4,078 research outputs found
Protective Measurements
Protective measurements yield properties of the quantum state of a single
quantum system without affecting the quantum state. A protective measurement
involves adiabatic coupling to the measuring device together with a procedure
to protect the state from changing. For nondegenerate energy eigenstates the
protection is provided by the system itself. In this case it is actually
possible to measure the Schr\"odinger wave via measurements on a single system.
This fact provides an argument in favor of associating physical reality with a
quantum state of a single system, challenging the usual ensemble
interpretation. We also believe that the complete description of a quantum
system requires a two-state vector formalism involving (in addition to the
usual one)a future quantum state evolving backwards in time. Protective
measurements testing the two-state vector reality are constructed.Comment: 21 pages, 1 figur
Negative Kinetic Energy Between Past and Future State Vectors
An analysis of errors in measurement yields new insight into classically
forbidden quantum processes. In addition to "physical" values, a realistic
measurement can yield "unphysical" values; we show that in {\it sequences} of
measurements, the "unphysical" values can form a consistent pattern. An
experiment to isolate a particle in a classically forbidden region obtains a
negative value for its kinetic energy. It is the {\it weak value} of kinetic
energy between past and future state vectors.Comment: Talk presented at the Conference on Fundamental Problems in Quantum
Theory, Baltimore, MD, June 1994, 10 pp, plain Te
Measurement of the Schrodinger wave of a single particle
We show that it is possible to measure Schrodinger wave of a single quantum
system. This provides a strong argument for associating physical reality with
the quantum state of a single system, and challenges the usual assumption that
the quantum state has physical meaning only for an ensemble of identical
systems.Comment: 12, TAUP 2019-93
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
Varieties of Quantum Measurement
Quantum measurement theory has fallen under the resticting influence of the
attempt to explain the fundamental axioms of quantum theory in terms of the
theory itself. This has not only led to confusion but has also restricted our
attention to a limited class of measurements. This paper outlines some of the
novel types of measurements which fall outside the usual textbook description.Comment: 14p
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
Weak cloning of an unknown quantum state
The impossibility to clone an unknown quantum state is a powerful principle
to understand the nature of quantum mechanics, especially within the context of
quantum computing and quantum information. This principle has been generalized
to quantitative statements as to what extent imperfect cloning is possible. We
delineate an aspect of the border between the possible and the impossible
concerning quantum cloning, by putting forward an entanglement-assisted scheme
for simulating perfect cloning in the context of weak measurements. This
phenomenon we call weak cloning of an unknown quantum state.Comment: Minor corrections, journal reference 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
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
Revisiting Hardy's Paradox: Counterfactual Statements, Real Measurements, Entanglement and Weak Values
Classical-realistic analysis of entangled systems have lead to retrodiction
paradoxes, which ordinarily have been dismissed on the grounds of
counter-factuality. Instead, we claim that such paradoxes point to a deeper
logical structure inherent to quantum mechanics, which is naturally described
in the language of weak values, and which is accessible experimentally via weak
measurements. Using as an illustration, a gedanken-experiment due to
Hardy\cite{hardy}, we show that there is in fact an exact numerical coincidence
between a) a pair of classically contradictory assertions about the locations
of an electron and a positron, and b) the results of weak measurements of their
location. The internal consistency of these results is due to the novel way by
which quantum mechanics "resolves" the paradox: first, by allowing for two
distinguishable manifestations of how the electron and positron can be at the
same location: either as single particles or as a pair; and secondly, by
allowing these properties to take either sign. In particular, we discuss the
experimental meaning of a {\em negative} number of electron-positron pairs.Comment: 7 pages, 1 figur
- …