32 research outputs found
Correspondence between continuous variable and discrete quantum systems of arbitrary dimensions
We establish a mapping between a continuous variable (CV) quantum system and
a discrete quantum system of arbitrary dimension. This opens up the general
possibility to perform any quantum information task with a CV system as if it
were a discrete system of arbitrary dimension. The Einstein-Podolsky-Rosen
state is mapped onto the maximally entangled state in any finite dimensional
Hilbert space and thus can be considered as a universal resource of
entanglement. As an explicit example of the formalism a two-mode CV entangled
state is mapped onto a two-qutrit entangled state.Comment: 4 pages, 1 figure, revised version, an example adde
Dynamical Recurrence and the Quantum Control of Coupled Oscillators
Controllability-the possibility of performing any target dynamics by applying a set of available operations-is a fundamental requirement for the practical use of any physical system. For finite-dimensional systems, such as spin systems, precise criteria to establish controllability, such as the so-called rank criterion, are well known. However, most physical systems require a description in terms of an infinite-dimensional Hilbert space whose controllability properties are poorly understood. Here, we investigate infinite-dimensional bosonic quantum systems-encompassing quantum light, ensembles of bosonic atoms, motional degrees of freedom of ions, and nanomechanical oscillators-governed by quadratic Hamiltonians (such that their evolution is analogous to coupled harmonic oscillators). After having highlighted the intimate connection between controllability and recurrence in the Hilbert space, we prove that, for coupled oscillators, a simple extra condition has to be fulfilled to extend the rank criterion to infinite-dimensional quadratic systems. Further, we present a useful application of our finding, by proving indirect controllability of a chain of harmonic oscillators
Entanglement between Collective Operators in a Linear Harmonic Chain
We investigate entanglement between collective operators of two blocks of
oscillators in an infinite linear harmonic chain. These operators are defined
as averages over local operators (individual oscillators) in the blocks. On the
one hand, this approach of "physical blocks" meets realistic experimental
conditions, where measurement apparatuses do not interact with single
oscillators but rather with a whole bunch of them, i.e., where in contrast to
usually studied "mathematical blocks" not every possible measurement is
allowed. On the other, this formalism naturally allows the generalization to
blocks which may consist of several non-contiguous regions. We quantify
entanglement between the collective operators by a measure based on the
Peres-Horodecki criterion and show how it can be extracted and transferred to
two qubits. Entanglement between two blocks is found even in the case where
none of the oscillators from one block is entangled with an oscillator from the
other, showing genuine bipartite entanglement between collective operators.
Allowing the blocks to consist of a periodic sequence of subblocks, we verify
that entanglement scales at most with the total boundary region. We also apply
the approach of collective operators to scalar quantum field theory.Comment: 7 pages, 4 figures, significantly revised version with new results,
journal reference adde
Tensor network states in time-bin quantum optics
The current shift in the quantum optics community towards large-size
experiments -- with many modes and photons -- necessitates new classical
simulation techniques that go beyond the usual phase space formulation of
quantum mechanics. To address this pressing demand we formulate linear quantum
optics in the language of tensor network states. As a toy model, we extensively
analyze the quantum and classical correlations of time-bin interference in a
single fiber loop. We then generalize our results to more complex time-bin
quantum setups and identify different classes of architectures for
high-complexity and low-overhead boson sampling experiments
Entanglement between two superconducting qubits via interaction with non-classical radiation
We propose a scheme to physically interface superconducting nano-circuits and
quantum optics. We address the transfer of quantum information between systems
having different physical natures and defined in Hilbert spaces of different
dimensions. In particular, we investigate the transfer of the entanglement
initially in a non-classical state of a continuous-variable system to a pair of
superconducting charge qubits. This set-up is able to drive an initially
separable state of the qubits into an almost pure, highly entangled state
suitable for quantum information processing.Comment: 4 pages, RevTeX; revised versio