共查询到20条相似文献,搜索用时 250 毫秒
1.
Jan Hamhalter 《International Journal of Theoretical Physics》1995,34(8):1431-1437
We summarize and deepen some recent results concerning the extension problem for states on operator algebras and general quantum logics. In particular, we establish equivalence between the Gleason extension property, the Hahn-Banach extension property, and the universal state extension property of projection logics. Extensions of Jauch-Piron states are investigated. 相似文献
2.
Wulf Rehder 《International Journal of Theoretical Physics》1980,19(7):523-536
On the basis of the Jauch-Piron quantum probability calculus a zero-one law for sequential terminal events is proven, and the significance of certain crucial axioms in the quantum probability calculus is discussed. The result shows that the Jauch-Piron set of axioms is appropriate for the non-Boolean algebra of sequential events. 相似文献
3.
Peter G. Ovchinnikov 《International Journal of Theoretical Physics》1993,32(6):885-890
It is shown that there exist non-Boolean unital and countable quantum logics which are Jauch-Piron. 相似文献
4.
Gottfried T. Rüttimann 《International Journal of Theoretical Physics》1994,33(1):149-156
The notion of a superposition of a set of states and that of a Jauch-Piron state are geometrically interpreted in the context of the facial structure of the state space of a finite quantum logic. 相似文献
5.
Vladimír Rogalewicz 《International Journal of Theoretical Physics》1991,30(4):437-445
We show that there are no non-Boolean block-finite orthomodular posets possessing a unital set of Jauch-Piron states. Thus, an orthomodular poset representing a quantum physical system must have infinitely many blocks. 相似文献
6.
Jan Hamhalter 《International Journal of Theoretical Physics》1993,32(10):1889-1892
We summarize recent results concerning states on projection lattices of von Neumann algebras. In particular, we present an analysis of the Jauch-Piron property in the von Neumann algebra setting. 相似文献
7.
V. Müller 《International Journal of Theoretical Physics》1993,32(3):433-442
We exhibit an example of a concrete (=set-representable) quantum logic which is not a Boolean algebra such that every state on it is Jauch-Piron. This gives a negative answer to a problem raised by Navara and Pták. Further we show that such an example does not exist in the class of complete (i.e., closed under arbitrary disjoint unions) concrete logics. 相似文献
8.
9.
K. Nagata 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2010,56(3):441-444
The theoretical resource state for the implementation of the Deutsch-Jozsa algorithm is a multiqubit pure uncorrelated state.
We show that N-qubit pure uncorrelated quantum states cannot admit rotationally invariant nonlocal realistic theories with
a violation factor of 3N. We find
the violation factor 3Nwhen the measurement setup is entire range of settings for each of the observers, that is, considering rotationally invariant
nonlocal realistic theories along with the property of a correlation function in the quantum theory. The implementation of
the Deutsch-Jozsa algorithm theoretically relying on N-qubit pure uncorrelated states rules out rotationally invariant nonlocal
realism with a violation factor of 3Nin an ideal case. Our analysis relies on the property of theoretical resource states for the algorithm. We cannot simulate
the Deutsch-Jozsa algorithm by using rotationally invariant nonlocal realistic theories due to the property of theoretical
resource states for the algorithm. 相似文献
10.
Alberto Rimini 《Foundations of Physics》1997,27(12):1689-1699
The property of fundamental mechanical theories which allows one to treat compound objects as particles under suitable conditions
is considered. It is argued that such a property, called composition invariance, is a nonreleasable property of any fundamental
mechanical theory. The proof that standard quantum mechanics enjoys composition invariance is reviewed. Finally, it is shown
that the requirement of composition invariance allows one to choose between two alternative forms of quantum mechanics with
spontaneous localization. 相似文献
11.
Quantum theory has the property of “local tomography”: the state of any composite system can be reconstructed from the statistics
of measurements on the individual components. In this respect the holism of quantum theory is limited. We consider in this
paper a class of theories more holistic than quantum theory in that they are constrained only by “bilocal tomography”: the
state of any composite system is determined by the statistics of measurements on pairs of components. Under a few auxiliary assumptions, we derive certain general features of such theories. In particular, we
show how the number of state parameters can depend on the number of perfectly distinguishable states. We also show that real-vector-space
quantum theory, while not locally tomographic, is bilocally tomographic. 相似文献
12.
13.
Helmut Rauch 《Foundations of Physics》2012,42(6):760-777
Neutron matter-wave optics provides the basis for new quantum experiments and a step towards applications of quantum phenomena.
Most experiments have been performed with a perfect crystal neutron interferometer where widely separated coherent beams can
be manipulated individually. Various geometric phases have been measured and their robustness against fluctuation effects
has been proven, which may become a useful property for advanced quantum communication. Quantum contextuality for single particle
systems shows that quantum correlations are to some extent more demanding than classical ones. In this case entanglement between
external and internal degrees of freedom offers new insights into basic laws of quantum physics. Non-contextuality hidden
variable theories can be rejected by arguments based on the Kochen-Specker theorem. 相似文献
14.
Generalized nuclearity conditions that are applicable in arbitrary superselection sectors of a quantum field theory and to theories with a maximal temperature are discussed. They are shown to imply the (distal) split property and to impose specific restrictions on the spectral properties of modular operators associated with local algebras and vectors of compact energy support. 相似文献
15.
We study the group of dressing transformations in soliton theories. We show that it is generated by the monodromy matrix. This provides a new proof of their Lie-Poisson property. We treat in detail the examples of the Toda field theories and the Heisenberg model. We show that the group of dressing transformations is the classical precursor of the various manifestations of quantum groups in these models, e.g. algebraic Bethe ansatz, non-local currents, or quantum group symmetries. Finally, we define field multiplets supporting a linear representation of the dressing group and we show that their exchange algebras are encoded in the classical double.Communicated by K. Gawedzki 相似文献
16.
F. Strocchi 《Communications in Mathematical Physics》1977,56(1):57-78
Spontaneous symmetry breakings in indefinite metric quantum field theories are analyzed and a generalization of the Goldstone theorem is proved. The case of local gauge quantum field theories is discussed in detail and a characterization is given of the occurrence of the Higgs mechanism versus the Goldstone mechanism. The Higgs phenomenon is explained on general grounds without the introduction of the so-called Higgs fields. The basic property is the relation between the local internal symmetry group and the local group of gauge transformations of the second kind. Spontaneous symmetry breaking ofc-number gauge transformations of the second kind is shown to always occur if there are charged local fields. The implications about the absence of mass gap in the Wightman functions and the occurrence of massless particles associated with the unbroken generators in the Higgs phenomenon are discussed. 相似文献
17.
The Lieb-Robinson bound states that local Hamiltonian evolution in nonrelativistic quantum mechanical theories gives rise to the notion of an effective light cone with exponentially decaying tails. We discuss several consequences of this result in the context of quantum information theory. First, we show that the information that leaks out to spacelike separated regions is negligible and that there is a finite speed at which correlations and entanglement can be distributed. Second, we discuss how these ideas can be used to prove lower bounds on the time it takes to convert states without topological quantum order to states with that property. Finally, we show that the rate at which entropy can be created in a block of spins scales like the boundary of that block. 相似文献
18.
Detlev Buchholz Claudio D'Antoni Roberto Longo 《Communications in Mathematical Physics》1990,129(1):115-138
A correspondence between spectral properties of modular operators appearing in quantum field theory and the Hamiltonian is established. It allows to prove the distal split property for a wide class of models. Conversely, any model having this property is shown to satisfy the Haag-Swieca compactness criterion. The results lead to a new type of nuclearity condition which can be applied to quantum field theories on arbitrary space-time manifolds.Supported by the A. von Humboldt Stiftung, BonnSupported in part by Ministero della Pubblica Instruzione and CNR-GNAFA 相似文献
19.
F. Jenč 《Reports on Mathematical Physics》1974,6(2):253-264
The “weak-maximality” condition is proved to be equivalent to atomicity of the lattice of “propositions” (“decision effects”) in quantum axiomatics, satisfying certain simple conditions. In particular, it is shown that these conditions are fulfilled in Ludwig's axiomatic formulation of quantum mechanics. It is further proved that atomicity of the lattice of propositions follows from the condition of “strong maximality”. The maximality conditions have a clear physical interpretation. They are also fulfilled in the Hilbert space formulation of quantum mechanics. Since the atomicity property is used in theories based on Type I factors, the connection between atomicity and maximality seems of general interest. Useful theorems are proved. 相似文献
20.
Gianpiero Cattaneo Carlo Dalla Pozza Claudio Garola Giuseppe Nisticò 《International Journal of Theoretical Physics》1988,27(11):1313-1349
We make a critical analysis of the basic concepts of the Jauch-Piron (JP) approach to quantum physics. Then, we exhibit a formalized presentation of the mathematical structure of the JP theory by introducing it as a completely formalized syntactic system, i.e., we construct a formalized languageL
e
and formally state the logical-deductive structure of the JP theory by means ofL
e
. Finally, we show that the JP syntactic system can be endowed with an intended interpretation, which yields a physical model of the system. A mathematical model endowed with a physical interpretation is given which establishes (in the usual sense of the model theory) the coherence of the JP syntactic system. 相似文献