1,898 research outputs found

### Measurements, errors, and negative kinetic energy

An analysis of errors in measurement yields new insight into the penetration
of quantum particles into classically forbidden regions. In addition to
``physical" values, realistic measurements yield ``unphysical" values which, we
show, can form a consistent pattern. An experiment to isolate a particle in a
classically forbidden region obtains negative values for its kinetic energy.
These values realize the concept of a {\it weak value}, discussed in previous
works.Comment: 22 pp, TAUP 1850-9

### On a Time Symmetric Formulation of Quantum Mechanics

We explore further the suggestion to describe a pre- and post-selected system
by a two-state, which is determined by two conditions. Starting with a formal
definition of a two-state Hilbert space and basic operations, we systematically
recast the basics of quantum mechanics - dynamics, observables, and measurement
theory - in terms of two-states as the elementary quantities. We find a simple
and suggestive formulation, that ``unifies'' two complementary observables:
probabilistic observables and non-probabilistic `weak' observables.
Probabilities are relevant for measurements in the `strong coupling regime'.
They are given by the absolute square of a two-amplitude (a projection of a
two-state). Non-probabilistic observables are observed in sufficiently `weak'
measurements, and are given by linear combinations of the two-amplitude. As a
sub-class they include the `weak values' of hermitian operators. We show that
in the intermediate regime, one may observe a mixing of probabilities and weak
values. A consequence of the suggested formalism and measurement theory, is
that the problem of non-locality and Lorentz non-covariance, of the usual
prescription with a `reduction', may be eliminated. We exemplify this point for
the EPR experiment and for a system under successive observations.Comment: LaTex, 44 pages, 4 figures included. Figure captions and related text
in sections 3.1, 4.2 are revised. A paragraph in pages 9-10 about non-generic
two-states is clarified. Footnotes adde

### Teleportation of Quantum States

Bennett et al. (PRL 70, 1859 (1993)) have shown how to transfer ("teleport")
an unknown spin quantum state by using prearranged correlated quantum systems
and transmission of classical information. I will show how their results can be
obtained in the framework of nonlocal measurements proposed by Aharonov and
Albert I will generalize the latter to the teleportation of a quantum state of
a system with continuous variables.Comment: 5 page

### The Effect of a Magnetic Flux Line in Quantum Theory

The nonloclal exchange of the conserved, gauge invariant quantity
$e^{\frac{i}{\hbar} (p_{k}-\frac{e}{c}A_{k})L^{k}}, L^{k}=const., k=1,2$
between the charged particle and the magnetic flux line (in the $k=3$
direction), is responsible for the Aharonov-Bohm effect. This exchange occurs
at a definite time, before the wavepackets are brought together to interfere,
and can be verified experimentally.Comment: LaTeX, 13 pages with 3 figure

### Paradoxes of the Aharonov-Bohm and the Aharonov-Casher effects

For a believer in locality of Nature, the Aharonov-Bohm effect and the
Aharonov-Casher effect are paradoxes. I discuss these and other Aharonov's
paradoxes and propose a local explanation of these effects. If the solenoid in
the Aharonov-Bohm effect is treated quantum mechanically, the effect can be
explained via local interaction between the field of the electron and the
solenoid. I argue that the core of the Aharonov-Bohm and the Aharonov-Casher
effects is that of quantum entanglement: the quantum wave function describes
all systems together.Comment: To be published in Yakir Aharonov 80th birthday Festschrif

### Comment on ``Protective measurements of the wave function of a single squeezed harmonic-oscillator state''

Alter and Yamamoto [Phys. Rev. A 53, R2911 (1996)] claimed to consider
``protective measurements'' [Phys. Lett. A 178, 38 (1993)] which we have
recently introduced. We show that the measurements discussed by Alter and
Yamamoto ``are not'' the protective measurements we proposed. Therefore, their
results are irrelevant to the nature of protective measurements.Comment: 2 pages LaTe

### IS THERE A CLASSICAL ANALOG OF A QUANTUM TIME-TRANSLATION MACHINE?

In a recent article [D. Suter, Phys. Rev. {\bf A 51}, 45 (1995)] Suter has
claimed to present an optical implementation of the quantum time-translation
machine which ``shows all the features that the general concept predicts and
also allows, besides the quantum mechanical, a classical description.'' It is
argued that the experiment proposed and performed by Suter does not have the
features of the quantum time-translation machine and that the latter has no
classical analog.Comment: 7 pages, LaTe

### Measuring Energy, Estimating Hamiltonians, and the Time-Energy Uncertainty Relation

Suppose that the Hamiltonian acting on a quantum system is unknown and one
wants to determine what is the Hamiltonian. We show that in general this
requires a time $\Delta t$ which obeys the uncertainty relation $\Delta t
\Delta H \gtrsim 1$ where $\Delta H$ is a measure of how accurately the unknown
Hamiltonian must be estimated. We then apply this result to the problem of
measuring the energy of an unknown quantum state. It has been previously shown
that if the Hamiltonian is known, then the energy can in principle be measured
in an arbitrarily short time. On the other hand we show that if the Hamiltonian
is not known then an energy measurement necessarily takes a minimum time
$\Delta t$ which obeys the uncertainty relation $\Delta t \Delta E \gtrsim 1$
where $\Delta E$ is the precision of the energy measurement. Several examples
are studied to address the question of whether it is possible to saturate these
uncertainty relations. Their interpretation is discussed in detail.Comment: 12pages, revised version with small correction

### Variance Control in Weak Value Measurement Pointers

The variance of an arbitrary pointer observable is considered for the general
case that a complex weak value is measured using a complex valued pointer
state. For the typical cases where the pointer observable is either its
position or momentum, the associated expressions for the pointer's variance
after the measurement contain a term proportional to the product of the weak
value's imaginary part with the rate of change of the third central moment of
position relative to the initial pointer state just prior to the time of the
measurement interaction when position is the observable - or with the initial
pointer state's third central moment of momentum when momentum is the
observable. These terms provide a means for controlling pointer position and
momentum variance and identify control conditions which - when satisfied - can
yield variances that are smaller after the measurement than they were before
the measurement. Measurement sensitivities which are useful for estimating weak
value measurement accuracies are also briefly discussed.Comment: submitted to Phys Rev

### How to protect the interpretation of the wave function against protective measurements

A new type of procedures, called protective measurements, has been proposed
by Aharonov, Anandan and Vaidman. These authors argue that a protective
measurement allows the determination of arbitrary observables of a single
quantum system and claim that this favors a realistic interpretation of the
quantum state. This paper proves that only observables that commute with the
system's Hamiltonian can be measured protectively. It is argued that this
restriction saves the coherence of alternative interpretations.Comment: 13 pages, 1 figur

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