories. The utility of three different types of designed wavefronts in terms of MOEs are discussed. Combining hybrid states with wavefronts designed using Lie optics offers significant MOE improvements greatly expanding communication range, sensing range and significantly improving the information carrying content of signals. Extensive numerical results are provided.
An atmospheric imaging system based on quantum hyper-entanglement has been developed. Hyper-entanglement refers to entanglement in more than one degree of freedom, e.g. polarization, energy-time and orbital angular momentum (OAM). The system functions at optical or infrared frequencies. Only the signal photon propagates in the atmosphere, the ancilla photon is retained within the detector. This results in loss being essentially classical, giving rise to stronger forms of entanglement. Bell state generation and Bell state measurement, i.e. the ability to distinguish the various Bell states is discussed. A mathematical representation of Bell state generation and the Bell state analyzer, including a projection operator describing the measurement process is provided. Signatures for unique detection of the various Bell states are developed. A method and design for creating states hyper-entangled in polarization, energy-time, OAM and the radial quantum number is examined. Hermite-Gaussian (HG) modes, Laguerre-Gaussian (LG) modes, OAM dependence of the LG modes and a method of mode conversion are discussed. A projection operator that represents the combined measurements between the different degrees of freedom is provided. A model of generation and detection efficiencies for the different degrees of freedom and the implications for signal to noise ratio (SNR), signal to interference ratio (SIR), the quantum Cramer-Rao lower bound, and the measurement time are provided in closed form. A formula describing how hyper-entanglement greatly improves the maximum detection range of the system is derived. The formalism permits random noise and entangled or non-entangled sources of interference to be modeled.
Methods of improving quantum LADARs and related sensors are developed based on quantum entanglement and hyperentanglement. Multiple single photon states are used to obtain a multiphoton entangled state. These states can be N00N states, M&N states (M&N), or a linear combination of M&N states (LCMNS) or generalized states kindred to LCMNS. The procedure for doing this derives from the fundamental theorem of algebra. Various states generated by this process are developed. A diagram of a device for producing such states is examined. They are related to a simpler version of this concept introduced in the seminal experiment by Mitchell-Lundeen and Steinberg. A certain class of states obtained through the Schrodinger kitten process are shown to be effective for generating states hyper-entangled in polarization and energy-time. A diagram of a device for producing such states is considered. Alternate methods of generating hyperentanglement in polarization and energy-time are discussed. Improvements offered by networks are discussed. The utility of these procedures for sensing and communications is examined. An open systems analysis based on density operator theory is conducted including both noise and loss mechanisms. The susceptibility to noise and loss of the various hyper-entanglement procedures is examined. Various measures of effectiveness (MOEs) are derived to quantize system performance. MOEs include but are not limited to, SNR, signal-to-interference ratio, quantum Cramer Rao’ lower bound, quantum Chernoff bound, measurement time, the Holevo bound, sensing range, and resolution. A summary table with expanded MOEs results drawing from multiple papers is provided.
Theory and related designs for enhancing communications and more generally information transfer by using quantum hyper-entanglement are discussed. Quantum hyper-entanglement refers to entanglement in more than one quantum mechanical degree of freedom, e.g. polarization, energy-time, orbital angular momentum, radial quantum number and frequency. Each extra degree of freedom increases the dimensionality d of the underlying Hilbert space. The hyperentangled signal-to-noise ratio (SNR) and signal-to-interference ratio (SIR) are d times the related classical quantity due to the enhancement born of hyper-entanglement. Communication time can be reduced by a factor d or d ⋅ M, where M is the number of message photons used. Errors in parameter estimation related to information stored in the signal experience a factor of d ⋅ M reduction. This paper considers the use of generalized Bell states and discusses circuitry for their transmission, analysis and detection. Holevo bounds and Von-Neumann entropies are calculated for both the hyper-entangled case and non-entangled case. It is shown that hyper-entanglement can increase the maximum information transferrable by more than log2 (d) bits. The Holevo bound results are discussed in the context of the types of generalized Bell states. Generalized measures of effectiveness (MOEs) are introduced that hold for linear combinations of generalized Bell states. Different sets of complete orthogonal projection operators and their applications are discussed. Loss mechanisms due to transmission hardware such as orbital angular moment polarization rotation, and polarizing beam splitter cross-talk are calculated. Propagation and detection loss as well as noise are considered.