100 research outputs found
Entropy-power uncertainty relations : towards a tight inequality for all Gaussian pure states
We show that a proper expression of the uncertainty relation for a pair of
canonically-conjugate continuous variables relies on entropy power, a standard
notion in Shannon information theory for real-valued signals. The resulting
entropy-power uncertainty relation is equivalent to the entropic formulation of
the uncertainty relation due to Bialynicki-Birula and Mycielski, but can be
further extended to rotated variables. Hence, based on a reasonable assumption,
we give a partial proof of a tighter form of the entropy-power uncertainty
relation taking correlations into account and provide extensive numerical
evidence of its validity. Interestingly, it implies the generalized
(rotation-invariant) Schr\"odinger-Robertson uncertainty relation exactly as
the original entropy-power uncertainty relation implies Heisenberg relation. It
is saturated for all Gaussian pure states, in contrast with hitherto known
entropic formulations of the uncertainty principle.Comment: 15 pages, 5 figures, the new version includes the n-mode cas
Quantum thermodynamics in a multipartite setting: A resource theory of local Gaussian work extraction for multimode bosonic systems
Quantum thermodynamics can be cast as a resource theory by considering free
access to a heat bath, thereby viewing the Gibbs state at a fixed temperature
as a free state and hence any other state as a resource. Here, we consider a
multipartite scenario where several parties attempt at extracting work locally,
each having access to a local heat bath (possibly with a different
temperature), assisted with an energy-preserving global unitary. As a specific
model, we analyze a collection of harmonic oscillators or a multimode bosonic
system. Focusing on the Gaussian paradigm, we construct a reasonable resource
theory of local activity for a multimode bosonic system, where we identify as
free any state that is obtained from a product of thermal states (possibly at
different temperatures) acted upon by any linear-optics (passive Gaussian)
transformation. The associated free operations are then all linear-optics
transformations supplemented with tensoring and partial tracing. We show that
the local Gaussian extractable work (if each party applies a Gaussian unitary,
assisted with linear optics) is zero if and only if the covariance matrix of
the system is that of a free state. Further, we develop a resource theory of
local Gaussian extractable work, defined as the difference between the trace
and symplectic trace of the covariance matrix of the system. We prove that it
is a resource monotone that cannot increase under free operations. We also
provide examples illustrating the distillation of local activity and local
Gaussian extractable work.Comment: 22 pages, 5 figures, minor corrections to make it close to the
published version, updated list of reference
A tight uniform continuity bound for the Arimoto-R\'enyi conditional entropy and its extension to classical-quantum states
We prove a tight uniform continuity bound for Arimoto's version of the
conditional -R\'enyi entropy, for the range . This
definition of the conditional R\'enyi entropy is the most natural one among the
multiple forms which exist in the literature, since it satisfies two desirable
properties of a conditional entropy, namely, the fact that conditioning reduces
entropy, and that the associated reduction in uncertainty cannot exceed the
information gained by conditioning. Furthermore, it has found interesting
applications in various information theoretic tasks such as guessing with side
information and sequential decoding. This conditional entropy reduces to the
conditional Shannon entropy in the limit , and this in turn
allows us to recover the recently obtained tight uniform continuity bound for
the latter from our result. Finally, we apply our result to obtain a tight
uniform continuity bound for the conditional -R\'enyi entropy of a
classical-quantum state, for in the same range as above. This again
yields the corresponding known bound for the conditional entropy of the state
in the limit .Comment: 23 pages. Changes in v2: new references added and minor corrections
to existing reference
Complexity of Gaussian quantum optics with a limited number of non-linearities
It is well known in quantum optics that any process involving the preparation
of a multimode gaussian state, followed by a gaussian operation and gaussian
measurements, can be efficiently simulated by classical computers. Here, we
provide evidence that computing transition amplitudes of Gaussian processes
with a single-layer of non-linearities is hard for classical computers. To do
so, we show how an efficient algorithm to solve this problem could be used to
efficiently approximate outcome probabilities of a Gaussian boson sampling
experiment. We also extend this complexity result to the problem of computing
transition probabilities of Gaussian processes with two layers of
non-linearities, by developing a Hadamard test for continuous-variable systems
that may be of independent interest. Given recent experimental developments in
the implementation of photon-photon interactions, our results may inspire new
schemes showing quantum computational advantage or algorithmic applications of
non-linear quantum optical systems realizable in the near-term.Comment: 5 pages for the main file, 8 pages for the appendix, 3 figure
Two-boson quantum interference in time
The celebrated Hong-Ou-Mandel effect is the paradigm of two-particle quantum
interference. It has its roots in the symmetry of identical quantum particles,
as dictated by the Pauli principle. Two identical bosons impinging on a beam
splitter (of transmittance 1/2) cannot be detected in coincidence at both
output ports, as confirmed in numerous experiments with light or even matter.
Here, we establish that partial time reversal transforms the beamsplitter
linear coupling into amplification. We infer from this duality the existence of
an unsuspected two-boson interferometric effect in a quantum amplifier (of gain
2) and identify the underlying mechanism as timelike indistinguishability. This
fundamental mechanism is generic to any bosonic Bogoliubov transformation, so
we anticipate wide implications in quantum physics.Comment: 12 pages, 9 figure
Bosonic autonomous entanglement engines with weak bath coupling are impossible
Entanglement is a fundamental feature of quantum physics and a key resource
for quantum communication, computing and sensing. Entangled states are fragile
and maintaining coherence is a central challenge in quantum information
processing. Nevertheless, entanglement can be generated and stabilised through
dissipative processes. In fact, entanglement has been shown to exist in the
steady state of certain interacting quantum systems subject solely to
incoherent coupling to thermal baths. This has been demonstrated in a range of
bi- and multipartite settings using systems of finite dimension. Here we focus
on the steady state of infinite-dimensionsional bosonic systems. Specifically,
we consider any set of bosonic modes undergoing excitation-number-preserving
interactions of arbitrary strength and divided between an arbitrary number of
parties that each couple weakly to thermal baths at different temperatures. We
show that the steady state is always separable.Comment: 10 pages, 1 figur
Majorization ladder in bosonic Gaussian channels
We show the existence of a majorization ladder in bosonic Gaussian channels,
that is, we prove that the channel output resulting from the
energy eigenstate (Fock state) majorizes the channel output resulting from the
energy eigenstate (Fock state). This reflects a remarkable
link between the energy at the input of the channel and a disorder relation at
its output as captured by majorization theory. This result was previously known
in the special cases of a pure-loss channel and quantum-limited amplifier, and
we achieve here its nontrivial generalization to any single-mode
phase-covariant (or -contravariant) bosonic Gaussian channel. The key to our
proof is the explicit construction of a column-stochastic matrix that relates
the outputs of the channel for any two subsequent Fock states at its input,
which is made possible by exploiting a recently found recurrence relation on
multiphoton transition probabilities for Gaussian unitaries [M. G. Jabbour and
N. J. Cerf, Phys. Rev. Research 3, 043065 (2021)]. We then discuss possible
generalizations and implications of our results.Comment: 7 pages, 3 figures, 1 tabl
Majorization preservation of Gaussian bosonic channels
It is shown that phase-insensitive Gaussian bosonic channels are majorization-preserving over the set of passive states of the harmonic oscillator. This means that comparable passive states under majorization are transformed into equally comparable passive states by any phase-insensitive Gaussian bosonic channel. Our proof relies on a new preorder relation called Fock-majorization, which coincides with regular majorization for passive states but also induces another order relation in terms of mean boson number, thereby connecting the concepts of energy and disorder of a quantum state. The consequences of majorization preservation are discussed in the context of the broadcast communication capacity of Gaussian bosonic channels. Because most of our results are independent of the specific nature of the system under investigation, they could be generalized to other quantum systems and Hamiltonians, providing a new tool that may prove useful in quantum information theory and especially quantum thermodynamics.SCOPUS: ar.jinfo:eu-repo/semantics/publishe
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