Using the result of Navascues, Pironio and Acin [New J. Phys. 10, 073013
(2008)], we show that any causality respecting reversible theory, which is
consistent with the non-demolition principle, has no predictions different from
those of quantum theory. The non-demolition principle, which was quantified by
Leggett and Garg [PRL 54, 857 (1985)], states that physical properties can be
observed without irreversible disturbance. Quantum theory has a limit of weak
measurements analyzed By Aharonov et. al, where sequential weak values
[Mitchison, Jozsa and Popescu, PRA 76, 062105 (2007)] manifest all the
conditions of the non-demolition principle. A theory which obeys the
nondemolition principle automatically admits a local-hidden-variable
description in the macroscopic limit.
We present rigorous performance bounds for the optimal dynamical decoupling
pulse sequence protecting a quantum bit (qubit) against pure dephasing. Our
bounds apply under the assumption of instantaneous pulses and of bounded
perturbing environment and qubit-environment Hamiltonians. We show that if the
total sequence time is fixed the optimal sequence can be used to make the
distance between the protected and unperturbed qubit states arbitrarily small
in the number of applied pulses. If, on the other hand, the minimum pulse
interval is fixed and the total sequence time is allowed to scale with the
number of pulses, then longer sequences need not always be advantageous. The
rigorous bound may serve as testbed for approximate treatments of optimal
decoupling in bounded models of decoherence.
Title:
Indistinguishability and Interference in the Coherent Control of Atomic
and Molecular Processes
Authors:
Jiangbin Gong,
Paul Brumer
The subtle and fundamental issue of indistinguishability and interference
between independent pathways to the same target state is examined in the
context of coherent control of atomic and molecular processes, with emphasis
placed on possible "which-way" information due to quantum entanglement
established in the quantum dynamics. Because quantum interference between
independent pathways to the same target state occurs only when the independent
pathways are indistinguishable, it is first shown that creating useful
coherence (as defined in the paper) between nondegenerate states of a molecule
for subsequent quantum interference manipulation cannot be achieved by
collisions between atoms or molecules that are prepared in momentum and energy
eigenstates. Coherence can, however, be transferred from light fields to atoms
or molecules. Using a particular coherent control scenario, it is shown that
this coherence transfer and the subsequent coherent phase control can be
readily realized by the most classical states of light, i.e., coherent states
of light. It is further demonstrated that quantum states of light may suppress
the extent of phase-sensitive coherent control by leaking out some which-way
information while "incoherent interference control" scenarios proposed in the
literature have automatically ensured the indistinguishability of multiple
excitation pathways. The possibility of quantum coherence in photodissociation
product states is also understood in terms of the disentanglement between
photodissociation fragments. Results offer deeper insights into quantum
coherence generation in atomic and molecular processes.
We investigate a system consisting of a single, as well as two emitters
strongly coupled to surface plasmon modes of a nano-wire using a Green function
approach. Explicit expressions are derived for the spontaneous decay rate into
the plasmon modes and for the atom-plasmon coupling as well as a
plasmon-mediated atom-atom coupling. Phenomena due to the presence of losses in
the metal are discussed. In case of two atoms, we observe Dicke sub- and
superradiance resulting from their plasmon-mediated interaction. Based on this
phenomenon, we propose a scheme for a deterministic two-qubit quantum gate. We
also discuss a possible realization of interesting many-body Hamiltonians, such
as the spin-boson model, using strong emitter-plasmon coupling.
Title:
Quantum Mechanics: From Realism to Intuitionism
Authors:
Ronnie Hermens
The interpretation of quantum mechanics has been a problem since its founding
days. A large contribution to the discussion of possible interpretations of
quantum mechanics is given by the so-called impossibility proofs for hidden
variable models; models that allow a realist interpretation.
In this thesis some of these proofs are discussed, like von Neumann's
Theorem, the Kochen-Specker Theorem and the Bell-inequalities. Some more recent
developments are also investigated, like Meyer's nullification of the
Kochen-Specker Theorem, the MKC-models and Conway and Kochen's Free Will
Theorem. This last one is taken to suggest that the problems that arise for
certain interpretations of quantum mechanics are not limited to realist
interpretations only, but also affect certain instrumentalist interpretations.
It is argued that one may arrive at a more satisfying interpretation of
quantum mechanics if one adopts a logic that seems more compatible with the
instrumentalist viewpoint namely, intuitionistic logic. The motivations for
adopting this form of logic rather than classical logic or quantum logic are
linked to some of the philosophical ideas of Bohr. In particular a new
interpretation of Bohr's notion of complementarity is proposed. Finally some
possibilities are explored for linking the intuitionistic interpretation of
quantum mechanics to the mathematical formalism of the theory.
In 1960 Schwinger [J. Schwinger, Proc.Natl.Acad.Sci. 46 (1960) 570- 579]
proposed the algorithm for factorization of unitary operators in the finite M
dimensional Hilbert space according to a coprime decomposition of M. Using a
special permutation operator A we generalize the Schwinger factorization to
every decomposition of M. We obtain the factorized pairs of unitary operators
and show that they obey the same commutation relations as Schwinger's. We apply
the new factorization to two problems. First, we show how to generate two
kq-like mutually unbiased bases for any composite dimension. Then, using a
Harper-like Hamiltonian model in the finite dimension M = M1M2, we show how to
design a physical system with M1 energy levels, each having degeneracy M2.
Title:
The Free Will Theorem, Stochastic Quantum Dynamics and True Becoming in
Relativistic Quantum Physics
Authors:
Nicolas Gisin
In Bell inequality tests, the evolution of the wavefunction is not covariant,
i.e. not invariant under velocity boost that change the time ordering of
events, but the laws that govern the probability distribution of possible
results are. In this note I investigate what this could mean and whether there
could be some covariant "real quantum stuff". This clarifies the implication of
the Free Will Theorem and of relativistic spontaneous localization models based
on the flash ontology (rGRWf). Some implications for the concept of time(s) are
spelled out.
Title:
On the Impossibility of Covariant Nonlocal "hidden" Variables in Quantum
Physics
Authors:
Nicolas Gisin
Local variables can't describe the quantum correlations observed in tests of
Bell inequalities. Likewise, we show that nonlocal variables can't describe
quantum correlations in a relativistic time-order invariant way.
We induce quantum jumps between the hyperfine ground states of one and two
Cesium atoms, strongly coupled to the mode of a high-finesse optical resonator,
and analyze the resulting random telegraph signals. We identify experimental
parameters to deduce the atomic spin state nondestructively from the stream of
photons transmitted through the cavity, achieving a compromise between a good
signal-to-noise ratio and minimal measurement-induced perturbations. In order
to extract optimum information about the spin dynamics from the photon count
signal, a Bayesian update formalism is employed, which yields time-dependent
probabilities for the atoms to be in either hyperfine state. We discuss the
effect of super-Poissonian photon number distributions caused by atomic motion.
Title:
Particle Entanglement in Rotating Gases
Authors:
Zhao Liu,
Heng Fan
In this paper, we investigate the particle entanglement in 2D
weakly-interacting rotating Bose and Fermi gases. We find that both particle
localization and vortex localization can be indicated by particle entanglement.
We also use particle entanglement to show the occurrence of edge reconstruction
of rotating fermions. The different properties of condensate phase and vortex
liquid phase of bosons can be reflected by particle entanglement and in vortex
liquid phase we construct a trial wave function in the viewpoint of
entanglement to relate the ground state with quantum Hall state. Finally, the
relation between particle entanglement and interaction strength is studied.
Title:
Fast quantum logical gates with four-level SQUIDs coupled to a
superconducting resonator: A scheme without adjustment of the level spacings
and with tolerance for nonuniform device parameter
Authors:
Xiao-Ling He,
Chui-Ping Yang,
Sheng Li,
Jun-Yan Luo,
Siyuan Han
We propose a new scheme for realizing a two-qubit controlled phase gate with
superconducting quantum interference devices (SQUIDs) coupled to a
superconducting resonator. In this scheme, the two lowest levels of each SQUID
serve as the logical states and two intermediate levels of each SQUID are used
for the gate realization. We show that neither adjustment of SQUID level
spacings during the gate operation nor uniformity in SQUID parameters is
required by this proposal. In addition, the present scheme does not require the
adiabatic passage or a second-order detuning and thus the gate is much faster.
Complete information about the Hamiltonian of a quantum system is sufficient
to predict its future behavior with arbitrary accuracy. There is presently no
method for efficient estimation of Hamiltonian parameters due to the
exponentially rising number of the required experimental configurations with
respect to the system degrees of freedom and inherent nonlinear dependence of
measurement outcomes on the Hamiltonian parameters. Here, we develop a
compressed sensing method for scalable Hamiltonian identification of
multipartite quantum systems. We demonstrate that with only O(s log(d)) random
measurement settings one can estimate the Hamiltonian of a d-dimensional
system, provided that the Hamiltonian is known to be almost s-sparse in a
basis. This approach is robust to noise and experimental imperfections in data
extraction. We numerically simulate the performance of this algorithm for
three- and four-body interactions in spin-coupled quantum dots and atoms in
optical lattices. Furthermore, we apply the algorithm to characterize
Hamiltonian fine structure and system-bath couplings in open quantum systems.
Title:
Simple Protocols for Oblivious Transfer and Secure Identification in the
Noisy-Quantum-Storage Model
Authors:
Christian Schaffner
We present simple protocols for oblivious transfer and password-based
identification which are secure against general attacks in the
noisy-quantum-storage model as defined in [KWW09]. We argue that a technical
tool from [KWW09] suffices to prove security of the known protocols. Whereas
the more involved protocol for oblivious transfer from [KWW09] requires less
noise in storage to achieve security, our "canonical" protocols have the
advantage of being simpler to implement and the security error is easier
control. Therefore, our protocols yield higher OT-rates for many realistic
noise parameters.
Furthermore, the first proof of security of a direct protocol for
password-based identification against general noisy-quantum-storage attacks is
given.
Quantum coherence of open quantum systems is usually compromised because of
the interaction with the ambient environment. A "decoherence-free subspace"
(DFS) of the system Hilbert space is defined where the evolution remains
unitary. In the absence of a priori existence of such subspaces, it seems
natural that utilizing quantum control may help generate and/or retain a
decoherence-free evolution. Here, we generalize the traditional notion of DFS,
and introduce time-varying DFS wherein the system's density matrix has a
unitarily evolving sub-density corresponding to some given set of its
eigenvalues (which we aim to preserve). This subspace is characterized from
both topological and algebraic perspectives. In particular, we show that this
DFS admits a complex vector bundle structure over a real-analytic manifold (the
decoherence-free manifold).
We give a theoretical description of a coherently driven opto-mechanical
system with a single added photon. The photon source is modeled as a cavity
which initially contains one photon and which is irreversibly coupled to the
opto-mechanical system. We show that the probability for the additional photon
to be emitted by the opto-mechanical cavity will exhibit oscillations under a
Lorentzian envelope, when the driven interaction with the mechanical resonator
is strong enough. Our scheme provides a feasible route towards quantum state
transfer between optical photons and micromechanical resonators.
Here we show that by applying optimal control theory to the design of the
refocusing pulses applied in the CPMG sequence we can extend the robust
refocusing of the sequence to larger resonance offsets while simultaneously
accounting for RF inhomogeneity. In order to compactly characterize the nature
and severity of pulse errors that occur during the application of a large
number of pulses, we introduce a model that describes the CPMG sequence as a
dephasing channel.
Title:
On causality, apparent 'superluminality' and reshaping in barrier
penetration
Authors:
D. Sokolovski
We consider tunnelling of a non-relativistic particle across a potential
barrier. It is shown that the barrier acts as an effective beam splitter which
builds up the transmitted pulse from the copies of the initial envelope shifted
in the coordinate space backwards relative to the free propagation. Although
along each pathway causality is explicitly obeyed, in special cases reshaping
can result an overall reduction of the initial envelope, accompanied by an
arbitrary coordinate shift. In the case of a high barrier the delay amplitude
distribution (DAD) mimics a Dirac $\delta$-function, the transmission amplitude
is superoscillatory for finite momenta and tunnelling leads to an accurate
advancement of the (reduced) initial envelope by the barrier width. In the case
of a wide barrier, initial envelope is accurately translated into the complex
coordinate plane. The complex shift, given by the first moment of the DAD,
accounts for both the displacement of the maximum of the transmitted
probability density and the increase in its velocity. It is argued that
analysing apparent 'superluminality' in terms of spacial displacements helps
avoid contradiction associated with time parameters such as the phase time.
The population distribution within the ground-state of an atomic ensemble is
of large significance in a variety of quantum optics processes. We present a
method to reconstruct the detailed population distribution from a set of
absorption measurements with various frequencies and polarizations, by
utilizing the differences between the dipole matrix elements of the probed
transitions. The technique is experimentally implemented on a thermal rubidium
vapor, demonstrating a population-based analysis in two optical pumping
examples. The results are used to verify and calibrate an elaborated numerical
model, and the limitations of the reconstruction scheme which result from the
symmetry properties of the dipole matrix elements are discussed.
We report on the dissipative dynamics of an entangled, bipartite interacting
system. We show how to induce and control the so-called early stage
disentanglement (and the delayed entanglement generation) dynamics by means of
a driving laser field. We demonstrate that some of the features currently
associated with pure non-Markovian effects in such entanglement behavior can
actually take place in Markovian environments if background noise QED
fluctuations are considered. We illustrate this for the case of a dimer
interacting molecular system for which emission rates, interaction strength,
and radiative corrections have been previously measured. We also show that even
in the absence of collective decay mechanisms and qubit-qubit interactions, the
entanglement still exhibits collapse-revival behavior. Our results indicate
that zero point energy fluctuations should be taken into account when
formulating precise entanglement dynamics statements.
We propose and demonstrate scheme for direct experimental testing of quantum
commutation relations for Pauli operators. The implemented device is an
advanced quantum processor that involves two programmable quantum gates.
Depending on a state of two-qubit program register, we can test either
commutation or anti-commutation relations. Very good agreement between theory
and experiment is observed, indicating high-quality performance of the
implemented quantum processor and reliable verification of commutation
relations for Pauli operators.
Title:
Bhomian Mechanics vs. Standard Quantum Mechanics: a Difference in
Experimental Predictions
Authors:
Artur Szczepanski
Standard Quantum Mechanics (QM) predicts an anti-intuitive fenomenon here
referred to as "quantum autoscattering", which is excluded by Bhomian
Mechanics. The scheme of a gedanken experiment testing the QM prediction is
briefly discussed.
Measurement based quantum computation (MBQC), which requires only single
particle measurements on a universal resource state to achieve the full power
of quantum computing, has been recognized as one of the most promising models
for the physical realization of quantum computers. Despite considerable
progress in the last decade, it remains a great challenge to search for new
universal resource states with naturally occurring Hamiltonians, and to better
understand the entanglement structure of these kinds of states. Here we show
that most of the resource states currently known can be reduced to the cluster
state, the first known universal resource state, via adaptive local
measurements at a constant cost. This new quantum state reduction scheme
provides simpler proofs of universality of resource states and opens up plenty
of space to the search of new resource states, including an example based on
the one-parameter deformation of the AKLT state studied in [Commun. Math. Phys.
144, 443 (1992)] by M. Fannes et al. about twenty years ago.
The Pancharatnam phase was discovered in the context of amplitude
interferometry of polarised light and anticipates Berry's discovery of the
geometric phase. We propose a polarised intensity interferometry experiment
which measures the nonlocal Pancharatnam phase acquired by a pair of Hanbury
Brown-Twiss photons. The experimental setup involves two polarised thermal
sources illuminating two polarised detectors. Varying the relative polarisation
angle of the detectors introduces a geometric phase equal to half the solid
angle traced out on the Poincare sphere by a pair of photons. Local
measurements at either detector do not reveal the effects of the phase, which
appears only in the coincidence counts of the two detectors and is a genuinely
multiparticle and nonlocal effect. The phase is an optical analog of the
multiparticle Aharonov-Bohm effect which has been measured in Quantum Hall
systems.
The past decade has demonstrated increasing interests in using optimal
control based methods within coherent quantum controllable systems. The
versatility of such methods has been demonstrated with particular elegance
within nuclear magnetic resonance (NMR) where natural separation between
coherent and dissipative spin dynamics processes has enabled coherent quantum
control over long periods of time to shape the experiment to almost ideal
adoption to the spin system and external manipulations. This has led to new
design principles as well as powerful new experimental methods within magnetic
resonance imaging, liquid-state and solid-state NMR spectroscopy. For this
development to continue and expand, it is crucially important to constantly
improve the underlying numerical algorithms to provide numerical solutions
which are optimally compatible with implementation on current instrumentation
and at same time are numerically stable and offer fast monotonic convergence
towards the target. Addressing such aims, we here present a smoothing
monotonically convergent algorithm for pulse sequence design in magnetic
resonance which with improved optimization stability lead to smooth pulse
sequence easier to implement experimentally and potentially understand within
the analytical framework of modern NMR spectroscopy.
We show that the threshold error rates of preparation and measurement for
fault tolerant quantum computing can be improved considerably. By removing the
dependence on measurements & feedback in quantum error correction using gadgets
based on coherent feedback, one can circumvent the problem of noisy and slow
measurements present in many physical systems. We develop the method for the
Bacon-Shor code, and show fault-tolerant universal quantum computing is
achievable when gate error rates are below p_{(g)thresh} = 2.89 x 10^{-5} and,
assuming the gate error rate is below the threshold, measurement and
preparation error rates can be as high as p_{(p,m)thresh}~7%.
In this Comment, we reanalyze the experiments on the collision frequency
shift of the b-c and a-d hyperfine transitions in three-dimensional atomic
hydrogen in the presence of, respectively, a and b-state atoms. Accurate
consideration of the symmetry of the spatial and spin part of the diatomic
wavefunction yields the difference a_T-a_S=0.30(5) \AA between the triplet and
singlet s-wave scattering lengths of hydrogen atoms. This corrects the
factor-of two error of the commented work [Phys. Rev. Lett. 101, 263003
(2008)].
Title:
Parameter estimation with mixed quantum states
Authors:
Daniel Braun
We consider quantum enhanced measurements with initially mixed states. We
show very generally that for any linear propagation of the initial state that
depends smoothly on the parameter to be estimated, the sensitivity is bound by
the maximal sensitivity that can be achieved for any of the pure states from
which the initial density matrix is mixed. This provides a very general proof
that purely classical correlations cannot improve the sensitivity of parameter
estimation schemes in quantum enhanced measurement schemes.
Title:
A simpel and versatile cold-atom simulator of non-Abelian gauge
potentials
Authors:
Daniel Braun
We show how a single, harmonically trapped atom in a tailored magnetic field
can be used for simulating the effects of a broad class of non-abelian gauge
potentials. We demonstrate how to implement Rashba or Linear-Dresselhaus
couplings, or observe {\em Zitterbewegung} of a Dirac particle.
Intense laser ionization expands Einstein's photoelectric effect rules giving
a wealth of phenomena widely studied over the last decades. In all cases, so
far, photons were assumed to carry one unit of angular momentum. However it is
now clear that photons can possess extra angular momentum, the orbital angular
momentum (OAM), related to their spatial profile. We show a complete
description of photoionization by OAM photons, including new selection rules
involving more than one unit of angular momentum. We explore theoretically the
interaction of a single electron atom located at the center of an intense
ultraviolet beam bearing OAM, envisaging new scenarios for quantum optics.
Title:
Fermionic Casimir densities in toroidally compactified spacetimes with
applications to nanotubes
Authors:
S. Bellucci,
A. A. Saharian
Fermionic condensate and the vacuum expectation values of the energy-momentum
tensor are investigated for a massive spinor fields in higher-dimensional
spacetimes with an arbitrary number of toroidally compactified spatial
dimensions. By using the Abel-Plana summation formula and the zeta function
technique we present the vacuum expectation values in two different forms.
Applications of the general formulae to cylindrical and toroidal carbon
nanotubes are given. We show that the topological Casimir energy is positive
for metallic cylindrical nanotubes and is negative for semiconducting ones. The
toroidal compactification of a cylindrical nanotube along its axis increases
the Casimir energy for metallic-type (periodic) boundary conditions along its
axis and decreases the Casimir energy for the semiconducting-type
compactifications.
Title:
Vacuum fluctuations and topological Casimir effect in
Friedmann-Robertson-Walker cosmologies with compact dimensions
Authors:
A. A. Saharian,
A. L. Mkhitaryan
We investigate the Wightman function, the vacuum expectation values of the
field squared and the energy-momentum tensor for a massless scalar field with
general curvature coupling parameter in spatially flat
Friedmann-Robertson-Walker universes with an arbitrary number of toroidally
compactified dimensions. The topological parts in the expectation values are
explicitly extracted and in this way the renormalization is reduced to that for
the model with trivial topology. In the limit when the comoving lengths of the
compact dimensions are very short compared to the Hubble length, the
topological parts coincide with those for a conformal coupling and they are
related to the corresponding quantities in the flat spacetime by standard
conformal transformation. In the opposite limit of large comoving lengths of
the compact dimensions, in dependence of the curvature coupling parameter, two
regimes are realized with monotonic or oscillatory behavior of the vacuum
expectation values. In the monotonic regime and for nonconformally and
nonminimally coupled fields the vacuum stresses are isotropic and the equation
of state for the topological parts in the energy density and pressures is of
barotropic type. In the oscillatory regime, the amplitude of the oscillations
for the topological part in the expectation value of the field squared can be
either decreasing or increasing with time, whereas for the energy-momentum
tensor the oscillations are damping.
Title:
Topological Casimir effect in nanotubes and nanoloopes
Authors:
A. A. Saharian
The Casimir effect is investigated in cylindrical and toroidal carbon
nanotubes within the framework of the Dirac-like model for the electronic
states. The topological Casimir energy is positive for metallic cylindrical
nanotubes and is negative for semiconducting ones. The toroidal
compactification of a cylindrical nanotube along its axis increases the Casimir
energy for metallic-type (periodic) boundary conditions along its axis and
decreases the Casimir energy for the semiconducting-type compactifications. For
finite length metallic nanotubes the Casimir forces acting on the tube edges
are always attractive, whereas for semiconducting-type ones they are attractive
for small lengths of the nanotube and repulsive for large lengths.
Careful exploration of the idea that equation for radial wave function must
be compatible with the full Schrodinger equation shows appearance of the
delta-function while reduction of full Schrodinger equation in spherical
coordinates. Elimination of this extra term produces a boundary condition for
the radial wave function, which is the same both for regular and singular
potentials.
We derive the different forms of BRST symmetry by using the
Batalin-Fradkin-Vilkovisky formalism in a rigid rotor. The so called
"dual-BRST" symmetry is obtained from usual BRST symmetry by making a canonical
transformation in the ghost sector. On the other hand, a canonical
transformation in the sector involving Lagrange multiplier and its
corresponding momentum leads to a new form of BRST as well as dual-BRST
symmetry.
For scalar and electromagnetic fields we evaluate the vacuum expectation
value of the energy-momentum tensor induced by a curved boundary in the
Robertson--Walker spacetime with negative spatial curvature. In order to
generate the vacuum densities we use the conformal relation between the
Robertson-Walker and Rindler spacetimes and the corresponding results for a
plate moving by uniform proper acceleration through the Fulling--Rindler
vacuum. For the general case of the scale factor the vacuum energy-momentum
tensor is presented as the sum of the boundary free and boundary induced parts.
1002.0846ari.mizel : I've never used Scirate before, and my experience is that it's very hard to communicate physics clearly via short text messages. But, I'm g...
1002.0846matt.hastings : Indeed, as I think about it more, I would really like to see the error correction explained better. The example I gave above shows that, if...
1002.0846RS : I find this paper hard to follow. In particular, I don't see how to "apply a GSQC version of quantum error detecting codes" without making t...
1002.0846matt.hastings : This is really an amazing advance if it works. I still do not quite understand it yet, though, so I am not sure of all the details.
0909.0931jontyson : Cedric (cbeny above) and his co-author Ogden have indeed made impressive progress since my paper was posted by obtaining dimension-independe...
0909.0931cbeny : Since it wasn't cited yet in this work, let me mention also my paper
http://arxiv.org/abs/0907.5391
Contrary to Jon's...
0909.0931jontyson : The authors are simply mistaken in their above assertion on Scirate that the transpose channel is identical to the quadratic recovery channe...
0909.0931nghk : The paper 0907.3386 referred to by jontyson deals with a different problem from the one considered in our paper. 0907.3386 discusses reversi...
1001.3735selvarani : This paper doesnot have any idea or text match with Stephen cook s description what so ever, and it is not removed from arxive. It is an ori...