20 research outputs found
Quantifying entanglement in two-mode Gaussian states
Entangled two-mode Gaussian states are a key resource for quantum information
technologies such as teleportation, quantum cryptography and quantum
computation, so quantification of Gaussian entanglement is an important
problem. Entanglement of formation is unanimously considered a proper measure
of quantum correlations, but for arbitrary two-mode Gaussian states no
analytical form is currently known. In contrast, logarithmic negativity is a
measure straightforward to calculate and so has been adopted by most
researchers, even though it is a less faithful quantifier. In this work, we
derive an analytical lower bound for entanglement of formation of generic
two-mode Gaussian states, which becomes tight for symmetric states and for
states with balanced correlations. We define simple expressions for
entanglement of formation in physically relevant situations and use these to
illustrate the problematic behavior of logarithmic negativity, which can lead
to spurious conclusions.Comment: 8 pages,3 figs; The original submission gave an analytical formula
that was claimed to give the entanglement of formation for arbitrary two-mode
Gaussian states - this was incorrect. The formula gives a lower bound of EoF
which saturates for symmetric states and for states with balanced
correlations, and is a good approximation for most other states. This error
is corrected in the revised versio
Quantifying entanglement of formation for two-mode Gaussian states: Analytical expressions for upper and lower bounds and numerical estimation of its exact value
Entanglement of formation quantifies the entanglement of a state in terms of
the entropy of entanglement of the least entangled pure state needed to prepare
it. An analytical expression for this measure exists only for special cases,
and finding a closed formula for an arbitrary state still remains an open
problem. In this work we focus on two-mode Gaussian states, and we derive
narrow upper and lower bounds for the measure that get tight for several
special cases. Further, we show that the problem of calculating the actual
value of the entanglement of formation for arbitrary two-mode Gaussian states
reduces to a trivial single parameter optimization process, and we provide an
efficient algorithm for the numerical calculation of the measure.Comment: 5 pages, 2 figures In this third version a few typos of the first and
second versions have been correcte
Simulation of Gaussian channels via teleportation and error correction of Gaussian states
Gaussian channels are the typical way to model the decoherence introduced by
the environment in continuous-variable quantum states. It is known that those
channels can be simulated by a teleportation protocol using as a resource state
either a maximally entangled state passing through the same channel, i.e., the
Choi-state, or a state that is entangled at least as much as the Choi-state.
Since the construction of the Choi-state requires infinite mean energy and
entanglement, i.e. it is unphysical, we derive instead every physical state
able to simulate a given channel through teleportation with finite resources,
and we further find the optimal ones, i.e., the resource states that require
the minimum energy and entanglement. We show that the optimal resource states
are pure and equally entangled to the Choi-state as measured by the
entanglement of formation. We also show that the same amount of entanglement is
enough to simulate an equally decohering channel, while even more entanglement
can simulate less decohering channels. We, finally, use that fact to generalize
a previously known error correction protocol by making it able to correct noise
coming not only from pure loss but from thermal loss channels as well.Comment: 12 pages, 8 figure
Teleportation-based collective attacks in Gaussian quantum key distribution
In Gaussian quantum key distribution eavesdropping attacks are conventionally modeled through the universal entangling cloner scheme, which is based on the premise that the whole environment is under control of the adversary, i.e., the eavesdropper purifies the system. This assumption implies that the eavesdropper has either access to an identity (noiseless) channel or an infinite amount of entanglement in order to simulate such an identity channel. In this work we challenge the necessity of this assumption and we propose a teleportation-based eavesdropping attack, where the eavesdropper is not assumed to have access to the shared channel, that represents the unavoidable noise due to the environment. Under collective measurements, this attack reaches optimality in the limit of an infinite amount of entanglement, while for finite entanglement resources it outperforms the corresponding optimal individual attack. We also calculate the minimum amount of distributed entanglement that is necessary for this eavesdropping scheme, since we consider it as the operationally critical quantity capturing the limitations of a realistic attack. We conclude that the fact that an infinite amount of entanglement is required for an optimal collective eavesdropping attack signifies the robustness of Gaussian quantum key distribution
Simulation of Open Quantum Systems via Low-Depth Convex Unitary Evolutions
Simulating physical systems on quantum devices is one of the most promising
applications of quantum technology. Current quantum approaches to simulating
open quantum systems are still practically challenging on NISQ-era devices,
because they typically require ancilla qubits and extensive controlled
sequences. In this work, we propose a hybrid quantum-classical approach for
simulating a class of open system dynamics called random-unitary channels.
These channels naturally decompose into a series of convex unitary evolutions,
which can then be efficiently sampled and run as independent circuits. The
method does not require deep ancilla frameworks and thus can be implemented
with lower noise costs. We implement simulations of open quantum systems up to
dozens of qubits and with large channel rank.Comment: 6 pages, 5 figure
Multipartite Gaussian Entanglement of Formation
Entanglement of formation is a fundamental measure that quantifies the
entanglement of bipartite quantum states. This measure has recently been
extended into multipartite states taking the name -entanglement of
formation. In this work, we follow an analogous multipartite extension for the
Gaussian version of entanglement of formation, and focusing on the the finest
partition of a multipartite Gaussian state we show this measure is fully
additive and computable for 3-mode Gaussian states
Maximum entanglement of formation for a two-mode Gaussian state over passive operations
We quantify the maximum amount of entanglement of formation (EoF) that can be
achieved by continuous-variable states under passive operations, which we refer
to as EoF-potential. Focusing, in particular, on two-mode Gaussian states we
derive analytical expressions for the EoF-potential for specific classes of
states. For more general states, we demonstrate that this quantity can be
upper-bounded by the minimum amount of squeezing needed to synthesize the
Gaussian modes, a quantity called squeezing of formation. Our work, thus,
provides a new link between non-classicality of quantum states and the
non-classicality of correlations.Comment: Revised versio
Tight bounds for private communication over bosonic Gaussian channels based on teleportation simulation with optimal finite resources
Upper bounds for private communication over quantum channels can be derived
by adopting channel simulation, protocol stretching, and relative entropy of
entanglement. All these ingredients have led to single-letter upper bounds to
the secret key capacity which can be directly computed over suitable resource
states. For bosonic Gaussian channels, the tightest upper bounds have been
derived by employing teleportation simulation over asymptotic resource states,
namely the asymptotic Choi matrices of these channels. In this work, we adopt a
different approach. We show that teleporting over an analytical class of
finite-energy resource states allows us to closely approximate the ultimate
bounds for increasing energy, so as to provide increasingly tight upper bounds
to the secret-key capacity of one-mode phase-insensitive Gaussian channels. We
then show that an optimization over the same class of resource states can be
used to bound the maximum secret key rates that are achievable in a finite
number of channel uses.Comment: 10 pages, 5 figure
On the equivalence between squeezing and entanglement potential for two-mode Gaussian states
The maximum amount of entanglement achievable under passive transformations
by continuous-variable states is called the entanglement potential. Recent work
has demonstrated that the entanglement potential is upper-bounded by a simple
function of the squeezing of formation, and that certain classes of two-mode
Gaussian states can indeed saturate this bound, though saturability in the
general case remains an open problem. In this study, we introduce a larger
class of states that we prove saturates the bound, and we conjecture that all
two-mode Gaussian states can be passively transformed into this class, meaning
that for all two-mode Gaussian states, entanglement potential is equivalent to
squeezing of formation. We provide an explicit algorithm for the passive
transformations and perform extensive numerical testing of our claim, which
seeks to unite the resource theories of two characteristic quantum properties
of continuous-variable systems.Comment: 10 pages, 2 figure
Optimal probes for continuous variable quantum illumination
Quantum illumination is the task of determining the presence of an object in
a noisy environment. We determine the optimal continuous variable states for
quantum illumination in the limit of zero object reflectivity. We prove that
the optimal single mode state is a coherent state, while the optimal two mode
state is the two-mode squeezed-vacuum state. We find that these probes are not
optimal at non-zero reflectivity, but remain near optimal. This demonstrates
the viability of the continuous variable platform for an experimentally
accessible, near optimal quantum illumination implementation.Comment: 7 pages, 3 figures