242 research outputs found
Minimum-energy pulses for quantum logic cannot be shared
We show that if an electromagnetic energy pulse with average photon number
is used to carry out the same quantum logical operation on a set of N
atoms, either simultaneously or sequentially, the overall error probability in
the worst case scenario (i.e., maximized over all the possible initial atomic
states) scales as N^2/. This means that in order to keep the error
probability bounded by N\epsilon, with \epsilon ~ 1/, one needs to use
N/\epsilon photons, or equivalently N separate "minimum-energy'' pulses: in
this sense the pulses cannot, in general, be shared. The origin for this
phenomenon is found in atom-field entanglement. These results may have
important consequences for quantum logic and, in particular, for large-scale
quantum computation.Comment: To appear in Phys. Rev. A, Rapid Communication
Gate fidelity of arbitrary single-qubit gates constrained by conservation laws
Recent investigations show that conservation laws limit the accuracy of gate
operations in quantum computing. The inevitable error under the angular
momentum conservation law has been evaluated so far for the CNOT, Hadamard, and
NOT gates for spin 1/2 qubits, while the SWAP gate has no constraint. Here, we
extend the above results to general single-qubit gates. We obtain an upper
bound of the gate fidelity of arbitrary single-qubit gates implemented under
arbitrary conservation laws, determined by the geometry of the conservation law
and the gate operation on the Bloch sphere as well as the size of the ancilla.Comment: Title changed; to appear in J. Phys. A: Math. Theor.; 19 pages, 2
figure
Quantum limits in interferometric measurements
Quantum noise limits the sensitivity of interferometric measurements. It is
generally admitted that it leads to an ultimate sensitivity, the ``standard
quantum limit''. Using a semi-classical analysis of quantum noise, we show that
a judicious use of squeezed states allows one in principle to push the
sensitivity beyond this limit. This general method could be applied to large
scale interferometers designed for gravitational wave detection.Comment: 4 page
Constraints for quantum logic arising from conservation laws and field fluctuations
We explore the connections between the constraints on the precision of
quantum logical operations that arise from a conservation law, and those
arising from quantum field fluctuations. We show that the conservation-law
based constraints apply in a number of situations of experimental interest,
such as Raman excitations, and atoms in free space interacting with the
multimode vacuum. We also show that for these systems, and for states with a
sufficiently large photon number, the conservation-law based constraint
represents an ultimate limit closely related to the fluctuations in the quantum
field phase.Comment: To appear in J. Opt. B: Quantum Semiclass. Opt., special issue on
quantum contro
Effects of random localizing events on matter waves: formalism and examples
A formalism is introduced to describe a number of physical processes that may
break down the coherence of a matter wave over a characteristic length scale l.
In a second-quantized description, an appropriate master equation for a set of
bosonic "modes" (such as atoms in a lattice, in a tight-binding approximation)
is derived. Two kinds of "localizing processes" are discussed in some detail
and shown to lead to master equations of this general form: spontaneous
emission (more precisely, light scattering), and modulation by external random
potentials. Some of the dynamical consequences of these processes are
considered: in particular, it is shown that they generically lead to a damping
of the motion of the matter-wave currents, and may also cause a "flattening" of
the density distribution of a trapped condensate at rest.Comment: v3; a few corrections, especially in Sections IV and
Field Purification in the intensity-dependent Jaynes-Cummings model
We have found that, in the intensity-dependent Jaynes-Cummings model, a field
initially prepared in a statistical mixture of two coherent states,
and , evolves toward a pure state. We have also shown that an
even-coherent state turns periodically a into rotated odd-coherent state during
the evolution.Comment: 14 pages, RevTex, 3 figures, accepted for publication in Physics
Letters
Robust unravelings for resonance fluorescence
Monitoring the fluorescent radiation of an atom unravels the master equation
evolution by collapsing the atomic state into a pure state which evolves
stochastically. A robust unraveling is one that gives pure states that, on
average, are relatively unaffected by the master equation evolution (which
applies once the monitoring ceases). The ensemble of pure states arising from
the maximally robust unraveling has been suggested to be the most natural way
of representing the system [H.M. Wiseman and J.A. Vaccaro, Phys. Lett. A {\bf
250}, 241 (1998)]. We find that the maximally robust unraveling of a resonantly
driven atom requires an adaptive interferometric measurement proposed by
Wiseman and Toombes [Phys. Rev. A {\bf 60}, 2474 (1999)]. The resultant
ensemble consists of just two pure states which, in the high driving limit, are
close to the eigenstates of the driving Hamiltonian . This
ensemble is the closest thing to a classical limit for a strongly driven atom.
We also find that it is possible to reasonably approximate this ensemble using
just homodyne detection, an example of a continuous Markovian unraveling. This
has implications for other systems, for which it may be necessary in practice
to consider only continuous Markovian unravelings.Comment: 12 pages including 5 .eps figures, plus one .jpg figur
Computation using Noise-based Logic: Efficient String Verification over a Slow Communication Channel
Utilizing the hyperspace of noise-based logic, we show two string
verification methods with low communication complexity. One of them is based on
continuum noise-based logic. The other one utilizes noise-based logic with
random telegraph signals where a mathematical analysis of the error probability
is also given. The last operation can also be interpreted as computing
universal hash functions with noise-based logic and using them for string
comparison. To find out with 10^-25 error probability that two strings with
arbitrary length are different (this value is similar to the error probability
of an idealistic gate in today's computer) Alice and Bob need to compare only
83 bits of the noise-based hyperspace.Comment: Accepted for publication in European Journal of Physics B (November
10, 2010
Information Erasure and Recover in Quantum Memory
We show that information in quantum memory can be erased and recovered
perfectly if it is necessary. That the final states of environment are
completely determined by the initial states of the system allows that an easure
operation can be realized by a swap operation between system and an ancilla.
Therefore, the erased information can be recoverd. When there is an
irreversible process, e.g. an irreversible operation or a decoherence process,
in the erasure process, the information would be erased perpetually. We present
that quantum erasure will also give heat dissipation in environment. And a
classical limit of quantum erasure is given which coincides with Landauer's
erasure principle.Comment: PACS: 0365.Bz. 03.67.Hk;3page
Dynamical localization simulated on a few qubits quantum computer
We show that a quantum computer operating with a small number of qubits can
simulate the dynamical localization of classical chaos in a system described by
the quantum sawtooth map model. The dynamics of the system is computed
efficiently up to a time , and then the localization length
can be obtained with accuracy by means of order computer runs,
followed by coarse grained projective measurements on the computational basis.
We also show that in the presence of static imperfections a reliable
computation of the localization length is possible without error correction up
to an imperfection threshold which drops polynomially with the number of
qubits.Comment: 8 pages, 8 figure
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