An array of hyper-entanglement based sensors made up of quantum hyper-entangled systems will be considered. Each hyper-entangled system will consists of a single hyper-entangled signal and single ancilla photon. The effect of noise in every mode as well as loss is included. The signal photon will experience classical loss and each ancilla photon will suffer a low level of loss. Forming an array offers the further advantage of a greater reduction in measurement time. It is shown mathematically that in the large d limit, where d is the number of modes, that different members of the array do not interfere with each other implying they can be put close together. This permits an enormous reduction in the measurement time, i.e. the time-on-target. Each hyper-entangled system making up the array receives a factor of d improvement in the signal-to-noise ratio (SNR), signal-to-interference ratio (SIR) and a factor of d reduction in measurement time. If M measurements are needed for a given level of resolution or decision quality then instead of having one hyper-entanglement pair, M hyper-entanglement pairs can be used. Unlike a classical radar or ladar, this system can image a target essentially with a snapshot from the many photon sources making up the array. Closed form results for the wave function, reduced density operator, gamma-expansion, probability of detection, probability of false alarm, SNR, SIR, Quantum Fisher information (QFI), quantum-Cramer-Rao lower bound (QCRLB), quantum Chernoff bound (QCB), and estimates for the number of required measurements are provided.
An array of hyper-entanglement based sensors made up of quantum hyper-entangled systems will be considered. Each hyper-entangled system will consists of a single hyper-entangled signal and single ancilla photon. The effect of noise in every mode as well as loss is included. The signal photon will experience classical loss and each ancilla photon will suffer a low level of loss. Forming an array offers the further advantage of a greater reduction in measurement time. It is shown mathematically that in the large d limit, where d is the number of modes, that different members of the array do not interfere with each other implying they can be put close together. This permits an enormous reduction in the measurement time, i.e. the time-on-target. Each hyper-entangled system making up the array receives a factor of d improvement in the signal-to-noise ratio (SNR), signal-to-interference ratio (SIR) and a factor of d reduction in measurement time. If M measurements are needed for a given level of resolution or decision quality then instead of having one hyper-entanglement pair, M hyper-entanglement pairs can be used. Unlike a classical radar or ladar, this system can image a target essentially with a snapshot from the many photon sources making up the array. Closed form results for the wave function, reduced density operator, gamma-expansion, probability of detection, probability of false alarm, SNR, SIR, Quantum Fisher information (QFI), quantum-Cramer-Rao lower bound (QCRLB), quantum Chernoff bound (QCB), and estimates for the number of required measurements are provided.
A method of improving situation awareness in a degraded environment based on a distributed array made up of quantum hyperentangled sensors is considered. This approach greatly reduces the effect of interference, noise, and signal loss mechanisms. It offers significant increases in the performance range for sensor or communications applications. It simultaneously improves resolution, signal-to-interference ratio (SIR), diminishes time-on-target (TOT), information transfer rates, etc. Each hyperentangled system consists of a single hyperentangled signal and single ancilla photon. The effect of noise in every single photon state as well as loss is included. The signal photon will experience classical loss and each ancilla photon will suffer a low level of loss. Forming an array offers further advantage of an increased reduction in measurement time. Let d be the number of single photon states, i.e., the dimensionality of the underlying Hilbert space resulting from hyperentanglement. It is shown mathematically that in the large d limit, that different members of the array do not interfere with each other, implying they can be put close together. This permits an enormous reduction in the measurement time, i.e., the TOT. Each hyperentangled system making up the array receives a factor of d improvement in the signal-to-noise ratio, SIR, and a factor of d reduction in measurement time.
A hyper-entanglement based atmospheric imaging/detection system involving only a signal and an ancilla photon will be considered for optical and infrared frequencies. Only the signal photon will propagate in the atmosphere and its loss will be classical. The ancilla photon will remain within the sensor experiencing low loss. Closed form expressions for the wave function, normalization, density operator, reduced density operator, symmetrized logarithmic derivative, quantum Fisher information, quantum Cramer-Rao lower bound, coincidence probabilities, probability of detection, probability of false alarm, probability of error after M measurements, signal to noise ratio, quantum Chernoff bound, time-on-target expressions related to probability of error and resolution will be provided. The effect of noise in every mode will be included as well as loss. The system will provide the basic design for an imaging/detection systems functioning at optical or infrared frequencies that offer better than classical angular and range resolution. Optimization for enhanced resolution will be included. The signal to noise ratio will be increased by a factor equal to the number of modes employed during the hyper-entanglement process. Likewise, the measurement time can be reduced by the same factor. The hyper-entanglement generator will typically make use of entanglement in polarization, energy-time, orbital angular momentum, etc. Mathematical results will be provided describing the system’s performance as a function of loss mechanisms and noise.
A hyperentanglement-based atmospheric imaging/detection system involving only a signal and an ancilla photon will be considered for optical and infrared frequencies. Only the signal photon will propagate in the atmosphere and its loss will be classical. The ancilla photon will remain within the sensor experiencing low loss. Closed form expressions for the wave function, normalization, density operator, reduced density operator, symmetrized logarithmic derivative, quantum Fisher information, quantum Cramer–Rao lower bound, coincidence probabilities, probability of detection, probability of false alarm, probability of error after M measurements, signal-to-noise ratio, quantum Chernoff bound, time-on-target expressions related to probability of error, and resolution will be provided. The effect of noise in every mode will be included as well as loss. The system will provide the basic design for an imaging/detection system functioning at optical or infrared frequencies that offers better than classical angular and range resolution. Optimization for enhanced resolution will be included. The signal-to-noise ratio will be increased by a factor equal to the number of modes employed during the hyperentanglement process. Likewise, the measurement time can be reduced by the same factor. The hyperentanglement generator will typically make use of entanglement in polarization, energy-time, orbital angular momentum and so on. Mathematical results will be provided describing the system’s performance as a function of loss mechanisms and noise.
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.
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.
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.