268 research outputs found
Generalized Quantum Theory: Overview and Latest Developments
The main formal structures of Generalized Quantum Theory are summarized.
Recent progress has sharpened some of the concepts, in particular the notion of
an observable, the action of an observable on states (putting more emphasis on
the role of proposition observables), and the concept of generalized
entanglement. Furthermore, the active role of the observer in the structure of
observables and the partitioning of systems is emphasized.Comment: 14 pages, update in reference
Quantum correlations from local amplitudes and the resolution of the Einstein-Podolsky-Rosen nonlocality puzzle
The Einstein-Podolsky-Rosen nonlocality puzzle has been recognized as one of
the most important unresolved issues in the foundational aspects of quantum
mechanics. We show that the problem is resolved if the quantum correlations are
calculated directly from local quantities which preserve the phase information
in the quantum system. We assume strict locality for the probability amplitudes
instead of local realism for the outcomes, and calculate an amplitude
correlation function.Then the experimentally observed correlation of outcomes
is calculated from the square of the amplitude correlation function. Locality
of amplitudes implies that the measurement on one particle does not collapse
the companion particle to a definite state. Apart from resolving the EPR
puzzle, this approach shows that the physical interpretation of apparently
`nonlocal' effects like quantum teleportation and entanglement swapping are
different from what is usually assumed. Bell type measurements do not change
distant states. Yet the correlations are correctly reproduced, when measured,
if complex probability amplitudes are treated as the basic local quantities. As
examples we discuss the quantum correlations of two-particle maximally
entangled states and the three-particle GHZ entangled state.Comment: Std. Latex, 11 pages, 1 table. Prepared for presentation at the
International Conference on Quantum Optics, ICQO'2000, Minsk, Belaru
Does Quantum Mechanics Clash with the Equivalence Principle - and Does it Matter?
With an eye on developing a quantum theory of gravity, many physicists have
recently searched for quantum challenges to the equivalence principle of
general relativity. However, as historians and philosophers of science are well
aware, the principle of equivalence is not so clear. When clarified, we think
quantum tests of the equivalence principle won't yield much. The problem is
that the clash/not-clash is either already evident or guaranteed not to exist.
Nonetheless, this work does help teach us what it means for a theory to be
geometric.Comment: 12 page
An experimental test of non-local realism
Most working scientists hold fast to the concept of 'realism' - a viewpoint
according to which an external reality exists independent of observation. But
quantum physics has shattered some of our cornerstone beliefs. According to
Bell's theorem, any theory that is based on the joint assumption of realism and
locality (meaning that local events cannot be affected by actions in space-like
separated regions) is at variance with certain quantum predictions. Experiments
with entangled pairs of particles have amply confirmed these quantum
predictions, thus rendering local realistic theories untenable. Maintaining
realism as a fundamental concept would therefore necessitate the introduction
of 'spooky' actions that defy locality. Here we show by both theory and
experiment that a broad and rather reasonable class of such non-local realistic
theories is incompatible with experimentally observable quantum correlations.
In the experiment, we measure previously untested correlations between two
entangled photons, and show that these correlations violate an inequality
proposed by Leggett for non-local realistic theories. Our result suggests that
giving up the concept of locality is not sufficient to be consistent with
quantum experiments, unless certain intuitive features of realism are
abandoned.Comment: Minor corrections to the manuscript, the final inequality and all its
conclusions do not change; description of corrections (Corrigendum) added as
new Appendix III; Appendix II replaced by a shorter derivatio
Dissipative systems: uncontrollability, observability and RLC realizability
The theory of dissipativity has been primarily developed for controllable
systems/behaviors. For various reasons, in the context of uncontrollable
systems/behaviors, a more appropriate definition of dissipativity is in terms
of the dissipation inequality, namely the {\em existence} of a storage
function. A storage function is a function such that along every system
trajectory, the rate of increase of the storage function is at most the power
supplied. While the power supplied is always expressed in terms of only the
external variables, whether or not the storage function should be allowed to
depend on unobservable/hidden variables also has various consequences on the
notion of dissipativity: this paper thoroughly investigates the key aspects of
both cases, and also proposes another intuitive definition of dissipativity.
We first assume that the storage function can be expressed in terms of the
external variables and their derivatives only and prove our first main result
that, assuming the uncontrollable poles are unmixed, i.e. no pair of
uncontrollable poles add to zero, and assuming a strictness of dissipativity at
the infinity frequency, the dissipativities of a system and its controllable
part are equivalent. We also show that the storage function in this case is a
static state function.
We then investigate the utility of unobservable/hidden variables in the
definition of storage function: we prove that lossless autonomous behaviors
require storage function to be unobservable from external variables. We next
propose another intuitive definition: a behavior is called dissipative if it
can be embedded in a controllable dissipative {\em super-behavior}. We show
that this definition imposes a constraint on the number of inputs and thus
explains unintuitive examples from the literature in the context of
lossless/orthogonal behaviors.Comment: 26 pages, one figure. Partial results appeared in an IFAC conference
(World Congress, Milan, Italy, 2011
Experimental delayed-choice entanglement swapping
Motivated by the question, which kind of physical interactions and processes
are needed for the production of quantum entanglement, Peres has put forward
the radical idea of delayed-choice entanglement swapping. There, entanglement
can be "produced a posteriori, after the entangled particles have been measured
and may no longer exist". In this work we report the first realization of
Peres' gedanken experiment. Using four photons, we can actively delay the
choice of measurement-implemented via a high-speed tunable bipartite state
analyzer and a quantum random number generator-on two of the photons into the
time-like future of the registration of the other two photons. This effectively
projects the two already registered photons onto one definite of two mutually
exclusive quantum states in which either the photons are entangled (quantum
correlations) or separable (classical correlations). This can also be viewed as
"quantum steering into the past"
Decision Making for Inconsistent Expert Judgments Using Negative Probabilities
In this paper we provide a simple random-variable example of inconsistent
information, and analyze it using three different approaches: Bayesian,
quantum-like, and negative probabilities. We then show that, at least for this
particular example, both the Bayesian and the quantum-like approaches have less
normative power than the negative probabilities one.Comment: 14 pages, revised version to appear in the Proceedings of the QI2013
(Quantum Interactions) conferenc
Can a falling tree make a noise in two forests at the same time?
It is a commonplace to claim that quantum mechanics supports the old idea
that a tree falling in a forest makes no sound unless there is a listener
present. In fact, this conclusion is far from obvious. Furthermore, if a
tunnelling particle is observed in the barrier region, it collapses to a state
in which it is no longer tunnelling. Does this imply that while tunnelling, the
particle can not have any physical effects? I argue that this is not the case,
and moreover, speculate that it may be possible for a particle to have effects
on two spacelike separate apparatuses simultaneously. I discuss the measurable
consequences of such a feat, and speculate about possible statistical tests
which could distinguish this view of quantum mechanics from a ``corpuscular''
one. Brief remarks are made about an experiment underway at Toronto to
investigate these issues.Comment: 9 pp, Latex, 3 figs, to appear in Proc. Obsc. Unr. Conf.; Fig 2
postscript repaired on 26.10.9
Direct generation of photon triplets using cascaded photon-pair sources
Non-classical states of light, such as entangled photon pairs and number
states, are essential for fundamental tests of quantum mechanics and optical
quantum technologies. The most widespread technique for creating these quantum
resources is the spontaneous parametric down-conversion (SPDC) of laser light
into photon pairs. Conservation of energy and momentum in this process, known
as phase-matching, gives rise to strong correlations which are used to produce
two-photon entanglement in various degrees of freedom. It has been a
longstanding goal of the quantum optics community to realise a source that can
produce analogous correlations in photon triplets, but of the many approaches
considered, none have been technically feasible. In this paper we report the
observation of photon triplets generated by cascaded down-conversion. Here each
triplet originates from a single pump photon, and therefore quantum
correlations will extend over all three photons in a way not achievable with
independently created photon pairs. We expect our photon-triplet source to open
up new avenues of quantum optics and become an important tool in quantum
technologies. Our source will allow experimental interrogation of novel quantum
correlations, the post-selection free generation of tripartite entanglement
without post- selection and the generation of heralded entangled-photon pairs
suitable for linear optical quantum computing. Two of the triplet photons have
a wavelength matched for optimal transmission in optical fibres, ideally suited
for three-party quantum communication. Furthermore, our results open
interesting regimes of non-linear optics, as we observe spontaneous
down-conversion pumped by single photons, an interaction also highly relevant
to optical quantum computing.Comment: 7 pages, 3 figures, 1 table; accepted by Natur
Preparation and Measurement of Three-Qubit Entanglement in a Superconducting Circuit
Traditionally, quantum entanglement has played a central role in foundational
discussions of quantum mechanics. The measurement of correlations between
entangled particles can exhibit results at odds with classical behavior. These
discrepancies increase exponentially with the number of entangled particles.
When entanglement is extended from just two quantum bits (qubits) to three, the
incompatibilities between classical and quantum correlation properties can
change from a violation of inequalities involving statistical averages to sign
differences in deterministic observations. With the ample confirmation of
quantum mechanical predictions by experiments, entanglement has evolved from a
philosophical conundrum to a key resource for quantum-based technologies, like
quantum cryptography and computation. In particular, maximal entanglement of
more than two qubits is crucial to the implementation of quantum error
correction protocols. While entanglement of up to 3, 5, and 8 qubits has been
demonstrated among spins, photons, and ions, respectively, entanglement in
engineered solid-state systems has been limited to two qubits. Here, we
demonstrate three-qubit entanglement in a superconducting circuit, creating
Greenberger-Horne-Zeilinger (GHZ) states with fidelity of 88%, measured with
quantum state tomography. Several entanglement witnesses show violation of
bi-separable bounds by 830\pm80%. Our entangling sequence realizes the first
step of basic quantum error correction, namely the encoding of a logical qubit
into a manifold of GHZ-like states using a repetition code. The integration of
encoding, decoding and error-correcting steps in a feedback loop will be the
next milestone for quantum computing with integrated circuits.Comment: 7 pages, 4 figures, and Supplementary Information (4 figures)
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