An atmospheric imaging system based on quantum hyperentanglement has been developed. Hyper-entanglement can increase the maximum detection range of the system by more than a factor of 10, improve the signal-to-noise ratio (SNR) by more than a factor of 10,000, and decrease measurement time. Hyperentanglement refers to entanglement in more than one degree of freedom. A design for creating states hyperentangled in the degrees of freedom polarization, energy-time, orbital angular momentum (OAM), and the radial quantum number is examined. The design helps reduce propagation loss. Figures of merit related to generation and detection efficiencies, the SNR, signal to interference ratio, the measurement time, and phase estimation are provided in closed form. A formula describing how hyperentanglement greatly improves the maximum detection range of the system is derived. Hermite–Gaussian modes, Laguerre–Gaussian (LG) modes, OAM dependence of the LG modes, and mode conversion are discussed. Bell state generation and Bell state measurement, i.e., the ability to distinguish the various Bell states, is discussed. Mathematical and circuit representations of Bell state generation and the Bell state analyzer are provided. Signatures for unique detection of the various Bell states are developed. The formalism permits random noise and entangled or nonentangled sources of interference to be modeled.
An atmospheric imaging system based on quantum hyperentanglement has been developed. Hyper-entanglement can increase the maximum detection range of the system by more than a factor of 10, improve the signal-to-noise ratio (SNR) by more than a factor of 10,000, and decrease measurement time. Hyperentanglement refers to entanglement in more than one degree of freedom. A design for creating states hyperentangled in the degrees of freedom polarization, energy-time, orbital angular momentum (OAM), and the radial quantum number is examined. The design helps reduce propagation loss. Figures of merit related to generation and detection efficiencies, the SNR, signal to interference ratio, the measurement time, and phase estimation are provided in closed form. A formula describing how hyperentanglement greatly improves the maximum detection range of the system is derived. Hermite–Gaussian modes, Laguerre–Gaussian (LG) modes, OAM dependence of the LG modes, and mode conversion are discussed. Bell state generation and Bell state measurement, i.e., the ability to distinguish the various Bell states, is discussed. Mathematical and circuit representations of Bell state generation and the Bell state analyzer are provided. Signatures for unique detection of the various Bell states are developed. The formalism permits random noise and entangled or nonentangled sources of interference to be modeled.
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.
Hyper-entanglement with an emphasis on mode type is used to extend a previously developed atmospheric imaging system. Angular spectrum expansions combined with second quantization formalism permits many different mode types to be considered using a common formalism. Fundamental Gaussian, standard Hermite-Gaussian, standard Laguerre- Gaussian, and Bessel modes are developed. Hyper-entanglement refers to entanglement in more than one degree of freedom, e.g. polarization, energy-time and orbital angular momentum. 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. A simple atomic physics based model of the scattering target is developed. This model permits the derivation in closed form of the loss coefficient for photons with a given mode type scattering from the target. Signal loss models for propagation, transmission, detection, and scattering are developed and applied. The probability of detection of photonic orbital angular momentum is considered in terms of random media theory. A model of generation and detection efficiencies for the different degrees of freedom is also considered. The implications of loss mechanisms for signal to noise ratio (SNR), and other quantum information theoretic quantities are discussed. Techniques for further enhancing the system’s SNR and resolution through adaptive optics are examined. The formalism permits random noise and entangled or nonentangled sources of interference to be modeled.
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.
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.
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.
Methods of generating N00N, M&N, linear combinations of M&N states as well as more complicated quantum entangled and quantum hyper-entangled states will be considered. Quantum hyper-entanglement refers to quantum entanglement in more than one degree of freedom, e.g. energy-time, polarization, orbital angular momentum, etc. Internal noise and loss within the entanglement or hyper-entanglement generators and external noise and loss due to atmospheric effects and detectors are modeled. Analysis related to the devices that generate these entangled or hyperentangled states will be provided. The following will be derived: closed form expressions for wave function normalization, wave function, density operator, reduced density operator, phase error bound, the symmetrized logarithmic derivative, the quantum Fisher information, the quantum Cramer-Rao lower bound, the relevant projection operators and the related probability of detection expressions. Generation and detection of the entangled or hyperentangled states will be considered. The entanglement generators will use linear and nonlinear optical devices. Optimization criteria for the quantum states, generation and detection schemes and designs optimal with respect to the criteria will be discussed. Applications of the generated states for producing super sensitivity and super resolution will be discussed. The fundamental role of coincidence measurement for generating entanglement is included. Hyperentanglement offers N times classical resolution, where N is a quantum number associated with the system.