Quantum Computation and Many Worlds
Dominic Horsman
本文阐述Saunders与Zurek的Everett多世界诠释，并以此物理描述量子计算过程，同时讨论相关反对意见。
本文详细介绍了由Saunders和Zurek提出的量子力学Everett（“多世界”）诠释。该诠释被用于对量子计算过程进行物理描述。文中还讨论了针对这种理解的反对意见。
An Everett (`Many Worlds') interpretation of quantum mechanics due to Saunders and Zurek is presented in detail. This is used to give a physical description of the process of a quantum computation. Objections to such an understanding are discussed.
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"All-Possible-Worlds" is a novel interpretation of quantum physics, which results from a unified reformulation of Many-Worlds and Copenhagen ("collapse") in the light of quantum contextuality, and proposes "nonlocality at detection" as a principle ruling the whole quantum realm, including single qubit and qutrit experiments.
Many-Worlds quantum mechanics differs from standard quantum mechanics in that in Many-Worlds, the wave function is a relative density of universes in the multiverse amplitude rather than a probability amplitude. This means that in Many-Worlds, the Born frequencies are approached rather than given a priori. Thus in Many-Worlds the rate of approach to the final frequencies can be calculated and compared with observation. I use Many-Worlds to derive the rate of approach in the double slit experiment, and show that it agrees with observation. Standard quantum theory has never been used to derive a…
Probability in many-worlds theories
本文研究确定性多世界理论中自然概率分布的定义，提出三个公理导出 Born rule，以解释量子理论的经验成功。
Discussions about whether quantum theory is determinism or indeterminism has lasted for a century. A new approach to standard quantum mechanics called many-interacting-worlds method based on many-worlds interpretation and de Broglie-Bohm mechanics provided the possibility to demonstrate probability from deterministic universe.The many-interacting-worlds method has been proved successful in the ground state of harmonic oscillator. In this article we extend this method to one dimensional Coulomb potential and construct a corresponding empirical density function. We also provide a theoretical pro…
The many-worlds interpretation (MWI) of quantum mechanics is studied from an unprecedented ontological perspective based on the reality of (semi-) deterministic parallel worlds in the interpretation. It is demonstrated that with thanks to the uncertainty principle there would be no consistent way to specify the correct ontology of the Universe, hence the MWI is subject to an inherent contradiction which claims that the world where we live in is unreal.
This is a philosophical paper in favor of the Many-Worlds Interpretation (MWI) of quantum theory. The concept of the ``measure of existence of a world'' is introduced and some difficulties with the issue of probability in the framework of the MWI are resolved. Brief comparative analyses of the Bohm theory and the Many-Minds Interpretation are given.
Quantum Suicide in Many-Worlds Implies P=NP
本文提出了一种严肃的算法，通过在许多世界解释下量子自杀的赌注，证明 NP 问题可以在多项式时间内解决。
It is argued that the lesson we should learn from Bell's inequalities is not that quantum mechanics requires some kind of action at a distance, but that it leads us to believe in parallel worlds.
This is a manuscript to be published as a book chapter. The text summarizes some of my critics concerning Everett's theory as seen from the perspective of a Bohmian. This is the second draft and comments are still welcome.
The many-worlds interpretation of quantum mechanics predicts the formation of distinct parallel worlds as a result of a quantum mechanical measurement. Communication among these parallel worlds would experimentally rule out alternatives to this interpretation. A procedure for ``interworld'' exchange of information and energy, using only state of the art quantum optical equipment, is described. A single ion is isolated from its environment in an ion trap. Then a quantum mechanical measurement with two discrete outcomes is performed on another system, resulting in the formation of two parallel w…
There have been many attempts over the years to derive the Born Rule from the wave equation since Everett's Many Worlds Interpretation was proposed; however, none of these have been satisfactory as shown when critics pointed out loopholes and unsupported assumptions. In this paper the case is made that the currently fashionable decision-theoretic approach founded by David Deutsch and explicated by David Wallace is likewise unsatisfactory. A more fundamental computationalist approach is advocated.
Valentini [arXiv:0811.0810] has recently defended the de Broglie-Bohm pilot-wave version of quantum theory from the claim that it is essentially Everett theory encumbered with the redundant postulation of point particles. In this note, Valentini's central arguments are questioned.
The fallacy that the many worlds intepretation (MWI) of quantum mechanics implies certain survival in quantum Russian roulette-like situations (the 'Quantum Suicide' (QS) thought experiment) has become common enough that it is now necessary to publicly debunk this belief despite the risk of further publicizing it. 'Quantum Immortality' is an extension of the QS Fallacy (QSF) with some additional unlikely assumptions. The QS/QI ideas are examined here and shown to be false.
In this brief note I argue that putting conscious observers at the center of the considerations clarifies and strengthens the many-worlds interpretation. The basic assumption, which seems extremely plausible based on our current understanding of the brain and of decoherence, is that quantum states corresponding to distinct conscious experiences have to be orthogonal. I show that, once this is accepted, probabilistic measurement outcomes corresponding to basis elements and following Born's rule emerge naturally from global unitary dynamics.
The linear mathematics of quantum mechanics gives many versions of reality instead of the single version we perceive, with the perceived version chosen at random according to a probability law. Because of these peculiarities, the theory requires an interpretation to be fully understood. Over 50 years ago, Everett proposed in his many-worlds interpretation that these characteristics could be accounted for if the mathematics itself, with no collapse or hidden variables, was carefully analyzed. We show this is incorrect; the linear mathematics cannot account for the probability law. Thus the many…
We suggest to combine the Anthropic Principle with Many-Worlds Interpretation of Quantum Theory. Realizing the multiplicity of worlds it provides an opportunity of explanation of some important events which are assumed to be extremely improbable. The Mesoscopic Anthropic Principle suggested here is aimed to explain appearance of such events which are necessary for emergence of Life and Mind. It is complementary to Cosmological Anthropic Principle explaining the fine tuning of fundamental constants. We briefly discuss various possible applications of Mesoscopic Anthropic Principle including the…
We investigate whether quantum theory can be understood as the continuum limit of a mechanical theory, in which there is a huge, but finite, number of classical 'worlds', and quantum effects arise solely from a universal interaction between these worlds, without reference to any wave function. Here a `world' means an entire universe with well-defined properties, determined by the classical configuration of its particles and fields. In our approach each world evolves deterministically; probabilities arise due to ignorance as to which world a given observer occupies; and we argue that in the lim…
The many worlds interpretation of quantum mechanics (MWI) states that the world we live in is just one among many parallel worlds. It is widely believed that because of this commitment to parallel worlds, the MWI violates common sense. Some go so far as to reject the MWI on this basis. This is despite its myriad of advantages to physics (e.g. consistency with relativity theory, mathematical simplicity, realism, determinism, etc.). Here, we make the case that common sense in fact favors the MWI. We argue that causal explanations are commonsensical only when they are local causal explanations. W…
Observing the violation of Bell's inequality tells us something about all possible future theories: they must all predict nonlocal correlations. Hence Nature is nonlocal. After an elementary introduction to nonlocality and a brief review of some recent experiments, I argue that Nature's nonlocality together with the existence of free will is incompatible with the many-worlds view of quantum physics.
It is emphasized that a many-worlds interpretation of quantum theory exists only to the extent that the associated basis problem is solved. The core basis problem is that the robust enduring states specified by environmental decoherence effects are essentially Gaussian wave packets that form continua of non-orthogonal states. Hence they are not a discrete set of orthogonal basis states to which finite probabilities can be assigned by the usual rules. The natural way to get an orthogonal basis without going outside the Schroedinger dynamics is to use the eigenstates of the reduced density matri…
The Many Worlds of Uncertainty
本文在新埃弗里特多重世界诠释下考察不确定性关系的含义，并分析不相容可观测量的联合与重复测量问题，揭示该理论对统计陈述的根本不同诠释。
The Born Interpretation of the wave function gives only the relative frequencies as the number of observations approaches infinity. Using the Many-Worlds Interpretation of quantum mechanics, specifically the fact that there must exist other versions of ourselves in the multiverse, I show that the observed frequencies should approach the Born frequencies as 1/N, where N is the number of observations. In the body of the paper I state this convergence rate precisely as AN EASILY TESTABLE FORMULA. We can therefore test the central claim of the MWI by measuring the convergence rate to the final Bor…
The paper entitled ``Against Many-Worlds Interpretations'' by A. Kent, which has recently been submitted to the e-Print archive (gr-qc/9703089) contained some misconceptions. The claims on Everett's many-worlds interpretation are quoted and answered.
In this paper we attempt to physically interpret the Modal Kochen- Specker (MKS) theorem. In order to do so, we analyze the features of the possible properties of quantum systems arising from the elements in an orthomodular lattice and distinguish the use of "possibility" in the classical and quantum formalisms. Taking into account the modal and many worlds non-collapse interpretation of the projection postulate, we discuss how the MKS theorem rules the constraints to actualization, and thus, the relation between actual and possible realms.
Many Retrocausal Worlds: A Foundation for Quantum Probability
针对量子力学多世界诠释的概率阐述缺陷，提出以时间延伸世界的自定位概率解决不一致性问题，将玻恩规则作为波函数通用模式确立概率，结合时间对称的不动点公式为量子概率提供基础。
Quantum nonlocality may be an artifact of the assumption that observers obey the laws of classical mechanics, while observed systems obey quantum mechanics. I show that, at least in the case of Bell's Theorem, locality is restored if observed and observer are both assumed to obey quantum mechanics, as in the Many-Worlds Interpretation. Using the MWI, I shall show that the apparently "non-local" expectation value for the product of the spins of two widely separated particles --- the "quantum" part of Bell's Theorem --- is really due to a series of three purely local measurements. Thus, experime…
Simulation of smooth models of potentials with singular point using Many-Interacting-Worlds Method
本文使用多相互作用世界方法，通过渐近光滑方法处理库仑势和有限陷阱势等奇异点，数值模拟了二维有界系统的稳态，并与标准量子力学中的矩阵Numerov方法结果一致。
The stability of dynamical systems against perturbations (variations in initial conditions/model parameters) is a property referred to as structural stability. The study of sensitivity to perturbation is essential because in experiment initial conditions are not fixed, nor are model parameters known, to arbitrarily high precision. Additionally, if a physical system under study exhibits stability (insensitivity to initial conditions) then a theoretical description of the system must exhibit structural stability. Consequently, stability can be a useful indicator of the correctness of a theoretic…
I discuss an experiment demonstrating nonlocality and conservation of energy under the assumption that the decision of the outcome happens at detection. The experiment does not require Bell's inequalities and is loophole-free. I further argue that the local hidden variables assumed in Bell's theorem involve de Broglie's "empty waves", and therefore "many worlds" achieves to reconcile locality with the violation of Bell's inequalities. Accordingly, the discussed experiment may be the first loophole-free demonstration of nonlocality.
The extended Wigner's friend, many- and single-worlds and reasoning from observation
本文探讨了孤立系统的概念及弗拉乌奇格与雷纳的扩展威格纳朋友情景，指出测量过程可能使孤立系统近似失效，且任何涉及主观坍缩的量子理论解释均无法成立，同时指出多重世界与单一世界解释无差异，并强调观察推理需考虑量子擦除的可能性。
I argue that the many worlds explanation of quantum computation is not licensed by, and in fact is conceptually inferior to, the many worlds interpretation of quantum mechanics from which it is derived. I argue that the many worlds explanation of quantum computation is incompatible with the recently developed cluster state model of quantum computation. Based on these considerations I conclude that we should reject the many worlds explanation of quantum computation.
An introduction to many worlds in quantum computation
本文从量子计算视角介绍并辩护新埃弗里特多世界诠释，回应概率等质疑，说明其局域性及对量子计算的基础优势。
We combine the ideas of Dirac's orthonormal representation, Everett's relative state, and 't Hooft's ontological basis to define the notion of a world for quantum mechanics. Mathematically, for a quantum system $\mathcal{Q}$ with an associated Hilbert space $\mathbb{H},$ a world of $\mathcal{Q}$ is defined to be an orthonormal basis of $\mathbb{H}.$ The evolution of the system is governed by Schrödinger's equation for the worlds of it. An observable in a certain world is a self-adjoint operator diagonal under the corresponding basis. Moreover, a state is defined in an associated world but can …
How can probabilities make sense in a deterministic many-worlds theory? We address two facets of this problem: why should rational agents assign subjective probabilities to branching events, and why should branching events happen with relative frequencies matching their objective probabilities. To address the first question, we generalise the Deutsch-Wallace theorem to a wide class of many-world theories, and show that the subjective probabilities are given by a norm that depends on the dynamics of the theory: the 2-norm in the usual Many-Worlds interpretation of quantum mechanics, and the 1-n…
An assessment of the anthology, 'Many Worlds? Everett, Quantum Theory and Reality', edited by Simon Saunders, Jonathan Barrett, Adrian Kent and David Wallace.
From Quantum Cryptography to Intuitionism and beyond: relativity, many-worlds and non-locality
本文在纪念 Gilles Brassard 七十岁生日时，提出有限速率创造新信息的想法，并发展“不确定性是相对的”观点，以阐明相对论与非定域性的相容性。
In Everett's many worlds interpretation, where quantum measurements are seen as decoherence events, inexact decoherence may let large worlds mangle the memories of observers in small worlds, creating a cutoff in observable world size. I solve a growth-drift-diffusion-absorption model of such a mangled worlds scenario, and show that it reproduces the Born probability rule closely, though not exactly. Thus deviations from exact decoherence can allow the Born rule to be derived in a many worlds approach via world counting, using a finite number of worlds and no new fundamental physics.
Many advocates of the Everettian interpretation consider that theirs is the only approach to take quantum mechanics really seriously, and that this approach allows to deduce a fantastic scenario for our reality, one that consists of an infinite number of parallel worlds that branch out continuously. In this article, written in dialogue form, we suggest that quantum mechanics can be taken even more seriously, if the 'many-worlds' view is replaced by a 'many-measurements' view. This allows not only to derive the Born rule, thus solving the measurement problem, but also to deduce a one-world 'non…
Many worlds interpretations (MWI) of quantum mechanics avoid the measurement problem by considering every term in the quantum superposition as actual. A seemingly opposed solution is proposed by modal interpretations (MI) which state that quantum mechanics does not provide an account of what `actually is the case', but rather deals with what `might be the case', i.e. with possibilities. In this paper we provide an algebraic framework which allows us to analyze in depth the modal aspects of MWI. Within our general formal scheme we also provide a formal comparison between MWI and MI, in particul…
Fundamental principle of classical physics -- local realism, means that freely chosen observations can be explained by a local (slower than light) real process. It is apparently violated in quantum mechanics as shown by Bell theorem. Despite extreme efforts experiments have not conclusively confirmed this violation due to loopholes. We propose a new postulate that the description of quantum processes must be consistent with local realism, It also assumes existence of many worlds/copies of the same system, interacting weakly microscopically but strongly macroscopically, whose number can be esti…
An emergent theory of quantum measurement arises directly by considering the particular subset of many body wavefunctions that can be associated with classical condensed matter and its interaction with delocalized wavefunctions. This transfers questions of the "strangeness" of quantum mechanics from the wavefunction to the macroscopic material itself. An effectively many-worlds picture of measurement results for long times and induces a natural arrow of time. The challenging part is then justifying why our macroscopic world is dominated by such far-from-eigenstate matter. Condensing cold mesos…
The Quantum Many-Worlds Interpretation, Simply Told
本文探讨多世界解释如何通过原子干涉仪中测路径的波色计探测器模型，展示微观物体、测量设备和观察者在同一框架下的一致性，并讨论其与实验观测的匹配性及无超距作用的特点。
'Locality' is a fraught word, even within the restricted context of Bell's theorem. As one of us has argued elsewhere, that is partly because Bell himself used the word with different meanings at different stages in his career. The original, weaker, meaning for locality was in his 1964 theorem: that the choice of setting by one party could never affect the outcome of a measurement performed by a distant second party. The epitome of a quantum theory violating this weak notion of locality (and hence exhibiting a strong form of nonlocality) is Bohmian mechanics. Recently, a new approach to quantu…
I argue that accepting quantum mechanics to be universally true means that you should also believe in parallel universes. I give my assessment of Everett's theory as it celebrates its 50th anniversary.
Two works related to the concept of probability in the framework of the many-worlds interpretation are presented. The first deals with recent controversy in classical probability theory. Elga and D. Lewis argues that Sleeping Beauty should have different credences for the result of a fair coin toss in a particular situation. It is argued that when the coin is replaced by a quantum coin, the credence is unambiguous and since one should not expect a difference between classical and quantum coins, this provides a particular resolution of the controversy. Second work is an analysis of a recent cri…
More than a speculative technology, quantum computing seems to challenge our most basic intuitions about how the physical world should behave. In this thesis I show that, while some intuitions from classical computer science must be jettisoned in the light of modern physics, many others emerge nearly unscathed; and I use powerful tools from computational complexity theory to help determine which are which.
We propose a method for finding an initial state vector which by ordinary Hamiltonian time evolution follows a single branch of many-worlds quantum mechanics. The resulting deterministic system appears to exhibit random behavior as a result of the successive emergence over time of information present in the initial state but not previously observed.
The interpretation of the squared norm as probability and the apparent stochastic nature of observation in quantum mechanics are derived from the strong law of large numbers and the algebraic properties of infinite sequences of simultaneous quantum observables. It is argued that this result validates the many-worlds view of quantum reality.
In a recent paper, S. Gao has claimed that, under the assumption that the initial state of the universe is a pure quantum state, only the many worlds interpretation can account for the observed arrow of time. We show that his argument is untenable and that if endorsed it potentially leads to undermine the search for a scientific explanation of certain phenomena.
A minimal approach to the measurement problem and the quantum-to-classical transition assumes a universally valid quantum formalism, i.e. unitary time evolution governed by a Schrödinger-type equation. As had been pointed out long ago, in this view the measurement process can be described by decoherence which results in a "Many-Worlds" or "Many-Minds" scenario according to Everett and Zeh. A silent assumption for decoherence to proceed is however, that there exists incomplete information about the environment our object system gets entangled with in the measurement process. This paper addresse…
We propose a set of simple quantum optics experiments that test for an entirely new domain of physical laws that govern how an individual's conscious experience traverses the multiverse within Everett's many worlds interpretation of quantum mechanics. These experiments imply an exception to the Born rule in a proposed ''observer-specific'' reference frame. These experiments must be done by you, the reader. If it is performed by anyone else, other than you, the reader, you will observe that the person performing the experiment will observe an outcome that is not special, interesting, or differe…
We analyze the objective meaning of probabilities in the context of the many-worlds interpretation of Everett. For this purpose we study in details the weak law of large numbers and the role of typicality and universally negligible probabilities (through the works of Cournot and Borel). We demonstrate that Everett's theory doesn't provide any clue for fixing a probability rule and therefore contradicts irrevocably empirical facts and Born's law.
This paper has been withdrawn as it has been superseded by 0808.2697
Classical Many-Worlds Interpretation
本文提出一种将量子力学重构为完全经典理论的初步方法，通过引入多个共存的经典世界，构建了具有内置概率和宏观经典性的多世界诠释版本，且该理论等价于量子场论。
As is well known, the double slit experiment contains every key concepts of quantum mechanics such as phase effect, probability wave, quantum interference, quantum superposition. In this article, I will clarify the meaning of quantum superposition in terms of phase effect between states. After applying standard quantum theory, it leads to serious questions about the unitary process of an isolated system. It implies that non collapsing interpretations including many worlds may not be justified. This also could explain that there is no such boundary between classical and quantum domains.
A review of Peter Byrne's biography of Hugh Everett III, "The Many Worlds of Hugh Everett III: Multiple Universes, Mutual Assured Destruction, and the Meltdown of a Nuclear Family", (Oxford University Press, 2010).
Against Many Worlds
在多世界诠释背景下探讨获取玻恩规则的方法，指出公理法、演绎法、归纳法这三种途径因结构原因均无法成功获得玻恩规则。
Schroedinger's first proposal for the interpretation of quantum mechanics was based on a postulate relating the wave function on configuration space to charge density in physical space. Schroedinger apparently later thought that his proposal was empirically wrong. We argue here that this is not the case, at least for a very similar proposal with charge density replaced by mass density. We argue that when analyzed carefully this theory is seen to be an empirically adequate many-worlds theory and not an empirically inadequate theory describing a single world. Moreover, this formulation--Schroedi…
Everett's Many-Worlds Interpretation of quantum mechanics is discussed in the context of other physics disputes and other proposed kinds of parallel universes. We find that only a small fraction of the usual objections to Everett's theory are specific to quantum mechanics, and that all of the most controversial issues crop up also in settings that have nothing to do with quantum mechanics.
Geometric phases, Everett's many-worlds interpretation of quantum mechanics, and wormholes
本文利用绝热几何相位构造几何实现，具象化埃弗雷特多世界诠释，并借虫洞概念与量子引力（矩阵模型）建立一致性。
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