arXiv subjects
Publications and source records attributed to Thomas Durt.
As a consequence of the equivalence principle and of the existence of a negative vacuum energy, we show how a weak but universal linear response of the vacuum to a local gravitational potential suffices to explain the main features of so-called Pioneer anomalies as well as the apparent departure from the third Kepler law which has been observed at the level of numerous galaxies.
Three paradigms commonly used in classical, pre-quantum physics to describe particles (that is: the material point, the test-particle and the diluted particle (droplet model)) can be identified as limit-cases of a quantum regime in which pairs of particles interact without getting entangled with each other. This entanglement-free regime also provides a simplified model of what is called in the decoherence approach "islands of classicality", that is, preferred bases that would be selected through evolution by a Darwinist mechanism that aims at optimising information. We show how, under very general conditions, coherent states are natural candidates for classical pointer states. This occurs essentially because, when a (supposedly bosonic) system coherently exchanges only one quantum at a time with the (supposedly bosonic) environment, coherent states of the system do not get entangled with the environment, due to the bosonic symmetry.
The role played by Time in the quantum theory is still mysterious by many aspects. In particular it is not clear today whether the distribution of decay times of unstable particles could be described by a Time Operator. As we shall discuss, different approaches to this problem (one could say interpretations) can be found in the literature on the subject. As we shall show, it is possible to conceive crucial experiments aimed at distinguishing the different approaches, by measuring with accuracy the statistical distribution of decay times of entangled particles. Such experiments can be realized in principle with entangled kaon pairs.
Mutually unbiased bases for quantum degrees of freedom are central to all theoretical investigations and practical exploitations of complementary properties. Much is known about mutually unbiased bases, but there are also a fair number of important questions that have not been answered in full as yet. In particular, one can find maximal sets of ${N+1}$ mutually unbiased bases in Hilbert spaces of prime-power dimension ${N=p^\m}$, with $p$ prime and $\m$ a positive integer, and there is a continuum of mutually unbiased bases for a continuous degree of freedom, such as motion along a line. But not a single example of a maximal set is known if the dimension is another composite number ($N=6,10,12,...$). In this review, we present a unified approach in which the basis states are labeled by numbers ${0,1,2,...,N-1}$ that are both elements of a Galois field and ordinary integers. This dual nature permits a compact systematic construction of maximal sets of mutually unbiased bases when they are known to exist but throws no light on the open existence problem in other cases. We show how to use the thus constructed mutually unbiased bases in quantum-informatics applications, including dense coding, teleportation, entanglement swapping, covariant cloning, and state tomography, all of which rely on an explicit set of maximally entangled states (generalizations of the familiar two--q-bit Bell states) that are related to the mutually unbiased bases. There is a link to the mathematics of finite affine planes. We also exploit the one-to-one correspondence between unbiased bases and the complex Hadamard matrices that turn the bases into each other. The ultimate hope, not yet fulfilled, is that open questions about mutually unbiased bases can be related to open questions about Hadamard matrices or affine planes, in particular the ...[rest deleted]
It has been conjectured that a complete set of mutually unbiased bases in a space of dimension d exists if and only if there is an affine plane of order d. We introduce affine constellations and compare their existence properties with those of mutually unbiased constellations, mostly in dimension six. The observed discrepancies make a deeper relation between the two existence problems unlikely.
In the present paper we show that the Temporal Wave Function approach of the decay process, which is a multicomponent version of the Time Operator approach leads to new, non-standard, predictions concerning the statistical properties of decay time distributions of single kaons and entangled pairs of mesons. These results suggest crucial experimental tests for the existence of a Time Operator for the decay process to be realized in High Energy Physics or Quantum Optics.
According to the so-called Quantum Darwinist approach, the emergence of "classical islands" from a quantum background is assumed to obey a (selection) principle of maximal information. We illustrate this idea by considering the coupling of two oscillators (modes). As our approach suggests that the classical limit could have emerged throughout a long and progressive Evolution mechanism, it is likely that primitive living organisms behave in a "more quantum", "less classical" way than more evolved ones. This brings us to seriously consider the possibility to measure departures from classicality exhibited by biological systems. We describe an experimental proposal the aimed at revealing the presence of entanglement in the biophotonic radiation emitted by biological sources.
This document is the Special Issue of the First International Conference on the Evolution and Development of the Universe (EDU 2008). Please refer to the preface and introduction for more details on the contributions. Keywords: acceleration, artificial cosmogenesis, artificial life, Big Bang, Big History, biological evolution, biological universe, biology, causality, classical vacuum energy, complex systems, complexity, computational universe, conscious evolution, cosmological artificial selection, cosmological natural selection, cosmology, critique, cultural evolution, dark energy, dark matter, development of the universe, development, emergence, evolution of the universe evolution, exobiology, extinction, fine-tuning, fractal space-time, fractal, information, initial conditions, intentional evolution, linear expansion of the universe, log-periodic laws, macroevolution, materialism, meduso-anthropic principle, multiple worlds, natural sciences, Nature, ontology, order, origin of the universe, particle hierarchy, philosophy, physical constants, quantum darwinism, reduction, role of intelligent life, scale relativity, scientific evolution, self-organization, speciation, specification hierarchy, thermodynamics, time, universe, vagueness.
Quantum cryptography makes it possible to expand a short shared key (of e.g. 256 bits[1]) into an arbitrary long shared key. The novelty of quantum cryptography is that whenever a spy tries to eavesdrop the communication he causes disturbances in the transmission of the message. Ultimately this unavoidable disturbance is a consequence of Heisenberg's uncertainty principle that limits the joint knowledge of complementary observables. Now, a problem remains: in order to initialize quantum key distribution, Alice and Bob need to share a short shared key in order to be able to identify each other unambiguously. Therefore a trusted courier is needed. We propose in this paper a solution to the trusted courrier problem that was inspired by quantum cryptography. The idea is to encode the key that Alice sends to Bob into unstable nuclei in such a way that the message gets revealed only after the courrier has delivered it to Bob. In this approach, we replace Heisenberg uncertainties by another type of uncertainty, that characterizes the knowledge of the time at which an unstable nucleus decays. As we shall show, this scheme makes it possible to refresh a key even in the case that we do not trust the courier who carries the key.
According to the so-called ``Quantum Darwinist'' approach, the emergence of ``classical islands'' from a quantum background is assumed to obey a (selection) principle of maximal information. We illustrate this idea by considering the coupling of two particles that interact through a position-dependent potential. This approach sheds a new light on the emergence of classical logics and of our classical preconceptions about the world. The distinction between internal and external world, the Cartesian prejudice according to which the whole can be reduced to the sum of its parts and the appearance of preferred representation bases such as the position is seen here as the result of a very long evolution and would correspond to the most useful way of extracting stable and useful information from the quantum correlations.
The meaning of superselection rules in Bohm-Bell theories (i.e., quantum theories with particle trajectories) is different from that in orthodox quantum theory. More precisely, there are two concepts of superselection rule, a weak and a strong one. Weak superselection rules exist both in orthodox quantum theory and in Bohm-Bell theories and represent the conventional understanding of superselection rules. We introduce the concept of strong superselection rule, which does not exist in orthodox quantum theory. It relies on the clear ontology of Bohm-Bell theories and is a sharper and, in the Bohm-Bell context, more fundamental notion. A strong superselection rule for the observable G asserts that one can replace every state vector by a suitable statistical mixture of eigenvectors of G without changing the particle trajectories or their probabilities. A weak superselection rule asserts that every state vector is empirically indistinguishable from a suitable statistical mixture of eigenvectors of G. We establish conditions on G for both kinds of superselection. For comparison, we also consider both kinds of superselection in theories of spontaneous wave function collapse.
We study different techniques that allow us to gain complete knowledge about an unknown quantum state, e.g. to perform full tomography of this state. We focus on two apparently simple cases, full tomography of one and two qubit systems. We analyze and compare those techniques according to two figures of merit. Our first criterion is the minimisation of the redundancy of the data acquired during the tomographic process. In the case of two-qubits tomography, we also analyze this process from the point of view of factorisability, so to say we analyze the possibility to realise the tomographic process through local operations and classical communications between local observers. This brings us naturally to study the possibility to factorize the (discrete) Wigner distribution of a composite system into the product of local Wigner distributions. The discrete Heisenberg-Weyl group is an essential ingredient of our approach. Possible extensions of our results to higher dimensions are discussed in the last section and in the conclusions.
When the state of a quantum system belongs to a N-dimensional Hilbert space, with N the power of a prime number, it is possible to associate to the system a finite field (Galois field) with N elements. In this paper, we introduce generalized Bell states that can be intrinsically expressed in terms of the field operations.These Bell states are in one to one correspondence with the N^2 elements of the generalised Pauli group or Heisenberg-Weyl group. This group consists of discrete displacement operators and provides a discrete realisation of the Weyl function.Thanks to the properties of generalised Bell states and of quadratic extensions of finite fields, we derive a particular solution for the Mean King's problem. This solution is in turn shown to be in one to one correspondence with a set of N^2 self-adjoint operators that provides a discrete realisation of the Wigner quasi-distribution.
The possibility of cloning a d-dimensional quantum system without an ancilla is explored, extending on the economical phase-covariant cloning machine found in [Phys. Rev. A {\bf 60}, 2764 (1999)] for qubits. We prove the impossibility of constructing an economical version of the optimal universal cloning machine in any dimension. We also show, using an ansatz on the generic form of cloning machines, that the d-dimensional phase-covariant cloner, which optimally clones all uniform superpositions, can be realized economically only in dimension d=2. The used ansatz is supported by numerical evidence up to d=7. An economical phase-covariant cloner can nevertheless be constructed for d>2, albeit with a lower fidelity than that of the optimal cloner requiring an ancilla. Finally, using again an ansatz on cloning machines, we show that an economical version of the Fourier-covariant cloner, which optimally clones the computational basis and its Fourier transform, is also possible only in dimension d=2.
Mutually unbiased bases generalize the X, Y and Z qubit bases. They possess numerous applications in quantum information science. It is well-known that in prime power dimensions N=p^m (with p prime and m a positive integer) there exists a maximal set of N+1 mutually unbiased bases. In the present paper, we derive an explicit expression for those bases, in terms of the (operations of the) associated finite field (Galois division ring) of N elements. This expression is shown to be equivalent to the expressions previously obtained by Ivanovic in odd prime dimensions (J. Phys. A, 14, 3241 (1981)), and Wootters and Fields (Ann. Phys. 191, 363 (1989)) in odd prime power dimensions. In even prime power dimensions, we derive a new explicit expression for the mutually unbiased bases. The new ingredients of our approach are, basically, the following: we provide a simple expression of the generalised Pauli group in terms of the additive characters of the field and we derive an exact groupal composition law inside the elements of the commuting subsets of the generalised Pauli group, renormalised by a well-chosen phase-factor.
When prior partial information about a state to be cloned is available, it can be cloned with a fidelity higher than that of universal quantum cloning. We experimentally verify this intriguing relationship between the cloning fidelity and the prior information by reporting the first experimental optimal quantum state-dependent cloning, using nuclear magnetic resonance techniques. Our experiments may further have important implications into many quantum information processing protocols.
Two or more quantum systems are said to be in an entangled or non-factorisable state if their joint (supposedly pure) wave-function is not expressible as a product of individual wave functions but is instead a superposition of product states. It is only when the systems are in a factorisable state that they can be considered to be separated (in the sense of Bell). We show that whenever two quantum systems interact with each other, it is impossible that all factorisable states remain factorisable during the interaction unless the full Hamiltonian does not couple these systems so to say unless they do not really interact. We also present certain conditions under which particular factorisable states remain factorisable although they represent a bipartite system whose components mutually interact. We identify certain quasi-classical regimes that satisfy these conditions and show that they correspond to classical, pre-quantum, paradigms associated to the concept of particle.
We study the relationship between Bell states, finite groups and complete sets of bases. We show how to obtain a set of N+1 bases in which Bell states are invariant. They generalize the X, Y and Z qubit bases and are associated to groups of unitary transformations that generalize the sigma operators of Pauli. When the dimension N is a prime power, we derive (in agreement with well-known results) a set of mutually unbiased bases. We show how they can be expressed in terms of the (operations of the) associated finite field of N elements.