54 research outputs found
Linking Measures for Macroscopic Quantum States via Photon-Spin Mapping
We review and compare several measures that identify quantum states that are
"macroscopically quantum". These measures were initially formulated either for
photonic systems or spin ensembles. Here, we compare them through a simple
model which maps photonic states to spin ensembles. On the one hand, we reveal
problems for some spin measures to handle correctly photonic states that
typically are considered to be macroscopically quantum. On the other hand, we
find significant similarities between other measures even though they were
differently motivated.Comment: 12 pages, 1 figure; published in a special issue of Optics
Communications: "Macroscopic quantumness: theory and applications in optical
sciences"; v2: minor change
Stable macroscopic quantum superpositions
We study the stability of superpositions of macroscopically distinct quantum
states under decoherence. We introduce a class of quantum states with
entanglement features similar to Greenberger-Horne-Zeilinger (GHZ) states, but
with an inherent stability against noise and decoherence. We show that in
contrast to GHZ states, these so-called concatenated GHZ states remain
multipartite entangled even for macroscopic numbers of particles and can be
used for quantum metrology in noisy environments. We also propose a scalable
experimental realization of these states using existing ion-trap set-ups.Comment: 4 pages, 1 figure; v2: minor changes due to referee report
Improved quantum metrology using quantum error-correction
We consider quantum metrology in noisy environments, where the effect of
noise and decoherence limits the achievable gain in precision by quantum
entanglement. We show that by using tools from quantum error-correction this
limitation can be overcome. This is demonstrated in two scenarios, including a
many-body Hamiltonian with single-qubit dephasing or depolarizing noise, and a
single-body Hamiltonian with transversal noise. In both cases we show that
Heisenberg scaling, and hence a quadratic improvement over the classical case,
can be retained. Moreover, for the case of frequency estimation we find that
the inclusion of error-correction allows, in certain instances, for a finite
optimal interrogation time even in the asymptotic limit.Comment: Version 2 is the published version. Appendices contain Supplemental
materia
A true concurrent model of smart contracts executions
The development of blockchain technologies has enabled the trustless
execution of so-called smart contracts, i.e. programs that regulate the
exchange of assets (e.g., cryptocurrency) between users. In a decentralized
blockchain, the state of smart contracts is collaboratively maintained by a
peer-to-peer network of mutually untrusted nodes, which collect from users a
set of transactions (representing the required actions on contracts), and
execute them in some order. Once this sequence of transactions is appended to
the blockchain, the other nodes validate it, re-executing the transactions in
the same order. The serial execution of transactions does not take advantage of
the multi-core architecture of modern processors, so contributing to limit the
throughput. In this paper we propose a true concurrent model of smart contract
execution. Based on this, we show how static analysis of smart contracts can be
exploited to parallelize the execution of transactions.Comment: Full version of the paper presented at COORDINATION 202
Uncertainty relations with the variance and the quantum Fisher information based on convex decompositions of density matrices
We present several inequalities related to the Robertson-Schr\"odinger
uncertainty relation. In all these inequalities, we consider a decomposition of
the density matrix into a mixture of states, and use the fact that the
Robertson-Schr\"odinger uncertainty relation is valid for all these components.
By considering a convex roof of the bound, we obtain an alternative derivation
of the relation in Fr\"owis et al. [Phys. Rev. A 92, 012102 (2015)], and we can
also list a number of conditions that are needed to saturate the relation. We
present a formulation of the Cram\'er-Rao bound involving the convex roof of
the variance. By considering a concave roof of the bound in the
Robertson-Schr\"odinger uncertainty relation over decompositions to mixed
states, we obtain an improvement of the Robertson-Schr\"odinger uncertainty
relation. We consider similar techniques for uncertainty relations with three
variances. Finally, we present further uncertainty relations that provide lower
bounds on the metrological usefulness of bipartite quantum states based on the
variances of the canonical position and momentum operators for two-mode
continuous variable systems. We show that the violation of well-known
entanglement conditions in these systems discussed in Duan et al., [Phys. Rev.
Lett. 84, 2722 (2000)] and Simon [Phys. Rev. Lett. 84, 2726 (2000)] implies
that the state is more useful metrologically than certain relevant subsets of
separable states. We present similar results concerning entanglement conditions
with angular momentum operators for spin systems.Comment: 17 pages including 3 figures, revtex4.2. See also the related work S.
H. Chiew and M. Gessner, Phys. Rev. Research 4, 013076 (2022
Two-mode squeezed states as Schrodinger-cat-like states
In recent years, there has been an increased interest in the generation of
superposition of coherent states with opposite phases, the so-called photonic
Schrodinger-cat states. These experiments are very challenging and so far, cats
involving small photon numbers only have been implemented. Here, we propose to
consider two-mode squeezed states as examples of a Schrodinger-cat-like state.
In particular, we are interested in several criteria aiming to identify quantum
states that are macroscopic superpositions in a more general sense. We show how
these criteria can be extended to continuous variable entangled states. We
apply them to various squeezed states, argue that two-mode squeezed vacuum
states belong to a class of general Schrodinger-cat states and compare the size
of states obtained in several experiments. Our results not only promote
two-mode squeezed states for exploring quantum effects at the macroscopic level
but also provide direct measures to evaluate their usefulness for quantum
metrology.Comment: 5 pages + appendix, one figur
Measures of macroscopicity for quantum spin systems
We investigate the notion of "macroscopicity" in the case of large quantum
spin systems and provide two main results. First, we motivate the Fisher
information as a measure for the macroscopicity of quantum states. Second, we
compare the existing literature of this topic. We report on a hierarchy among
the measures and we conclude that one should carefully distinguish between
"macroscopic quantum states" and "macroscopic superpositions", which is a
strict subclass of the former.Comment: Comments are welcome! v2: Minor improvements of the tex
A matrix product solution for a nonequilibrium steady state of an XX chain
A one dimensional XX spin chain of finite length coupled to reservoirs at
both ends is solved exactly in terms of a matrix product state ansatz. An
explicit representation of matrices of fixed dimension 4 independent of the
chain length is found. Expectations of all observables are evaluated, showing
that all connected correlations, apart from nearest neighbor z-z, are zero.Comment: 11 page
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