28 research outputs found
Fast optimization of parametrized quantum optical circuits
Parametrized quantum optical circuits are a class of quantum circuits in
which the carriers of quantum information are photons and the gates are optical
transformations. Classically optimizing these circuits is challenging due to
the infinite dimensionality of the photon number vector space that is
associated to each optical mode. Truncating the space dimension is unavoidable,
and it can lead to incorrect results if the gates populate photon number states
beyond the cutoff. To tackle this issue, we present an algorithm that is orders
of magnitude faster than the current state of the art, to recursively compute
the exact matrix elements of Gaussian operators and their gradient with respect
to a parametrization. These operators, when augmented with a non-Gaussian
transformation such as the Kerr gate, achieve universal quantum computation.
Our approach brings two advantages: first, by computing the matrix elements of
Gaussian operators directly, we don't need to construct them by combining
several other operators; second, we can use any variant of the gradient descent
algorithm by plugging our gradients into an automatic differentiation framework
such as TensorFlow or PyTorch. Our results will find applications in quantum
optical hardware research, quantum machine learning, optical data processing,
device discovery and device design.Comment: 21 pages, 10 figure
Hamiltonians for one-way quantum repeaters
Quantum information degrades over distance due to the unavoidable
imperfections of the transmission channels, with loss as the leading factor.
This simple fact hinders quantum communication, as it relies on propagating
quantum systems. A solution to this issue is to introduce quantum repeaters at
regular intervals along a lossy channel, to revive the quantum signal. In this
work we study unitary one-way quantum repeaters, which do not need to perform
measurements and do not require quantum memories, and are therefore
considerably simpler than other schemes. We introduce and analyze two methods
to construct Hamiltonians that generate a repeater interaction that can beat
the fundamental repeaterless key rate bound even in the presence of an
additional coupling loss, with signals that contain only a handful of photons.
The natural evolution of this work will be to approximate a repeater
interaction by combining simple optical elements.Comment: 8 pages, 3 figure
Full characterization of the quantum spiral bandwidth of entangled biphotons
Spontaneous parametric down-conversion has been shown to be a reliable source of entangled photons. Among the wide range of properties shown to be entangled, it is the orbital angular momentum that is the focus of our study. We investigate, in particular, the bi-photon state generated using a Gaussian pump beam. We derive an expression for the simultaneous correlations in the orbital angular momentum, l, and radial momentum, p, of the down-converted Laguerre-Gaussian beams. Our result allows us, for example, to calculate the spiral bandwidth with no restriction on the geometry of the beams: l, p, and the beam widths are all free parameters. Moreover, we show that, with the usual paraxial and collinear approximations, a fully analytic expression for the correlations can be derived
Recovering full coherence in a qubit by measuring half of its environment
When quantum systems interact with the environment they lose their quantum
properties, such as coherence. Quantum erasure makes it possible to restore
coherence in a system by measuring its environment, but accessing the whole of
it may be prohibitive: realistically one might have to concentrate only on an
accessible subspace and neglect the rest. If that is the case, how good is
quantum erasure? In this work we compute the largest coherence that we can expect to recover in a qubit, as a function of
the dimension of the accessible and of the inaccessible subspaces of its
environment. We then imagine the following game: we are given a uniformly
random pure state of qubits and we are asked to compute the largest
coherence that we can retrieve on one of them by optimally measuring a certain
number of the others. We find a surprising effect around the
value : the recoverable coherence sharply transitions between 0
and 1, indicating that in order to restore full coherence on a qubit we need
access to only half of its physical environment (or in terms of degrees of
freedom to just the square root of them). Moreover, we find that the
recoverable coherence becomes a typical property of the whole ensemble as
grows.Comment: 4 pages, 5 figure
A "fair sampling" perspective on an apparent violation of duality
In the event in which a quantum mechanical particle can pass from an initial
state to a final state along two possible paths, the duality principle states
that "the simultaneous observation of wave and particle behavior is
prohibited". [M. O. Scully, B.-G. Englert, and H. Walther. Nature, 351:111-116,
1991.] emphasized the importance of additional degrees of freedom in the
context of complementarity. In this paper, we show how the consequences of
duality change when allowing for biased sampling, that is, postselected
measurements on specific degrees of freedom of the environment of the two-path
state. Our work contributes to the explanation of previous experimental
apparent violations of duality [R. Menzel, D. Puhlmann, A. Heuer, and W. P.
Schleich. Proc. Natl. Acad. Sci., 109(24):9314-9319, 2012.] and opens up the
way for novel experimental tests of duality.Comment: 10 pages, 8 figure