Fault-tolerant quantum computing requires gates which function correctly
despite the presence of errors, and are scalable if the error
probability-per-gate is below a threshold value. To date, no method has been
described for calculating this probability from measurements on a gate. Here we
introduce a technique enabling quantitative benchmarking of quantum-logic gates
against fault-tolerance thresholds for any architecture. We demonstrate our
technique experimentally using a photonic entangling-gate. The relationship
between experimental errors and their quantum logic effect is non-trivial:
revealing this relationship requires a comprehensive theoretical model of the
quantum-logic gate. We show the first such model for any architecture, and find
multi-photon emission--a small effect previously regarded as secondary to
mode-mismatch--to be the dominant source of logic error. We show that reducing
this will move photonic quantum computing to within striking distance of
fault-tolerance.
Title:
Jahn-Teller models, Kerr nonlinearities, and nonclassical states with
superconducting qubits and nanoresonators
Authors:
F. L. Semião,
K. Furuya,
G. J. Milburn
In this letter, we show how a Josephson charge qubit coupled to a
transmission line and a nanomechanical resonator may be used to implement
Jahn-Teller models and Kerr nonlinearities. We show explicit implementations of
simple Jahn-Teller Hamiltonians in our system, and propose the generation of
the Yurke-Stoler state which is quantum superposition of a pair of
distinguishable coherent states. This is achieved by effectively implementing
Kerr nonlinearities induced by application of a strong external driving field.
We have computed the spectrum emitted spontaneously by an artificial atom
coupled to an arbitrarily detuned single mode cavity, taking into account pure
dephasing processes. We show that if the emitter is incoherent, the cavity can
efficiently emit photons with its own spectral characteristics. This result
sheds new light on puzzling recent experimental data obtained with quantum dots
and semiconductor optical microcavities. Cavity spectral filtering induced by
the emitter's decoherence can be exploited to produce photons with a high
degree of indistinguishability.
In some cases the state of a quantum system with a large number of subsystems
can be approximated efficiently by the density-matrix renormalization group
(DMRG), which makes use of redundancies in the description of the state. Here
we show that the achievable efficiency can be much better when performing DMRG
in the Heisenberg picture (H-DMRG), as only the observable of interest but not
the entire state is considered. In some non-trivial cases, H-DMRG can even be
exact for finite bond dimensions.
Title:
Insufficiency of the Quantum State for Deducing Observational
Probabilities
Authors:
Don N. Page
It is usually assumed that the quantum state is sufficient for deducing all
probabilities for a system. This may be true when there is a single observer,
but it is not true in a universe large enough that there are many copies of an
observer. Then the probability of an observation cannot be deduced simply from
the quantum state (say as the expectation value of the projection operator for
the observation, as in traditional quantum theory). One needs additional rules
to get the probabilities. What these rules are is not logically deducible from
the quantum state, so the quantum state itself is insufficient for deducing
observational probabilities.
We find the allowed complex numbers associated with the inner product of N
equally separated pure quantum states. The allowed areas on the unitary complex
plane have the form of petals. A point inside the petal-shape represents a set
of N linearly independent (LI) pure states, and a point on the edge of that
area represents a set of N linearly dependent (LD) pure states. For each one of
those LI sets we study the complete discrimination of its N equi-separated
states combining sequentially the two known strategies: first the unambiguous
identification protocol for LI states, followed, if necessary, by the
error-minimizing measurement scheme for LD states. We find that the
probabilities of success for both unambiguous and ambiguous discrimination
procedures depend on both the module and the phase of the involved inner
product complex number. We show that, with respect to the phase-parameter, the
maximal probability of discriminating unambiguously the N non-orthogonal pure
states holds just when there no longer be probability of obtaining ambiguously
information about the prepared state by applying the second protocol if the
first one was not successful.
We explicitate the relation between Hamiltonians for networks of interacting
qubits in the XYZ model and graph Laplacians. We then study evolution in
networks in which all sites can communicate with each other. These are modeled
by the complete graph K_{n} and called all-to-all networks. It turns out that
K_{n} does not exhibit perfect state transfer (PST). However, we prove that
deleting an edge in K_{n} allows PST between the two non-adjacent sites, when n
is a multiple of four. An application is routing a qubit over n different
sites, by switching off the link between the sites that we wish to put in
communication. Additionally, we observe that, in certain cases, the unitary
inducing evolution in K_{n} is equivalent to the Grover operator.
We experimentally measure the lower and upper bounds of concurrence for a set
of two-qubit mixed quantum states using photonic systems. The measured
concurrence bounds are in agreement with the results evaluated from the density
matrices reconstructed through quantum state tomography. In our experiment, we
propose and demonstrate a simple method to provide two faithful copies of a
two-photon mixed state required for parity measurements: Two photon pairs
generated by two neighboring pump laser pulses through optical parametric down
conversion processes represent two identical copies. This method can be
conveniently generalized for entanglement estimation of multi-photon mixed
states.
In quantum theory, symmetry has to be defined necessarily in terms of the
family of unit rays, the state space. The theorem of Wigner asserts that a
symmetry so defined at the level of rays can always be lifted into a linear
unitary or an antilinear antiunitary operator acting on the underlying Hilbert
space. We present a proof of this theorem which is both elementary and
economical. Central to our proof is the recognition that a given Wigner
symmetry can, by post-multiplication by a unitary symmetry, be taken into
either the identity or complex conjugation. Our analysis involves a judicious
interplay between the effect a given Wigner symmetry has on certain
two-dimensional subspaces and the effect it has on the entire Hilbert space.
Title:
The Parts Determine the Whole except for n-Qubit
Greenberger-Horne-Zeilinger States
Authors:
Scott N. Walck,
David W. Lyons
The generalized n-qubit Greenberger-Horne-Zeilinger (GHZ) states and their
local unitary equivalents are the only pure states of n qubits that are not
uniquely determined (among arbitrary states, pure or mixed) by their reduced
density matrices of n-1 qubits. Thus, the generalized GHZ states are the only
ones containing information at the n-party level.
Title:
Electrostatic Background Forces due to Varying Contact Potentials in
Casimir Experiments
Authors:
Steve K. Lamoreaux
The existence of a monotonic distance dependent contact potential between two
plates in a Casimir experiment leads to an additional electrostatic force that
is significantly different from the case of a constant potential. Such a
varying potential can arise if there is a uniform gradient in the work function
or contact potential across a plate, as opposed to random microscopic
fluctuations associated with patch potentials. A procedure to compensate for
this force is described for the case of an experiment where the electrostatic
force is minimized at each measurement distance by applying a voltage between
the plates. It is noted that the minimizing voltage is not the contact
potential.
Title:
Nonlocal Modulation of Entangled Photons
Authors:
S. E. Harris
We consider ramifications of the use of high speed light modulators to
questions of correlation and measurement of time-energy entangled photons.
Using phase modulators, we find that temporal modulation of one photon of an
entangled pair, as measured by correlation in the frequency domain, may be
negated or enhanced by modulation of the second photon. Using amplitude
modulators we describe a Fourier technique for measurement of biphoton wave
functions with slow detectors.
Title:
Exceptional points in quantum and classical dynamics
Authors:
A. V. Smilga
We notice that, when a quantum system involves exceptional points, i.e. the
special values of parameters where the Hamiltonian loses its self-adjointness
and acquires the Jordan block structure, the corresponding classical system
also exhibits a singular behaviour associated with restructuring of classical
trajectories. The system with the crypto-Hermitian Hamiltonian H = (p^2+z^2)/2
-igz^5 and hyper-ellictic classical dynamics is studied in details. Analogies
with supersymmetric Yang-Mills dynamics are elucidated.
0807.4935pak : So how does this work then? Is the information carried by entanglement between the two (individually) zero-capacity channels?
0807.3841QuantumMoxie : They missed a key point since they never discussed the operator-based uncertainty relations (i.e. the ones Schrödinger derived) which are a...
0807.4935patrick : A delightfully simple observation that shakes quantum Shannon theory to its foundations! Great paper.
0807.3369Benni : I have now updated my paper. It now contains an explanation of this object of a conditional probability with respect to a sigma algebra, whi...
0807.3369Benni : Dear Quantumcourious, thank you for your corrections of P(X_t \in A')=P(Y_t\in A')
But to your point:
But the set {\cup \...
0807.3369quantumcurious : It seems that this preprint has now been replaced twice since the first version (the July 27th one seems to have disappeared off the arXiv)....
0807.3369Benni : I have now updated the paper. Now it should be clear what mathematicians think when they write a conditional probability with respect to a s...
0807.3369Benni : Well, I now have looked again in some standard Textbooks of probability theory. For example:
http://www.amazon.de/Wahrscheinlichkeitst...
0807.3369Benni : Well, As the author of the paper above:
I just used the notation of Edward Nelson http://www.math.princeton.edu/~nelson/ himself ...