1,234 research outputs found
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
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 which obeys the uncertainty relation where 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
which obeys the uncertainty relation
where 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
Weak Measurement of the Arrival Times of Single Photons and Pairs of Entangled Photons
In this paper we propose a setup for the weak measurement of photon arrival
time. It is found that the weak values of this arrival time can lie far away
from the expectation value, and in principle also in regions forbidden by
special relativity. We discuss in brief the implications of these results as
well as their reconciliation with the principle of causality. Furthermore, an
analysis of the weak arrival times of a pair of photons in a Bell state shows
that these weak arrival times are correlated.Comment: 4 pages, 1 figur
Shutters, Boxes, But No Paradoxes: Time Symmetry Puzzles in Quantum Theory
The ``N-Box Experiment'' is a much-discussed thought experiment in quantum
mechanics. It is claimed by some authors that a single particle prepared in a
superposition of N+1 box locations and which is subject to a final
``post-selection'' measurement corresponding to a different superposition can
be said to have occupied ``with certainty'' N boxes during the intervening
time. However, others have argued that under closer inspection, this surprising
claim fails to hold. Aharonov and Vaidman have continued their advocacy of the
claim in question by proposing a variation on the N-box experiment, in which
the boxes are replaced by shutters and the pre- and post-selected particle is
entangled with a photon. These authors argue that the resulting ``N-shutter
experiment'' strengthens their original claim regarding the N-box experiment.
It is argued in this paper that the apparently surprising features of this
variation are no more robust than those of the N-box experiment and that it is
not accurate to say that the particle is ``with certainty'' in all N shutters
at any given time.Comment: Presentation improved; to appear in International Studies in
Philosophy of Scienc
Toward fault-tolerant quantum computation without concatenation
It has been known that quantum error correction via concatenated codes can be
done with exponentially small failure rate if the error rate for physical
qubits is below a certain accuracy threshold. Other, unconcatenated codes with
their own attractive features-improved accuracy threshold, local
operations-have also been studied. By iteratively distilling a certain
two-qubit entangled state it is shown how to perform an encoded Toffoli gate,
important for universal computation, on CSS codes that are either
unconcatenated or, for a range of very large block sizes, singly concatenated.Comment: 12 pages, 2 figures, replaced: new stuff on error models, numerical
example for concatenation criteri
Correspondences and Quantum Description of Aharonov-Bohm and Aharonov-Casher Effects
We establish systematic consolidation of the Aharonov-Bohm and
Aharonov-Casher effects including their scalar counterparts. Their formal
correspondences in acquiring topological phases are revealed on the basis of
the gauge symmetry in non-simply connected spaces and the adiabatic condition
for the state of magnetic dipoles. In addition, investigation of basic two-body
interactions between an electric charge and a magnetic dipole clarifies their
appropriate relative motions and discloses physical interrelations between the
effects. Based on the two-body interaction, we also construct an exact
microscopic description of the Aharonov-Bohm effect, where all the elements are
treated on equal footing, i.e., magnetic dipoles are described
quantum-mechanically and electromagnetic fields are quantized. This microscopic
analysis not only confirms the conventional (semiclassical) results and the
topological nature but also allows one to explore the fluctuation effects due
to the precession of the magnetic dipoles with the adiabatic condition relaxed
Weak measurement of arrival time
The arrival time probability distribution is defined by analogy with the
classical mechanics. The difficulty of requirement to have the values of
non-commuting operators is circumvented using the concept of weak measurements.
The proposed procedure is suitable to the free particles and to the particles
subjected to an external potential, as well. It is shown that such an approach
imposes an inherent limitation to the accuracy of the arrival time
determination.Comment: 3 figure
Backward Evolving Quantum States
The basic concept of the two-state vector formalism, which is the time
symmetric approach to quantum mechanics, is the backward evolving quantum
state. However, due to the time asymmetry of the memory's arrow of time, the
possible ways to manipulate a backward evolving quantum state differ from those
for a standard, forward evolving quantum state. The similarities and the
differences between forward and backward evolving quantum states regarding the
no-cloning theorem, nonlocal measurements, and teleportation are discussed. The
results are relevant not only in the framework of the two-state vector
formalism, but also in the framework of retrodictive quantum theory.Comment: Contribution to the J.Phys. A special issue in honor of GianCarlo
Ghirard
The Hartman effect and weak measurements "which are not really weak"
We show that in wavepacket tunnelling localisation of the transmitted
particle amounts to a quantum measurement of the delay it experiences in the
barrier. With no external degree of freedom involved, the envelope of the
wavepacket plays the role of the initial pointer state. Under tunnelling
conditions such 'self measurement' is necessarily weak, and the Hartman effect
just reflects the general tendency of weak values to diverge, as post-selection
in the final state becomes improbable. We also demonstrate that it is a good
precision, or 'not really weak' quantum measurement: no matter how wide the
barrier d, it is possible to transmit a wavepacket with a width {\sigma} small
compared to the observed advancement. As is the case with all weak
measurements, the probability of transmission rapidly decreases with the ratio
{\sigma}/d.Comment: 6 pages, 1 figur
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