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Articles 1 - 28 of 28
Full-Text Articles in Physics
Device-Independent Quantum Key Distribution With Generalized Two-Mode Schrödinger Cat States, Curtis J. Broadbent, Kevin Marshall, Christian Weedbrook, John C. Howell
Device-Independent Quantum Key Distribution With Generalized Two-Mode Schrödinger Cat States, Curtis J. Broadbent, Kevin Marshall, Christian Weedbrook, John C. Howell
Mathematics, Physics, and Computer Science Faculty Articles and Research
We show how weak nonlinearities can be used in a device-independent quantum key distribution (QKD) protocol using generalized two-mode Schrödinger cat states. The QKD protocol is therefore shown to be secure against collective attacks and for some coherent attacks. We derive analytical formulas for the optimal values of the Bell parameter, the quantum bit error rate, and the device-independent secret key rate in the noiseless lossy bosonic channel. Additionally, we give the filters and measurements which achieve these optimal values. We find that, over any distance in this channel, the quantum bit error rate is identically zero, in principle, and …
Qubit Measurement Error From Coupling With A Detuned Neighbor In Circuit Qed, Mostafa Khezri, Justin Dressel, Alexander N. Korotkov
Qubit Measurement Error From Coupling With A Detuned Neighbor In Circuit Qed, Mostafa Khezri, Justin Dressel, Alexander N. Korotkov
Mathematics, Physics, and Computer Science Faculty Articles and Research
In modern circuit QED architectures, superconducting transmon qubits are measured via the state-dependent phase and amplitude shift of a microwave field leaking from a coupled resonator. Determining this shift requires integrating the field quadratures for a nonzero duration, which can permit unwanted concurrent evolution. Here we investigate such dynamical degradation of the measurement fidelity caused by a detuned neighboring qubit. We find that in realistic parameter regimes, where the qubit ensemble-dephasing rate is slower than the qubit-qubit detuning, the joint qubit-qubit eigenstates are better discriminated by measurement than the bare states. Furthermore, we show that when the resonator leaks much …
Fast Hadamard Transforms For Compressive Sensing Of Joint Systems: Measurement Of A 3.2 Million-Dimensional Bi-Photon Probability Distribution, Daniel J. Lum, Samuel H. Knarr, John C. Howell
Fast Hadamard Transforms For Compressive Sensing Of Joint Systems: Measurement Of A 3.2 Million-Dimensional Bi-Photon Probability Distribution, Daniel J. Lum, Samuel H. Knarr, John C. Howell
Mathematics, Physics, and Computer Science Faculty Articles and Research
We demonstrate how to efficiently implement extremely high-dimensional compressive imaging of a bi-photon probability distribution. Our method uses fast-Hadamard-transform Kronecker-based compressive sensing to acquire the joint space distribution. We list, in detail, the operations necessary to enable fast-transform-based matrix-vector operations in the joint space to reconstruct a 16.8 million-dimensional image in less than 10 minutes. Within a subspace of that image exists a 3.2 million-dimensional bi-photon probability distribution. In addition, we demonstrate how the marginal distributions can aid in the accuracy of joint space distribution reconstructions.
Experimentally Quantifying The Advantages Of Weak-Value-Based Metrology, Gerardo I. Viza, Julián Martínez-Rincón, Gabriel B. Alves, Andrew N. Jordan, John C. Howell
Experimentally Quantifying The Advantages Of Weak-Value-Based Metrology, Gerardo I. Viza, Julián Martínez-Rincón, Gabriel B. Alves, Andrew N. Jordan, John C. Howell
Mathematics, Physics, and Computer Science Faculty Articles and Research
We experimentally investigate the relative advantages of implementing weak-value-based metrology versus standard methods. While the techniques outlined herein apply more generally, we measure small optical beam deflections both using a Sagnac interferometer with a monitored dark port (the weak-value-based technique), and by focusing the entire beam to a split detector (the standard technique). By introducing controlled external transverse detector modulations and transverse beam deflection momentum modulations, we quantify the mitigation of these sources in the weak-value-based experiment versus the standard focusing experiment. The experiments are compared using a combination of deterministic and stochastic methods. In all cases, the weak-value technique …
Device-Independent Relativistic Quantum Bit Commitment, Emily Adlam, Adrian Kent
Device-Independent Relativistic Quantum Bit Commitment, Emily Adlam, Adrian Kent
Mathematics, Physics, and Computer Science Faculty Articles and Research
We examine the possibility of device-independent relativistic quantum bit commitment, introducing three relativistic quantum bit commitment schemes that offer device-independent security against hypothetical postquantum adversaries subject only to the no-signaling principle. We discuss the potential threat of location attacks, in which the behavior of untrusted devices used in relativistic quantum cryptography depends on their space-time location and show that our protocols are secure against both location attacks and memory attacks. The protocols are compared to a relativistic classical bit commitment scheme with similar features and we note some advantages for the quantum schemes.
Comment On "Role Of Potentials In The Aharonov-Bohm Effect", Yakir Aharonov, Eliahu Cohen, Daniel Rohrlich
Comment On "Role Of Potentials In The Aharonov-Bohm Effect", Yakir Aharonov, Eliahu Cohen, Daniel Rohrlich
Mathematics, Physics, and Computer Science Faculty Articles and Research
Are the electromagnetic scalar and vector potentials dispensable? Vaidman [Phys. Rev. A 86, 040101(R) (2012)] has suggested that local interactions of gauge-invariant quantities, e.g., magnetic torques, suffice for the description of all quantum electromagnetic phenomena. We analyze six thought experiments that challenge this suggestion. All of them have explanations in terms of local interactions of gauge-dependent quantities, and, in addition, some have explanations in terms of nonlocal interactions of gauge-invariant quantities. We claim, however, that two of our examples have no gauge-invariant formal description and that, in general, no local description can dispense with electromagnetic potentials.
Superconducting Antenna Concept For Gravitational Waves, Armen Gulian, J Foreman, Vahan Nikoghosyan, Shmuel Nussinov, Louis Sica, Jeff Tollaksen
Superconducting Antenna Concept For Gravitational Waves, Armen Gulian, J Foreman, Vahan Nikoghosyan, Shmuel Nussinov, Louis Sica, Jeff Tollaksen
Mathematics, Physics, and Computer Science Faculty Articles and Research
The most advanced contemporary efforts and concepts for registering gravitational waves are focused on measuring tiny deviations in large arm (kilometers in case of LIGO and thousands of kilometers in case of LISA) interferometers via photons. In this report we discuss a concept for the detection of gravitational waves using an antenna comprised of superconducting electrons (Cooper pairs) moving in an ionic lattice. The major challenge in this approach is that the tidal action of the gravitational waves is extremely weak compared with electromagnetic forces. Any motion caused by gravitational waves, which violates charge neutrality, will be impeded by Coulomb …
Engineering Room-Temperature Superconductors Via Ab-Initio Calculations, Mamikon Gulian, Gurgen Melkonyan, Armen Gulian
Engineering Room-Temperature Superconductors Via Ab-Initio Calculations, Mamikon Gulian, Gurgen Melkonyan, Armen Gulian
Mathematics, Physics, and Computer Science Faculty Articles and Research
The BCS, or bosonic model of superconductivity, as Little and Ginzburg have first argued, can bring in superconductivity at room temperatures in the case of high-enough frequency of bosonic mode. It was further elucidated by Kirzhnits et al., that the condition for existence of high-temperature superconductivity is closely related to negative values of the real part of the dielectric function at finite values of the reciprocal lattice vectors. In view of these findings, the task is to calculate the dielectric function for real materials. Then the poles of this function will indicate the existence of bosonic excitations which can …
Current-Biased Transition-Edge Sensors Based On Re-Entrant Superconductors, Armen Gulian, Vahan Nikoghosyan, Jeff Tollaksen, V. Vardanyan, A. Kuzanyan
Current-Biased Transition-Edge Sensors Based On Re-Entrant Superconductors, Armen Gulian, Vahan Nikoghosyan, Jeff Tollaksen, V. Vardanyan, A. Kuzanyan
Mathematics, Physics, and Computer Science Faculty Articles and Research
Transition-edge sensors are widely recognized as one of the most sensitive tools for the photon and particles detection in many areas, from astrophysics to quantum computing. Their application became practical after understanding that rather than being biased in a constant current mode, they should be biased in a constant voltage mode. Despite the methods of voltage biasing of these sensors are well developed since then, generally the current biasing is more convenient for superconducting circuits. Thus transition-edge sensors designed inherently to operate in the current-biased mode are desirable. We developed a design for such detectors based on re-entrant superconductivity. In …
Prospective Solid-State Photonic Cryocooler Based On The “Phonon-Deficit Effect”, Gurgen Melkonyan, Armen Gulian
Prospective Solid-State Photonic Cryocooler Based On The “Phonon-Deficit Effect”, Gurgen Melkonyan, Armen Gulian
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this design microwave photons are propagating in a sapphire rod, and are being absorbed by a superconductor deposited on the surface of the rod. The frequency of the radiation is tuned to be less than the energy gap in the superconductor, so that the pair breaking is not taking place. This photon pumping redistributes the electron-hole quasiparticles: their distribution function is non-equilibrium, and the “phonon-deficit effect” takes place. There is a dielectric material deposited on top of superconductor, which serves asthe “cold finger” of the cooler. Its “acoustical density” is supposed to be smaller than that of the superconducting …
Shifting The Quantum-Classical Boundary: Theory And Experiment For Statistically Classical Optical Fields, Xiao-Feng Qian, Bethany Little, John C. Howell, Joseph H. Eberly
Shifting The Quantum-Classical Boundary: Theory And Experiment For Statistically Classical Optical Fields, Xiao-Feng Qian, Bethany Little, John C. Howell, Joseph H. Eberly
Mathematics, Physics, and Computer Science Faculty Articles and Research
The growing recognition that entanglement is not exclusively a quantum property, and does not even originate with Schrödinger’s famous remark about it [Proc. Cambridge Philos. Soc. 31, 555 (1935)], prompts the examination of its role in marking the quantum-classical boundary. We have done this by subjecting correlations of classical optical fields to new Bell-analysis experiments and report here values of the Bell parameter greater than ℬ=2.54. This is many standard deviations outside the limit ℬ=2 established by the Clauser–Horne–Shimony–Holt Bell inequality [Phys. Rev. Lett. 23, 880 (1969)], in agreement with our theoretical classical prediction, and not far from the Tsirelson …
How To Measure Magnetic Flux With A Single Position Measurement?, Eliahu Cohen, Lev Vaidman, Yakir Aharonov
How To Measure Magnetic Flux With A Single Position Measurement?, Eliahu Cohen, Lev Vaidman, Yakir Aharonov
Mathematics, Physics, and Computer Science Faculty Articles and Research
Current methods for measuring magnetic flux are based on performing many measurements over a large ensemble of electrons. We propose a novel method based on wave function "revival" for measuring the flux modulo using only a single electron. A preliminary analysis of the feasibility of the experiment is provided.
Spacetime Algebra As A Powerful Tool For Electromagnetism, Justin Dressel, Konstantin Y. Bliokh, Franco Nori
Spacetime Algebra As A Powerful Tool For Electromagnetism, Justin Dressel, Konstantin Y. Bliokh, Franco Nori
Mathematics, Physics, and Computer Science Faculty Articles and Research
We present a comprehensive introduction to spacetime algebra that emphasizes its practicality and power as a tool for the study of electromagnetism. We carefully develop this natural (Clifford) algebra of the Minkowski spacetime geometry, with a particular focus on its intrinsic (and often overlooked) complex structure. Notably, the scalar imaginary that appears throughout the electromagnetic theory properly corresponds to the unit 4-volume of spacetime itself, and thus has physical meaning. The electric and magnetic fields are combined into a single complex and frame-independent bivector field, which generalizes the Riemann-Silberstein complex vector that has recently resurfaced in studies of the single …
Paraxial Full-Field Cloaking, Joseph S. Choi, John C. Howell
Paraxial Full-Field Cloaking, Joseph S. Choi, John C. Howell
Mathematics, Physics, and Computer Science Faculty Articles and Research
We complete the ‘paraxial’ (small-angle) ray optics cloaking formalism presented previously [Opt. Express 22, 29465 (2014)], by extending it to the full-field of light. Omnidirectionality is then the only relaxed parameter of what may be considered an ideal, broadband, field cloak. We show that an isotropic plate of uniform thickness, with appropriately designed refractive index and dispersion, can match the phase over the whole visible spectrum. Our results support the fundamental limits on cloaking for broadband vs. omnidirectionality, and provide insights into when anisotropy may be required.
Power-Recycled Weak-Value-Based Metrology, Kevin Lyons, Justin Dressel, Andrew N. Jordan, John C. Howell, Paul G. Kwiat
Power-Recycled Weak-Value-Based Metrology, Kevin Lyons, Justin Dressel, Andrew N. Jordan, John C. Howell, Paul G. Kwiat
Mathematics, Physics, and Computer Science Faculty Articles and Research
We improve the precision of the interferometric weak-value-based beam deflection measurement by introducing a power recycling mirror, creating a resonant cavity. This results in all the light exiting to the detector with a large deflection, thus eliminating the inefficiency of the rare postselection. The signal-to-noise ratio of the deflection is itself magnified by the weak value. We discuss ways to realize this proposal, using a transverse beam filter and different cavity designs.
Violating The Modified Helstrom Bound With Nonprojective Measurements, Justin Dressel, Todd A. Brun, Alexander N. Korotkov
Violating The Modified Helstrom Bound With Nonprojective Measurements, Justin Dressel, Todd A. Brun, Alexander N. Korotkov
Mathematics, Physics, and Computer Science Faculty Articles and Research
We consider the discrimination of two pure quantum states with three allowed outcomes: a correct guess, an incorrect guess, and a nonguess. To find an optimum measurement procedure, we define a tunable cost that penalizes the incorrect guess and nonguess outcomes. Minimizing this cost over all projective measurements produces a rigorous cost bound that includes the usual Helstrom discrimination bound as a special case.We then show that nonprojective measurements can outperform this modified Helstrom bound for certain choices of cost function. The Ivanovic-Dieks-Peres unambiguous state discrimination protocol is recovered as a special case of this improvement.Notably, while the cost advantage …
Can A Future Choice Affect A Past Measurement's Outcome?, Yakir Aharonov, Eliahu Cohen, Avshalom C. Elitzur
Can A Future Choice Affect A Past Measurement's Outcome?, Yakir Aharonov, Eliahu Cohen, Avshalom C. Elitzur
Mathematics, Physics, and Computer Science Faculty Articles and Research
An EPR experiment is studied where each particle within the entangled pair undergoes a few weak measurements (WMs) along some pre-set spin orientations, with the outcomes individually recorded. Then the particle undergoes one strong measurement along an orientation chosen at the last moment. Bell-inequality violation is expected between the two final measurements within each EPR pair. At the same time, statistical agreement is expected between these strong measurements and the earlier weak ones performed on that pair. A contradiction seemingly ensues: (i) Bell’s theorem forbids spin values to exist prior to the choice of the orientation measured; (ii) A weak …
Heisenberg Scaling With Weak Measurement: A Quantum State Discrimination Point Of View, Andrew N. Jordan, Jeff Tollaksen, James E. Troupe, Justin Dressel, Yakir Aharonov
Heisenberg Scaling With Weak Measurement: A Quantum State Discrimination Point Of View, Andrew N. Jordan, Jeff Tollaksen, James E. Troupe, Justin Dressel, Yakir Aharonov
Mathematics, Physics, and Computer Science Faculty Articles and Research
We examine the results of the paper “Precision metrology using weak measurements” (Zhang et al. arXiv:1310.5302, 2013) from a quantum state discrimination point of view. The Heisenberg scaling of the photon number for the precision of the interaction parameter between coherent light and a spin one-half particle (or pseudo-spin) has a simple interpretation in terms of the interaction rotating the quantum state to an orthogonal one. To achieve this scaling, the information must be extracted from the spin rather than from the coherent state of light, limiting the applications of the method to phenomena such as cross-phase modulation. …
Weak Values As Interference Phenomena, Justin Dressel
Weak Values As Interference Phenomena, Justin Dressel
Mathematics, Physics, and Computer Science Faculty Articles and Research
Weak values arise experimentally as conditioned averages of weak (noisy) observable measurements that minimally disturb an initial quantum state, and also as dynamical variables for reduced quantum state evolution even in the absence of measurement. These averages can exceed the eigenvalue range of the observable ostensibly being estimated, which has prompted considerable debate regarding their interpretation. Classical conditioned averages of noisy signals only show such anomalies if the quantity being measured is also disturbed prior to conditioning. This fact has recently been rediscovered, along with the question whether anomalous weak values are merely classical disturbance effects. Here we carefully review …
Influence Of Microgel Packing On Raspberry-Like Heteroaggregate Assembly, Shalini Saxena, L. Andrew Lyon
Influence Of Microgel Packing On Raspberry-Like Heteroaggregate Assembly, Shalini Saxena, L. Andrew Lyon
Biology, Chemistry, and Environmental Sciences Faculty Articles and Research
We describe the influence of microgel packing on colloidal-phase mediated heteroaggregation using poly(N-isopropylacrylamide) and poly(N-isopropylmethacrylamide) microgels with 1% mol or 5% mol N,N’-methylenebis(acrylamide) cross-linker. This system is uniquely designed to interrogate the influence of microgel structure and stiffness on microgel deformation at a curved interface by elminating the necessity of electrostatic charge pairing. Microgel monomer and cross-linker content is expected to influence deformation at a curved interface. Microgel deformation and swelling were characterized via atomic force microscopy (AFM) and viscometry. A systematic study of colloidal-phase heteroaggregation was performed at varied effective volume fractions with all …
Probing The Transition State Region In Catalytic Co Oxidation On Ru, H. Öström, H. Öberg, H. Xin, Jerry L. Larue, M. Beye, M. Dell'angela, J. Gladh, M. L. Ng, J. A. Sellberg, S. Kaya, G. Mercurio, D. Nordlund, M. Hantschmann, F. Hieke, D. Kühn, W. F. Schlotter, G. L. Dakovski, J. J. Turner, M. P. Minitti, A. Mitra, S. P. Moeller, A. Föhlisch, M. Wolf, W. Wurth, M. Persson, J. K. Nørskov, F. Abild-Pedersen, H. Ogasawara, L. G. M. Pettersson, A. Nilsson
Probing The Transition State Region In Catalytic Co Oxidation On Ru, H. Öström, H. Öberg, H. Xin, Jerry L. Larue, M. Beye, M. Dell'angela, J. Gladh, M. L. Ng, J. A. Sellberg, S. Kaya, G. Mercurio, D. Nordlund, M. Hantschmann, F. Hieke, D. Kühn, W. F. Schlotter, G. L. Dakovski, J. J. Turner, M. P. Minitti, A. Mitra, S. P. Moeller, A. Föhlisch, M. Wolf, W. Wurth, M. Persson, J. K. Nørskov, F. Abild-Pedersen, H. Ogasawara, L. G. M. Pettersson, A. Nilsson
Biology, Chemistry, and Environmental Sciences Faculty Articles and Research
Femtosecond x-ray laser pulses are used to probe the CO oxidation reaction on Ru initiated by an optical laser pulse. On a timescale of a few hundred femtoseconds, the optical laser pulse excites motions of CO and O on the surface allowing the reactants to collide and, with a transient close to a picosecond (ps), new electronic states appear in the O K-edge x-ray absorption spectrum. Density functional theory calculations indicate that these result from changes in the adsorption site and bond-formation between CO and O with a distribution of OC—O bond lengths close to the transition state (TS). After …
Demonstrating Continuous Variable Einstein–Podolsky–Rosen Steering In Spite Of Finite Experimental Capabilities Using Fano Steering Bounds, James Schneeloch, Samuel H. Knarr, Gregory A. Howland, John C. Howell
Demonstrating Continuous Variable Einstein–Podolsky–Rosen Steering In Spite Of Finite Experimental Capabilities Using Fano Steering Bounds, James Schneeloch, Samuel H. Knarr, Gregory A. Howland, John C. Howell
Mathematics, Physics, and Computer Science Faculty Articles and Research
We show how one can demonstrate continuous-variable Einstein–Podolsky–Rosen (EPR) steering without needing to characterize entire measurement probability distributions. To do this, we develop a modified Fano inequality useful for discrete measurements of continuous variables and use it to bound the conditional uncertainties in continuous-variable entropic EPR-steering inequalities. With these bounds, we show how one can hedge against experimental limitations including a finite detector size, dead space between pixels, and any such factors that impose an incomplete sampling of the true measurement probability distribution. Furthermore, we use experimental data from the position and momentum statistics of entangled photon pairs in parametric …
Four Tails Problems For Dynamical Collapse Theories, Kelvin J. Mcqueen
Four Tails Problems For Dynamical Collapse Theories, Kelvin J. Mcqueen
Philosophy Faculty Articles and Research
The primary quantum mechanical equation of motion entails that measurements typically do not have determinate outcomes, but result in superpositions of all possible outcomes. Dynamical collapse theories (e.g. GRW) supplement this equation with a stochastic Gaussian collapse function, intended to collapse the superposition of outcomes into one outcome. But the Gaussian collapses are imperfect in a way that leaves the superpositions intact. This is the tails problem. There are several ways of making this problem more precise. But many authors dismiss the problem without considering the more severe formulations. Here I distinguish four distinct tails problems. The first (bare tails …
Mass Additivity And A Priori Entailment, Kelvin J. Mcqueen
Mass Additivity And A Priori Entailment, Kelvin J. Mcqueen
Philosophy Faculty Articles and Research
The principle of mass additivity states that the mass of a composite object is the sum of the masses of its elementary components. Mass additivity is true in Newtonian mechanics but false in special relativity. Physicists have explained why mass additivity is true in Newtonian mechanics by reducing it to Newton’s microphysical laws. This reductive explanation does not fit well with deducibility theories of reductive explanation such as the modern Nagelian theory of reduction, and the a priori entailment theory of reduction that is prominent in the philosophy of mind. Nonetheless, I argue that a reconstruction of the explanation that …
Logical Pre- And Post-Selection Paradoxes Are Proofs Of Contextuality, Matthew F. Pusey, Matthew S. Leifer
Logical Pre- And Post-Selection Paradoxes Are Proofs Of Contextuality, Matthew F. Pusey, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
If a quantum system is prepared and later post-selected in certain states, “paradoxical” predictions for intermediate measurements can be obtained. This is the case both when the intermediate measurement is strong, i.e. a projective measurement with Lüders-von Neumann update rule, or with weak measurements where they show up in anomalous weak values. Leifer and Spekkens [Phys. Rev. Lett. 95, 200405] identified a striking class of such paradoxes, known as logical pre- and postselection paradoxes, and showed that they are indirectly connected with contextuality. By analysing the measurement-disturbance required in models of these phenomena, we find that the strong measurement version …
Weak Values Obtained In Matter-Wave Interferometry, Stephan Sponar, Tobias Denkmayr, Hermann Geppert, Hartmutt Lemmel, Alexandre Matzkin, Jeff Tollaksen, Yuji Hasegawa
Weak Values Obtained In Matter-Wave Interferometry, Stephan Sponar, Tobias Denkmayr, Hermann Geppert, Hartmutt Lemmel, Alexandre Matzkin, Jeff Tollaksen, Yuji Hasegawa
Mathematics, Physics, and Computer Science Faculty Articles and Research
Weak values, introduced more than 25 years ago, underwent a metamorphosis from a theoretical curiosity to a powerful resource in photonics for exploring foundations of quantum mechanics, as well as a practical laboratory tool. Due to the tiny coherence volume of particles used in matter-wave optics, a straightforward implementation of weak measurements is not feasible. We have overcome this hurdle by developing a method to weakly measure a massive particle's spin component. A neutron optical approach is realized by utilizing neutron interferometry, where the neutron's spin is coupled weakly to its spatial degree of freedom. Here, we present how one …
Spatial Analyses On Seismo-Ionospheric Precursors Observed By Gim Tec And Demeter During The 2008 M8.0wenchuan Earthquake, Jann-Yenq Liu, Yuh-Ing Chen, Cheng-Chi Huang, Michel Parrot, Sergey Pulintets, Dimitar Ouzounov
Spatial Analyses On Seismo-Ionospheric Precursors Observed By Gim Tec And Demeter During The 2008 M8.0wenchuan Earthquake, Jann-Yenq Liu, Yuh-Ing Chen, Cheng-Chi Huang, Michel Parrot, Sergey Pulintets, Dimitar Ouzounov
Mathematics, Physics, and Computer Science Faculty Articles and Research
An abstract of the "Spatial analyses on seismo-ionospheric precursors observed by GIM TEC and DEMETER during the 2008 M8.0Wenchuan earthquake" paper presented at EGU General Assembly in 2015.
Fundamental Mathematics Of Consciousness, Menas Kafatos
Fundamental Mathematics Of Consciousness, Menas Kafatos
Mathematics, Physics, and Computer Science Faculty Articles and Research
We explore a mathematical formalism that ties together the observer with the observed in the view that Consciousness is primary, operating through three principles which apply at all levels, the essence of qualia of experience. The formalism is a simplified version of Hilbert space mathematics encountered in quantum mechanics. It does, however, go beyond specific interpretations of quantum mechanics and has strong philosophical foundations in Western philosophy as well as monistic systems of the East. The implications are explored and steps for the full development of this axiomatic mathematical approach to Consciousness are discussed.