64 research outputs found
Discrimination of Unitary Transformations and Quantum Algorithms
Quantum algorithms are typically understood in terms of the evolution of a
multi-qubit quantum system under a prescribed sequence of unitary
transformations. The input to the algorithm prescribes some of the unitary
transformations in the sequence with others remaining fixed. For oracle query
algorithms, the input determines the oracle unitary transformation. Such
algorithms can be regarded as devices for discriminating amongst a set of
unitary transformations. The question arises: "Given a set of known oracle
unitary transformations, to what extent is it possible to discriminate amongst
them?" We investigate this for the Deutsch-Jozsa problem. The task of
discriminating amongst the admissible oracle unitary transformations results in
an exhaustive collection of algorithms which can solve the problem with
certainty.Comment: Submitted to the proceedings of the QCMC 08 conferenc
Optimal covariant quantum networks
A sequential network of quantum operations is efficiently described by its
quantum comb, a non-negative operator with suitable normalization constraints.
Here we analyze the case of networks enjoying symmetry with respect to the
action of a given group of physical transformations, introducing the notion of
covariant combs and testers, and proving the basic structure theorems for these
objects. As an application, we discuss the optimal alignment of reference
frames (without pre-established common references) with multiple rounds of
quantum communication, showing that i) allowing an arbitrary amount of
classical communication does not improve the alignment, and ii) a single round
of quantum communication is sufficient.Comment: 10 pages, 3 figure
Bosonic CNOT gates with Quantum Interrogation
We put forward a new CNOT gate scheme with atoms and ions based on quantum
interrogation and a bosonic particle extension of the models of linear optics
quantum computation. We show how the possibility of particle collision can
provide the strong interaction that is needed for universal quantum gates. Two
atom optics proposals are provided. Unlike previous schemes, these gates are at
the same time nondestructive, valid for arbitrary inputs and can work with a
probability as close to unity as desired in the lossless case. Data is encoded
into position modes and the gates only require basic atom optics elements,
which gives potentially simpler quantum computer implementations.Comment: 5 pages, 3 figures, preliminar versio
Loss-tolerant quantum enhanced metrology and state engineering via the reverse Hong-Ou-Mandel effect
Preparing highly entangled quantum states between remote parties is a major
challenge for quantum communications [1-8]. Particularly promising in this
context are the N00N states, which are entangled N-photon wavepackets
delocalized between two different locations, providing measurement sensitivity
limited only by the uncertainty principle [1, 10-15]. However, these states are
notoriously vulnerable to losses, making it difficult both to share them
between remote locations, and to recombine them to exploit interference
effects. Here we address this challenge by utilizing the reverse version of the
Hong-Ou-Mandel effect [16] to prepare a high-fidelity two-photon N00N state
shared between two parties connected by a lossy optical channel. Furthermore,
we demonstrate that the enhanced phase sensitivity can be directly exploited in
the two distant locations, and we remotely prepare superpositions of coherent
states, known as Schr\"odinger's cat states" [17, 18]
The Consumption of Reference Resources
Under the operational restriction of the U(1)-superselection rule, states
that contain coherences between eigenstates of particle number constitute a
resource. Such resources can be used to facilitate operations upon systems that
otherwise cannot be performed. However, the process of doing this consumes
reference resources. We show this explicitly for an example of a unitary
operation that is forbidden by the U(1)-superselection rule.Comment: 4 pages 6x9 page format, 2 figure
Synthesis of the Einstein-Podolsky-Rosen entanglement in a sequence of two single-mode squeezers
Synthesis of the Einstein-Podolsky-Rosen entangled state --- the primary
entangled resource in continuous-variable quantum-optical information
processing --- is a technological challenge of great importance. Here we
propose and implement a new scheme of generating this state. Two nonlinear
optical crystals, positioned back-to-back in the waist of a pump beam, function
as single-pass degenerate optical parametric amplifiers and produce single-mode
squeezed vacuum states in orthogonal polarization modes, but in the same
spatiotemporal mode. A subsequent pair of waveplates acts as a beam splitter,
entangling the two polarization modes to generate the Einstein-Podolsky-Rosen
state. This technique takes advantage of the strong nonlinearity associated
with type-I phase-matching configuration while at the same time eliminating the
need for actively stabilizing the optical phase between the two squeezers,
which typically arises if these squeezers are spatially separated. We
demonstrate our method in an experiment, preparing a 1.4 dB two-mode squeezed
state and characterizing it via two-mode homodyne tomography.Comment: 4 pages, 3 figure
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