Quantum Physics

Characterizing and Quantifying Frustration in Quantum Many-Body Systems

by Alex Monras

Optimal full estimation of qubit mixed states

by Alex Monras

Immunity of information encoded in decoherence-free subspaces to particle loss

by Piotr Migdal

Quantum and semiclassical polarization correlations

by Piotr Migdal

Qubism: self-similar visualization of many-body wavefunctions

by Piotr Migdal

accepted to the New Journal of Physics

A visualization scheme for quantum many-body wavefunctions is described, which we have termed qubism. Its main... more A visualization scheme for quantum many-body wavefunctions is described, which we have termed qubism. Its main property is its recursivity: increasing the number of qubits reflects in an increase in the image resolution. Thus, the plots are typically fractal. As examples, we provide images for the ground states of commonly used Hamiltonians in condensed matter and cold atom physics, such as Heisenberg or ITF. Many features of the wavefunction, such as magnetization, correlations and criticality, can be visualized as properties of the images. In particular, factorizability can be easily spotted, and a way to estimate the entanglement entropy from the image is provided.

Quantum Multiplexers, Parrondo Games, and Proper Quantization

by Faisal Shah Khan

Doctoral Dissertation

A quantum logic gate of particular interest to both electrical engineers and game theorists is the quantum... more A quantum logic gate of particular interest to both electrical engineers and game theorists is the quantum multiplexer. This shared interest is due to the facts that an arbitrary quantum logic gate may be expressed, up to arbitrary accuracy, via a circuit consisting entirely of variations of the quantum multiplexer, and that certain one player games, the history dependent Parrondo games, can be quantized as games via a particular variation of the quantum multiplexer. However, to date all such quantizations have lacked a certain fundamental game theoretic property.
The main result in this dissertation is the development of quantizations of history dependent quantum Parrondo games that satisfy this fundamental game theoretic property. Our approach also yields fresh insight as to what should be considered as the proper quantum analogue of a classical Markov process and gives the first game theoretic measures of multiplexer behavior.

Gaming the Quantum

by Faisal Shah Khan

In the time since a merger of quantum mechanics and game theory was proposed formally in 1999, the two distinct... more In the time since a merger of quantum mechanics and game theory was proposed formally in 1999, the two distinct perspectives apparent in this merger of applying quantum mechanics to game theory, referred to henceforth as the theory of "quantized games", and of applying game theory to quantum mechanics, referred to henceforth as "gaming the quantum", have become synonymous under the single ill-defined term "quantum game". Here, these two perspectives are delineated and a game-theoretically proper description of what makes a multi-player, non-cooperative game quantum mechanical, is given. Within the context of this description, finding a Nash equilibrium in a quantum game is shown to be equivalent to finding a solution to a simultaneous best approximation problem in the state space of quantum objects, thus setting up a framework for a game theory inspired study of "equilibrium" behavior of quantum physical systems such as those utilized in quantum information processing and computation.

I can't get no (epistemic) satisfaction: Why the hard problem of consciousness entails a hard problem of explanation

by Brian Earp

Earp, B. D. (2012). I can’t get no (epistemic) satisfaction: Why the hard problem of consciousness entails a hard problem of explanation. Dialogues in Philosophy, Mental and Neuro Sciences, in press.

Daniel Dennett (1996) has disputed David Chalmers’ (1995) assertion that there is a “hard problem of consciousness”... more Daniel Dennett (1996) has disputed David Chalmers’ (1995) assertion that there is a “hard problem of consciousness” worth solving in the philosophy of mind. In this paper I defend Chalmers against Dennett on this point: I argue that there is a hard problem of consciousness, that it is distinct in kind from the so-called easy problems, and that it is vital for the sake of honest and productive research in the cognitive sciences to be clear about the difference. But I have my own rebuke for Chalmers on the point of explanation. Chalmers (1995, 1996) proposes to “solve” the hard problem of consciousness by positing qualia as fundamental features of the universe, alongside such ontological basics as mass and space-time. But this is an inadequate solution: to posit, I will urge, is not to explain. To bolster this view, I borrow from an account of explanation by which it must provide “epistemic satisfaction” to be considered successful (Rowlands, 2001; Campbell, 2009), and show that Chalmers’ proposal fails on this account. I conclude that research in the science of consciousness cannot move forward without greater conceptual clarity in the field.

Russian version of "Contradiction of Density matrix notion in quantum mechanics."

by Vladimir K. Ignatovich

The paper is submitted to JETP Lett on 22.01.2012
It was rejected on 15 March 2012.

It is shown that description of nonpolarized neutron beam with the unit density matrix is contradictory. For the... more It is shown that description of nonpolarized neutron beam with the unit density matrix is contradictory. For the density matrix all the quantization axes are equivalent, while physically they are distinguishable and therefore are not equivalent. A neutron experiment is discussed for distinguishing of two orthogonal quantization axes in nonpolarized neutron beam.

Determination of Planck's constant via radiation laws

by Claudio Polisseni

Laboratory carried out in my third year in order to investigate blackbody radiation

Determination of Planck's constant and photoelectric effect

by Claudio Polisseni

Report for a third year experiment based on determining Planck's constant via the photoelectric effect

Analytic influence functionals for numerical Feynman integrals in most open quantum systems

by Nike Dattani

Derivation of the Meaning of the Wave Function

by Shan Gao

Draft Version

We show that the physical meaning of the wave function can be derived based on the established parts of quantum... more We show that the physical meaning of the wave function can be derived based on the established parts of quantum mechanics. It turns out that the wave function represents the state of random discontinuous motion of particles, and its modulus square determines the probability density of the particles appearing in certain positions in space.

A quantum theory of consciousness

by Shan Gao

Minds and Machines 18, 39-52 (2008).

The relationship between quantum collapse and consciousness is reconsidered under the assumption that quantum collapse... more The relationship between quantum collapse and consciousness is reconsidered under the assumption that quantum collapse is an objective dynamical process. We argue that the conscious observer can have a distinct role from the physical measuring device during the process of quantum collapse owing to the intrinsic nature of consciousness; the conscious observer can know whether he is in a definite state or a quantum superposition of definite states, while the physical measuring device cannot “know”. As a result, the consciousness observer can distinguish the definite states and their quantum superposition, while the physical measuring device without consciousness cannot do. This provides a possible quantum physical method to distinguish man and machine. The new result also implies that consciousness has causal efficacies in the physical world when considering the existence of quantum collapse. Accordingly consciousness is not reducible or emergent, but a new fundamental property of matter. This may establish a quantum basis for panpsychism, and make it be a promising solution to the hard problem of consciousness. Furthermore, it is suggested that a unified theory of matter and consciousness includes two parts: one is the psychophysical principle or corresponding principle between conscious content and matter state, and the other is the complete quantum evolution of matter state, which includes the definite nonlinear evolution element introduced by consciousness and relating to conscious content. Lastly, some experimental schemes are presented to test the proposed quantum theory of consciousness.

A quantum physical argument for panpsychism

by Shan Gao

Forthcoming in Journal of Consciousness Studies

It has been widely thought that consciousness has no causal efficacy in the physical world. However, this may be not... more It has been widely thought that consciousness has no causal efficacy in the physical world. However, this may be not the case. In this paper, we show that a conscious being can distinguish definite perceptions and their quantum superpositions, while a physical measuring system without consciousness cannot distinguish such nonorthogonal quantum states. The possible existence of this distinct quantum physical effect of consciousness may have interesting implications for the science of consciousness. In particular, it suggests that consciousness is not emergent but a fundamental feature of the universe. This may provide a possible quantum basis for panpsychism.

Meaning of the wave function

by Shan Gao

International Journal of Quantum Chemistry, 111, 4124-4138 (2011).

We investigate the meaning of the wave function by analyzing the mass and charge density distributions of a quantum... more We investigate the meaning of the wave function by analyzing the mass and charge density distributions of a quantum system. According to protective measurement, a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wave function. In a realistic interpretation, the wave function of a quantum system can be taken as a description of either a physical field or the ergodic motion of a particle. The essential difference between a field and the ergodic motion of a particle lies in the property of simultaneity; a field exists throughout space simultaneously, whereas the ergodic motion of a particle exists throughout space in a time-divided way. If the wave function is a physical field, then the mass and charge density will be distributed in space simultaneously for a charged quantum system, and thus, there will exist gravitational and electrostatic self-interactions of its wave function. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Thus, the wave function cannot be a description of a physical field but a description of the ergodic motion of a particle. For the later, there is only a localized particle with mass and charge at every instant, and thus, there will not exist any self-interaction for the wave function. It is further argued that the classical ergodic models, which assume continuous motion of particles, cannot be consistent with quantum mechanics. On the basis of negative result, we suggest that the wave function is a description of the quantum motion of particles, which is random and discontinuous in nature. On this interpretation, the square of the absolute value of the wave function not only gives the probability of the particle being found in certain locations but also gives the objective probability of the particle being there. We show that this new interpretation of the wave function provides a natural realistic alternative to the orthodox interpretation, and its implications for other realistic interpretations of quantum mechanics are also briefly discussed.

The wave function and quantum reality

by Shan Gao

Proceedings of the International Conference on Advances in Quantum Theory, A. Khrennikov, G. Jaeger, M. Schlosshauer, G. Weihs (eds), AIP Conference Proceedings 1327, 334-338 (2011).

We suggest the wave function is a description of the quantum motion of particles, which is random and discontinuous in... more We suggest the wave function is a description of the quantum motion of particles, which is random and discontinuous in nature. On this interpretation, the square of the absolute value of the wave function not only gives the probability of the particle being found in certain locations, but also gives the probability of the particle being there.

Does gravity induce wavefunction collapse? An examination of Penrose's argument

by Shan Gao

Draft Version

According to Penrose, the fundamental conflict between the superposition principle of quantum mechanics and the... more According to Penrose, the fundamental conflict between the superposition principle of quantum mechanics and the general covariance principle of general relativity entails the existence of wavefunction collapse, e.g. a quantum superposition of two different space-time geometries will collapse to one of them due to the ill-definedness of the time-translation operator for the superposition. In this paper, we argue that Penrose's conjecture on gravity's role in wavefunction collapse is debatable. First of all, it is still a controversial issue what the exact nature of the conflict is and how to resolve it. Secondly, Penrose's argument by analogy is too weak to establish a necessary connection between wavefunction collapse and the conflict as understood by him. Thirdly, the conflict does not necessarily lead to wavefunction collapse. For the conflict or the problem of ill-definedness for a superposition of different space-time geometries also needs to be solved before the collapse of the superposition finishes, and once the conflict has been resolved, the wavefunction collapse will lose its physical basis relating to the conflict. In addition, we argue that Penrose's suggestions for the collapse time formula and collapse states are also problematic.

On Diósi-Penrose Criterion of Gravity-Induced Quantum Collapse

by Shan Gao

International Journal of Theoretical Physics 49, 849–853.

It is shown that the Diósi-Penrose criterion of gravity-induced quantum collapse may be inconsistent with the... more It is shown that the Diósi-Penrose criterion of gravity-induced quantum collapse may be inconsistent with the discreteness of space–time, which is generally considered as an indispensable element in a complete theory of quantum gravity. Moreover, the analysis also suggests that the discreteness of space–time may result in rapider collapse of the superposition of energy eigenstates than required by the Diósi-Penrose criterion.

A model of wavefunction collapse in discrete space-time

by Shan Gao

International Journal of Theoretical Physics 45, 1965-1979.

We give a new argument supporting a gravitational role in quantum collapse. It is demonstrated that the discreteness... more We give a new argument supporting a gravitational role in quantum collapse. It is demonstrated that the discreteness of space-time, which results from the proper combination of quantum theory and general relativity, may inevitably result in the dynamical collapse of the wave function. Moreover, the minimum size of discrete space-time yields a plausible collapse criterion consistent with experiments. By assuming that the source to collapse the wave function is the inherent random motion of particles described by the wave function, we further propose a concrete model of wavefunction collapse in the discrete space-time. It is shown that the model is consistent with the existing experiments and macroscopic experiences.