96,682 research outputs found
Experimental status of quaternionic quantum mechanics
Analysis of the logical foundations of quantum mechanics indicates the
possibility of constructing a theory using quaternionic Hilbert spaces. Whether
this mathematical structure reflects reality is a matter for experiment to
decide. We review the only direct search for quaternionic quantum mechanics yet
carried out and outline a recent proposal by the present authors to look for
quaternionic effects in correlated multi-particle systems. We set out how such
experiments might distinguish between the several quaternionic models proposed
in the literature.Comment: 8 pages, no figures, revtex. An update of paper appearing in journal
reference given below, with minor amendments and latest additional reference
On local-hidden-variable no-go theorems
The strongest attack against quantum mechanics came in 1935 in the form of a
paper by Einstein, Podolsky and Rosen. It was argued that the theory of quantum
mechanics could not be called a complete theory of Nature, for every element of
reality is not represented in the formalism as such. The authors then put forth
a proposition: we must search for a theory where, upon knowing everything about
the system, including possible hidden variables, one could make precise
predictions concerning elements of reality. This project was ultimatly doomed
in 1964 with the work of Bell Bell, who showed that the most general local
hidden variable theory could not reproduce correlations that arise in quantum
mechanics. There exist mainly three forms of no-go theorems for local hidden
variable theories. Although almost every physicist knows the consequences of
these no-go theorems, not every physicist is aware of the distinctions between
the three or even their exact definitions. Thus we will discuss here the three
principal forms of no-go theorems for local hidden variable theories of Nature.
We will define Bell inequalities, Bell inequalities without inequalities and
pseudo-telepathy. A discussion of the similarities and differences will follow.Comment: 7 pages, no figure, replaced "Bell inequalities" with "Bell theorems"
and updated the reference
Anthropic interpretation of quantum theory
The problem of interpreting quantum theory on a large (e.g. cosmological)
scale has been commonly conceived as a search for objective reality in a
framework that is fundamentally probabilistic. The Everett programme attempts
to evade the issue by the reintroduction of determinism at the global level of
a ``state vector of the universe''. The present approach is based on the
recognition that, like determinism, objective reality is an unrealistic
objective. It is shown how an objective theory of an essentially subjective
reality can be set up using an appropriately weighted probability measure on
the relevant set of Hilbert subspaces. It is suggested that an entropy
principle (superseding the weak anthropic principle) should be used to provide
the weighting that is needed.Comment: Latex file (7 pages) for exposition presented at Interdisciplinary
Colloquium ``La Philosophie de la Nature aujourd'hui?'', Paris, March 2003,
and 8th Peyresq Physics Meeting ``The Early Universe'', June 200
Student Challenges in Understanding Quantum Mechanics: Effect of the “Logic paradigm shift”
For three centuries Newtonian mechanics had been firmly established as a valid theory for the understanding of physical reality; if one understands the laws of physics, then one understands the whole universe. Classical physicists had contented themselves with the search for regularities in measurements and in the physical world. Irregularities were regarded as noises that interfered with the deterministic picture of physical reality. However, from 1900s onwards with the quantum hypothesis, physicists had begun to recognize that the physics of Newton and Maxwell were inadequate for the understanding of all of the physical reality. For example, the interaction of radiation with matter could not be explained from classical physics. This dilemma led to the discovery of quantum mechanics. In this article we explore the challenges that students face in understanding quantum mechanics that arises from paradigm shift in the mode of reasoning about the physical world. The description of physical reality in general and quantum reality in particular requires that we shift our mode of reasoning from classical Boolean logic to quantum non Boolean logic
Quantum error correction protects quantum search algorithms against decoherence
When quantum computing becomes a wide-spread commercial reality, Quantum Search Algorithms (QSA) and especially Grover’s QSA will inevitably be one of their main applications, constituting their cornerstone. Most of the literature assumes that the quantum circuits are free from decoherence. Practically, decoherence will remain unavoidable as is the Gaussian noise of classic circuits imposed by the Brownian motion of electrons, hence it may have to be mitigated. In this contribution, we investigate the effect of quantum noise on the performance of QSAs, in terms of their success probability as a function of the database size to be searched, when decoherence is modelled by depolarizing channels’ deleterious effects imposed on the quantum gates. Moreover, we employ quantum error correction codes for limiting the effects of quantum noise and for correcting quantum flips. More specifically, we demonstrate that, when we search for a single solution in a database having 4096 entries using Grover’s QSA at an aggressive depolarizing probability of 10-3, the success probability of the search is 0.22 when no quantum coding is used, which is improved to 0.96 when Steane’s quantum error correction code is employed. Finally, apart from Steane’s code, the employment of Quantum Bose-Chaudhuri-Hocquenghem (QBCH) codes is also considered
Quantum realism: axiomatization and quantification
The emergence of an objective reality in line with the laws of the
microscopic world has been the focus of longstanding debates. Recent approaches
seem to have reached a consensus at least with respect to one aspect, namely,
that the encoding of information about a given observable in a physical degree
of freedom is a necessary condition for such observable to become an element of
the physical reality. Taking this as a fundamental premise and inspired by
quantum information theory, here we build an axiomatization for quantum realism
-- a notion of realism compatible with quantum theory. Our strategy consists of
listing some physically-motivated principles able to characterize quantum
realism in a ``metric'' independent manner. We introduce some criteria defining
monotones and measures of realism and then search for potential candidates
within some celebrated information theories -- those induced by the von
Neumann, R\'enyi, and Tsallis entropies. We explicitly construct some classes
of entropic quantifiers that are shown to satisfy (almost all of) the proposed
axioms and hence can be taken as faithful estimates for the degree of reality
(or definiteness) of a given physical observable. Hopefully, our framework may
offer a formal ground for further discussions on foundational aspects of
quantum mechanics.Comment: 15 pages, 4 figure
Asymptotically Improved Grover's Algorithm in any Dimensional Quantum System with Novel Decomposed -qudit Toffoli Gate
As the development of Quantum computers becomes reality, the implementation
of quantum algorithms is accelerating in a great pace. Grover's algorithm in a
binary quantum system is one such quantum algorithm which solves search
problems with numeric speed-ups than the conventional classical computers.
Further, Grover's algorithm is extended to a -ary quantum system for
utilizing the advantage of larger state space. In qudit or -ary quantum
system n-qudit Toffoli gate plays a significant role in the accurate
implementation of Grover's algorithm. In this paper, a generalized -qudit
Toffoli gate has been realized using qudits to attain a logarithmic depth
decomposition without ancilla qudit. Further, the circuit for Grover's
algorithm has been designed for any d-ary quantum system, where d >= 2, with
the proposed -qudit Toffoli gate so as to get optimized depth as compared to
state-of-the-art approaches. This technique for decomposing an n-qudit Toffoli
gate requires access to higher energy levels, making the design susceptible to
leakage error. Therefore, the performance of this decomposition for the unitary
and erasure models of leakage noise has been studied as well
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