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ABSTRACT
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A non-local hidden variable model reproducing the quantum mechanical probabilities for a spin singlet is presented. The non-locality is concentrated in the distribution of the hidden variables. The model otherwise satisfies both the... more
A non-local hidden variable model reproducing the quantum mechanical probabilities for a spin singlet is presented. The non-locality is concentrated in the distribution of the hidden variables. The model otherwise satisfies both the hypothesis of outcome independence, made in the derivation of Bell inequality, and of compliance with Malus's law, made in the derivation of Leggett inequality. It is shown through the prescription of a protocol that the non-locality can be exploited to send information instantaneously provided that the hidden variables can be measured, even though they cannot be controlled.
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Physics textbooks introduce an inequality derived by Kennard that concerns the impossibility of preparing a quantum state with well defined momentum and position. However, Heisenberg had formulated two different inequalities: one stating... more
Physics textbooks introduce an inequality derived by Kennard that concerns the impossibility of preparing a quantum state with well defined momentum and position. However, Heisenberg had formulated two different inequalities: one stating the impossibility of a simultaneous detection of position and momentum with arbitrary precision, and another one imposing a tradeoff between the precision on the measurement of a variable and the backaction on a subsequent measurement of a conjugated variable. Here, we explore the connections among these three inequalities, and we show that the latter can be violated, if the detectors are initially entangled. The results, besides being of fundamental interest, can be useful for building up an ideal momentum, or position, detector (i.e. one that introduces no noise in the measurement, besides the intrinsic statistical noise of the input state).
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Three classes of local hidden-variable models that violate both Bell and Leggett inequalities are presented. The models, however, do not reproduce the quantum mechanical predictions, hence they are experimentally testable. It is concluded... more
Three classes of local hidden-variable models that violate both Bell and Leggett inequalities are presented. The models, however, do not reproduce the quantum mechanical predictions, hence they are experimentally testable. It is concluded that on one hand neither Bell or Leggett inequality fully captures the essential counterintuitiveness of quantum mechanics, while on the other hand the hypothesis of outcome independence and that of locality are uncorrelated.
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We derive exact formulas describing an indirect von Neumann measurement of a spin-1 system. The results hold for any interaction strength and for an arbitrary output variable $\\Hat{O}$.
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Generally, the measurement process consists in coupling a system to a detector that can give a continuous output. However, it may be interesting to use as a detector a system with a discrete spectrum, especially in view of applications to... more
Generally, the measurement process consists in coupling a system to a detector that can give a continuous output. However, it may be interesting to use as a detector a system with a discrete spectrum, especially in view of applications to quantum information. Here, we study 1) a two-level system measuring another two-level system (qubit); 2) a generic system measuring a qubit; 3) a qubit measuring a generic system. The results include the case when a postselection on the measured system is made. We provide the exact solution, and also a controlled expansion in the coupling parameter, giving formulas valid in the weak measurement regime for arbitrary preparation and postselection. The concept of generalized Wigner functions is introduced.
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Thermodynamic and transport properties of small metallic systems depend on the parity of the electron number [1,2]. In normal metal grains, these even-odd effects are observed when the temperature is lowered below the average level... more
Thermodynamic and transport properties of small metallic systems depend on the parity of the electron number [1,2]. In normal metal grains, these even-odd effects are observed when the temperature is lowered below the average level spacing δ, which is inversely proportional to the volume of the grain. Superconductivity, due to the formation of Cooper pairs, enhances parity effects as it was observed by Tuominen et al. [3] in submicron Al grains with δ still few orders of magnitude smaller than all other energy scales. The temperature scale at which parity effects set in signals that in the “superconducting” samples the even-odd asymmetry stems from a cooperative effect due to pair correlations rather than being simply related to the filling of single-particle energy spectrum, as it is in normal metal grains [1]. With a series of recent experiments Ralph, Black and Tinkham (RBT) [4,5] renewed the interest of the scientific community on a question which was posed since the early days of superconductivity [6]. What are the properties of a superconductor when the size of the sample becomes smaller and smaller? In samples of finite size (of the order of the coherence length) the superconducting transition is smeared out due to fluctuations of the order parameter [7]. In even smaller samples (for δ ∼ ∆, ∆ being the BCS gap) superconductivity should disappear, as was argued by Anderson [6]. Early experiments [8] were performed on ensembles of small grains, whereas RBT succeeded to study transport
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It is demonstrated that the 3-vector $$\varvec{S}$$ S currently associated to the spin in an inertial frame does not contract, but rather dilates, in the direction of the velocity. The correct vector $$\varvec{T}$$ T is individuated. The... more
It is demonstrated that the 3-vector $$\varvec{S}$$ S currently associated to the spin in an inertial frame does not contract, but rather dilates, in the direction of the velocity. The correct vector $$\varvec{T}$$ T is individuated. The equation of motion for the two vectors is shown to contain two terms, a common linear rotation, identified with Thomas precession, and also a nonlinear rotation depending on the direction of the spin itself.
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We propose a new classification for Lorentz transformations, relying on three real parameters and two mutually orthonormal vectors. Lorentz transformations can then be mapped to the movement of a rigid body inside the space defined by the... more
We propose a new classification for Lorentz transformations, relying on three real parameters and two mutually orthonormal vectors. Lorentz transformations can then be mapped to the movement of a rigid body inside the space defined by the three parameters. We show the usefulness of the classification, in that special subclasses of transformations, which are not limited to boosts and rotations, correspond to the eigenvalues of the Lorentz transformations taking the special values ±1. Based on the metric preserving properties of the Lorentz transformations, we reduce the quartic equation for its eigenvalues to a sequence of two quadratic equations, yielding the four eigenvalues. The eigenvalue-based classification is shown to hold for any symmetric metric with the same signature as the Minkowski metric. … Figure 1: A 4-vector field V is being transported along an accelerated worldline. It is represented as V in an inertial reference frame following the worldline O and as V in another frame O . On one hand because the axes of the two frames do not coincide, but also because of the relativity of simultaneity, the time associated with the proper time t P is different. At any instant t P , the connection between the representations is provided by a Lorentz transformation L. If the reference frames are not inertial, the Lorentz transformation is a function of t P .
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We establish a theorem connecting the relativistic law for the addition of velocities and the primitive pythagorean triples.
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The works of Bell and his epigons proved that a class of hidden variable theories is incompatible with quantum mechanics. Analogously, Leggett proved the incompatibility of a distinct class of theories. The union of the two classes does... more
The works of Bell and his epigons proved that a class of hidden variable theories is incompatible with quantum mechanics. Analogously, Leggett proved the incompatibility of a distinct class of theories. The union of the two classes does not exhaust, however, the class of all possible local hidden-variable theory. The derivation of Bell inequality relies on three hypotheses called measurement-independence, parameter-independence, and outcome-independence. Violation of the first two hypotheses may lead to non-locality, under additional assumptions on the nature of the hidden variables. In this work, the form of the hidden-variable models which violate outcome-independence and reproduce the quantum mechanical predictions for a spin singlet is determined. A wide class of local hidden-variable models is given as an example.
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Heisenberg formulated a noise-disturbance principle stating that there is a tradeoff between noise and disturbance when a measurement of position and a measurement of momentum are performed sequentially, and another principle imposing a... more
Heisenberg formulated a noise-disturbance principle stating that there is a tradeoff between noise and disturbance when a measurement of position and a measurement of momentum are performed sequentially, and another principle imposing a limitation on the product of the uncertainties in a joint measurement of position and momentum. We prove that the former, the Heisenberg sequential noise-disturbance principle, holds when the detectors are assumed to be initially uncorrelated from each other, but that it can be violated for some properly correlated initial preparations of the detectors.
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ABSTRACT
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It is shown that a classical experiment using an ordinary cat can reproduce the same results and it is argued that the quantum nature of the phenomenon could be revealed instead by making an experiment that detects cross-moments.
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In a seminal work, Aharonov, Albert, and Vaidman showed that by having a weak interaction between a system and a detecting apparatus, the average output of the latter could be much larger than the maximum eigenvalue of the observed... more
In a seminal work, Aharonov, Albert, and Vaidman showed that by having a weak interaction between a system and a detecting apparatus, the average output of the latter could be much larger than the maximum eigenvalue of the observed quantity (times the amplification factor). This does not always happen, however: the observed system must subsequently undergo a second measurement, on the output of which the result of the first one is conditioned. This procedure is known as postselection. On the other hand, linear response theory describes how the observables of a quan- tum system change upon perturbation by a weak classical external force. In a measurement, the measured system applies a generalized force to the measuring apparatus, leading to an observable change in the latter. It appears natural, then, to unify the treatment of weak measurements with an extended version of linear response theory that accounts for a force introduced by an external quantum system. Here, we show how the ...
We propose a new classification for Lorentz transformations, relying on three real parameters and two mutually orthonormal vectors. Lorentz transformations can then be mapped to the movement of a rigid body inside the space defined by the... more
We propose a new classification for Lorentz transformations, relying on three real parameters and two mutually orthonormal vectors. Lorentz transformations can then be mapped to the movement of a rigid body inside the space defined by the three parameters. We show the usefulness of the classification, in that special subclasses of transformations, which are not limited to boosts and rotations, correspond to the eigenvalues of the Lorentz transformations taking the special values ±1. Based on the metric preserving properties of the Lorentz transformations, we reduce the quartic equation for its eigenvalues to a sequence of two quadratic equations, yielding the four eigenvalues. The eigenvalue-based classification is shown to hold for any symmetric metric with the same signature as the Minkowski metric.
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Figure 1: A 4-vector field V is being transported along an accelerated worldline. It is represented as V in an inertial reference frame following the worldline O and as V in another frame O . On one hand because the axes of the two frames do not coincide, but also because of the relativity of simultaneity, the time associated with the proper time t P is different. At any instant t P , the connection between the representations is provided by a Lorentz transformation L. If the reference frames are not inertial, the Lorentz transformation is a function of t P .
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Figure 1: A 4-vector field V is being transported along an accelerated worldline. It is represented as V in an inertial reference frame following the worldline O and as V in another frame O . On one hand because the axes of the two frames do not coincide, but also because of the relativity of simultaneity, the time associated with the proper time t P is different. At any instant t P , the connection between the representations is provided by a Lorentz transformation L. If the reference frames are not inertial, the Lorentz transformation is a function of t P .
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Thomas precession is an important phenomenon in that it accounts for the correct factor in the spin-orbit interaction in atoms. Its history is fraught with misunderstandings, however. Some authors interpret it as a rotation that appears... more
Thomas precession is an important phenomenon in that it accounts for the correct factor in the spin-orbit interaction in atoms. Its history is fraught with misunderstandings, however. Some authors interpret it as a rotation that appears in an accelerated reference frame, others, more correctly, as a rotation of a vector Fermi-transported along an accelerated worldline that appears in an inertial reference frame. Even in the latter, correct interpretation, however, the accepted formula contains an error, that we correct. The correction is small for nonrelativistic velocities, but in principle it could be checked experimentally.An invariant, coordinate--free approach is used to obtain the correct formulas, which is then at the end represented in vector form in an inertial frame.
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We establish a theorem connecting the relativistic law for the addition of velocities and the primitive pythagorean triples.