# Geza TothIkerbasque - Basque Foundation for Science

Geza Toth

Ph.D.

## About

130

Publications

18,173

Reads

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12,063

Citations

Introduction

Research topic: quantum optics and quantum information
Home pages (with pdfs of all publications and transparencies):
http://www.gtoth.eu/
https://www.gtoth.eu/ResearchGroup.html
http://www.pitomography.eu/
The citation and cumulative impact factor statistics of ResearchGate is noisy. Please see the following web sites:
ResearcherID:
https://www.webofscience.com/wos/author/record/A-6693-2008
Google Scholar:
http://scholar.google.com/citations?user=7NYQHqoAAAAJ

Additional affiliations

September 2008 - present

January 2007 - August 2008

January 2006 - present

Education

January 1996 - December 2000

January 1990 - January 1994

September 1985 - July 1989

**ELTE Apáczai Csere János Gyakorló Gimnázium és Kollégium**

Field of study

- Highschool

## Publications

Publications (130)

Recent experiments demonstrate the production of many thousands of neutral atoms entangled in their spin degrees of freedom. We present a criterion for estimating the amount of entanglement based on a measurement of the global spin. It outperforms previous criteria and applies to a wider class of entangled states, including Dicke states. Experiment...

We show an efficient method to compute entanglement measures based on convex
roof constructions. In particular, our method is applicable to measures that,
for pure states, can be written as low order polynomials of operator
expectation values. We show how to compute the linear entropy of entanglement,
the linear entanglement of assistance, and a bo...

We show that multiparticle quantum states that have a positive partial transpose with respect to all bipartitions of the particles can outperform separable states in linear interferometers. We introduce a powerful iterative method to find such states. We present some examples for multipartite states and examine the scaling of the precision with the...

We consider bipartite entangled states that cannot outperform separable states in any linear interferometer. Then, we show that these states can still be more useful metrologically than separable states if several copies of the state are provided or an ancilla is added to the quantum system. We present a general method to find the local Hamiltonian...

We consider quantum metrology with several copies of bipartite and multipartite quantum states.
We characterize the metrological usefulness by determining how much the state outperforms separable
states. We identify a large class of entangled states that become maximally useful for metrology
in the limit of large number of copies, even if the state...

The concept of randomized measurements on individual particles has proven to be useful for analyzing quantum systems and is central for methods like shadow tomography of quantum states. We introduce randomized measurements as a tool in quantum information processing. Our idea is to perform measurements of collective angular momentum on a quantum sy...

Generalizing the well-known spin-squeezing inequalities, we study the relation between squeezing of collective $N$-particle $su(d)$ operators and many-body entanglement geometry in multi-particle systems. For that aim, we define the set of pseudo-separable states, which are mixtures of products of single-particle states that lie in the $(d^2-1)$-di...

We define the quantum Wasserstein distance such that the optimization of the coupling is carried out over bipartite separable states rather than bipartite quantum states in general, and examine its properties. Surprisingly, we find that the self-distance is related to the quantum Fisher information. We present a transport map corresponding to an op...

We use entanglement witnesses to detect entanglement in the XY chain in thermal equilibrium and determine the temperature bound below which the state is detected as entangled. We consider the entanglement witness based on the Hamiltonian. Such a witness detects a state as entangled if its energy is smaller than the energy of separable states. We al...

We present a method to detect bipartite entanglement based on number-phase-like uncertainty relations in split spin ensembles. First, we derive an uncertainty relation that plays the role of a number-phase uncertainty for spin systems. It is important that the relation is given with well-defined and easily measurable quantities, and that it does no...

This is a perspective on "k-stretchability of entanglement, and the duality of k-separability and k-producibility" by Szil\'ard Szalay, published in Quantum 3, 204 (2019).

We define the quantum Wasserstein distance such that the optimization is carried out over bipartite separable states rather than bipartite quantum states in general, and examine its properties. Surprisingly, we find that its self-distance is related to the quantum Fisher information. We discuss how the quantum Wasserstein distance introduced is con...

Entanglement witnesses for the XY-chain are calculated, either using upper bounds of the energy of separable states or through the calculation of bipartite entanglement negativity. We obtain temperature bound for the system in thermal equilibrium and determine entangled post-quench states after a sudden quench, when the parameters of the Hamiltonia...

We discuss efficient methods to optimize the metrological performance over local Hamiltonians in a bipartite quantum system. For a given quantum state, our methods find the best local Hamiltonian for which the state outperforms separable states the most from the point of view of quantum metrology. We show that this problem can be reduced to maximiz...

We consider quantum metrology with several copies of bipartite and multipartite quantum states. We identify a large class of states that become maximally useful for metrology in the limit of infinite number of copies. The maximally achievable metrological usefulness is attained exponentially fast in the number of copies. We show that, on the other...

We present several inequalities related to the Robertson-Schrödinger 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-Schrödinger uncertainty relation is valid for all these components. By considering a convex roof of the bound, we obtain...

We discuss recent findings relating the quantum Fisher information to convex roofs of variances. We present several improvements on the Robertson-Schr\"odinger uncertainty relation. In all these improvements, we consider a decomposition of the density matrix into a mixture of pure states, and use the fact that the Robertson-Schr\"odinger uncertaint...

Bipartite entangled quantum states with a positive partial transpose (PPT), i.e., PPT entangled states, are usually considered very weakly entangled. Since no pure entanglement can be distilled from them, they are also called bound entangled. In this paper, we present two classes of (2d×2d)-dimensional PPT entangled states for any d≥2 which outperf...

We discuss how to detect bipartite entanglement in a Dicke state of many spin-1/2 particles. The particles are split into two subensembles, then collective angular momentum measurements are carried out locally on the two parts. First, we present a bipartite Einstein-Podolsky-Rosen (EPR) steering criterion. Then, we present an entanglement condition...

We consider bipartite entangled states that cannot outperform separable states in any linear interferometer. We show that these states can be more useful metrologically than separable states if several copies of the state are provided or an ancilla is added.

Quantum technologies use entanglement to outperform classical technologies, and often employ strong cooling and isolation to protect entangled entities from decoherence by random interactions. Here we show that the opposite strategy—promoting random interactions—can help generate and preserve entanglement. We use optical quantum non-demolition meas...

Bipartite entangled quantum states with a positive partial transpose (in short PPT entangled states) are usually considered to be very weakly entangled, as no pure entanglement can be distilled from them. In this paper we present two classes of ($D\times D$)-dimensional PPT entangled states for any even $D\ge 4$ which outperform all separable state...

We consider bipartite entangled states that cannot outperform separable states in any linear interferometer. Then, we show that these states can still be more useful metrologically than separable states if several copies of the state are provided or an ancilla is added to the quantum system. We present a general method to find the local Hamiltonian...

We study gradient magnetometry with an ensemble of atoms with arbitrary spin. We consider the case of a very general spatial probability distribution function. We calculate precision bounds for estimating the gradient of the magnetic field based on the quantum Fisher information. For quantum states that are invariant under homogeneous magnetic fiel...

We study quantum entanglement loss due to environmental interaction in a condensed matter system with a complex geometry relevant to recent proposals for computing with single electrons at the nanoscale.
We consider a system consisting of two qubits, each realized by an electron in a quantum double-dot, which are initially in an entangled Bell sta...

We introduce a general scheme to detect various multiparticle entanglement structures from global non-permutationally invariant observables. In particular, we derive bounds on the variance of non-permutationally invariant and collective operators for the verification of $k$-party entanglement. For a family of observables related to the spin structu...

We introduce an entanglement-depth criterion optimized for Planar Quantum Squeezed (PQS) states. It is connected with the sensitivity of such states for estimating an arbitrary, not necessarily small phase. The criterion makes it possible to detect the minimal fraction of particles in $(k+1)$-partite entangled groups and improves past approaches fo...

Splitting the entanglement
When particles in a quantum mechanical system are entangled, a measurement performed on one part of the system can affect the results of the same type of measurement performed on another part—even if these subsystems are physically separated. Kunkel et al. , Fadel et al. , and Lange et al. achieved this so-called distribu...

We show how to verify the metrological usefulness of quantum states based on the expectation values of an arbitrarily chosen set of observables. In particular, we estimate the quantum Fisher information as a figure of merit of metrological usefulness. Our approach gives a tight lower bound on the quantum Fisher information for the given incomplete...

We examine important properties of the difference between the variance and the quantum Fisher information over four, i.e., $(\Delta A)^2-F_Q[\varrho,A]/4.$ We find that this quantity is equal to a generalized variance defined in Petz [J. Phys. A 35, 929 (2002)] and Gibilisco, Hiai, and Petz [IEEE Trans. Inf. Theory 55, 439 (2009)]. For the rank-2 c...

Wepresent criteria to detect the depth of entanglement in macroscopic ensembles of spin-j particles
using the variance and second moments of the collective spin components. The class of states detected
goes beyond traditional spin-squeezed states by including Dicke states and other unpolarized states.
The criteria derived are easy to evaluate numer...

We investigate phase and frequency estimation with different measurement strategies under the effect of collective phase noise. First, we consider the standard linear estimation scheme and present an experimentally realisable optimization of the initial probe states by collective rotations. We identify the optimal rotation angle for different measu...

The statistical nature of measurements alone easily causes unphysical
estimates in quantum state tomography. We show that multinomial or Poissonian
noise results in eigenvalue distributions converging to the Wigner semicircle
distribution for already a modest number of qubits. This enables to specify the
number of measurements necessary to avoid un...

We show how to verify the metrological usefulness of quantum states based on
few measurements. In particular, we estimate the quantum Fisher information as
a figure of merit of metrological usefulness. Our approach is optimal since it
gives a tight lower bound on the quantum Fisher information for the given
incomplete information. We apply our meth...

We present a method to verify the metrological usefulness of noisy Dicke
states of a particle ensemble with only a few collective measurements, without
the need for a direct measurement of the sensitivity. Our method determines the
usefulness of the state for the usual protocol for estimating the angle of
rotation with Dicke states, which is based...

We show how a test of macroscopic realism based on Leggett-Garg inequalities
(LGIs) can be performed in a macroscopic system. Using a continuous-variable
approach, we consider quantum non-demolition (QND) measurements applied to
atomic ensembles undergoing magnetically-driven coherent oscillation. We
identify measurement schemes requiring only Gaus...

Detection of entanglement in bipartite states is a fundamental
task in quantum information. The first method to verify entanglement
in mixed states was the partial-transpose criterion. Subsequently,
numerous quantifiers for bipartite entanglement were introduced,
among them concurrence and negativity. Surprisingly,
these quantities are often treate...

We summarize important recent advances in quantum metrology, in connection to experiments in cold gases, trapped cold atoms and photons. First we review simple metrological setups, such as quantum metrology with spin squeezed states, with Greenberger–Horne–Zeilinger states, Dicke states and singlet states. We calculate the highest precision achieva...

Quantum state tomography suffers from the measurement effort increasing exponentially with the number of qubits. Here, we demonstrate permutationally invariant tomography for which, contrary to conventional tomography, all resources scale polynomially with the number of qubits both in terms of the measurement effort as well as the computational pow...

We report the generation of a macroscopic singlet state in a cold atomic
sample via quantum non-demolition (QND) measurement induced spin squeezing. We
observe 3 dB of spin squeezing and detect entanglement of up to $5.5\times10^5
$ atoms with $5\sigma$ statistical significance using a generalized spin
squeezing inequality. The degree of squeezing...

Quantum state tomography suffers from the measurement effort increasing
exponentially with the number of qubits. Here, we demonstrate permutationally
invariant tomography for which, contrary to conventional tomography, all
resources scale polynomially with the number of qubits both in terms of the
measurement effort as well as the computational pow...

A complete set of generalized spin squeezing inequalities is derived for a
ensemble of particles with an arbitrary spin. Our conditions are formulated
with the expectation values and second moments of the collective angular
momentum coordinates. A method for mapping the spin squeezing inequalities for
spin-1/2 particles to entanglement conditions f...

DOI:https://doi.org/10.1103/PhysRevA.87.039912

The quantum variance of a self-adjoint operator depends on a density matrix whose particular example is a pure state (formulated by a projection). A general variance can be obtained from certain variances of pure states. This is very different from the probabilistic case. All rights reserved

In this paper we are discussing the question how a continuous quantum system
can be simulated by mean field fluctuations of a finite number of qubits. On
the kinematical side this leads to a convergence result which states that
appropriately chosen fluctuation operators converge in a certain weak sense
(i.e. we are comparing expectation values) to...

Feasible tomography schemes for large particle numbers must possess, besides
an appropriate data acquisition protocol, also an efficient way to reconstruct
the density operator from the observed finite data set. Since state
reconstruction typically requires the solution of a non-linear large-scale
optimization problem, this is a major challenge in...

We extend the criteria for $k$-particle entanglement from the spin squeezing
parameter presented in [A.S. S{\o}rensen and K. M{\o}lmer, Phys. Rev. Lett.
{\bf 86}, 4431 (2001)] to systems with a fluctating number of particles. We
also discuss how other spin squeezing inequalities can be generalized to this
situation. Further, we give an operational...

We present a method for measuring magnetic field gradients with macroscopic
singlet states realized with ensembles of spin-j particles. While the singlet
state is completely insensitive to homogeneous magnetic fields, the variance of
its collective spin components is highly sensitive to field gradients. We
compute the dynamics of this variance anal...

We report on an experiment for generating singlet states in a cold atomic ensemble. We use quantum non-demolition measurement and feedback control to produce a macroscopic spin state with total spin zero and reduced spin fluctuations.

We show that the variance is its own concave roof. For rank-2 density
matrices and operators with zero diagonal elements in the eigenbasis of the
density matrix, we prove analytically that the quantum Fisher information is 4
times the convex roof of the variance. Strong numerical evidence suggests that
this statement is true even for operators with...

Efficient analysis of multi-partite entangled quantum states is an important task. Here, we present a novel tomographic scheme where, under the restriction of permutational invariance, the measurement effort scales quadratically with the number of qubits.

We report on an experiment underway for generating singlet states in a cold atomic ensemble. We have developed a new detection system with the capability of real time measurement and feedback control.

We determine the complete set of generalized spin squeezing inequalities,
given in terms of the collective angular momentum components, for particles
with an arbitrary spin. They can be used for the experimental detection of
entanglement in an ensemble in which the particles cannot be individually
addressed. We also present a large set of criteria...

DOI:https://doi.org/10.1103/PhysRevA.83.019905

We define the generalized variance based on requiring that (i) it equals the usual variance for pure states and (ii) it is concave. For a quantum system of any size, we show that the usual variance is the smallest generalized variance, which makes it optimal for using it in entanglement criteria based on uncertainty relations. Similarly, we define...

We study the entangled states that can be generated using two species of atoms trapped in independently movable, two-dimensional optical lattices. We show that using two sets of measurements it is possible to measure a set of entanglement witness operators distributed over arbitrarily large regions of the lattice, and use these witnesses to produce...

We present several entanglement criteria in terms of the quantum Fisher
information that help to relate various forms of multipartite entanglement to
the sensitivity of phase estimation. We show that genuine multipartite
entanglement is necessary to reach the maximum sensitivity in some very general
metrological tasks using a two-arm linear interfe...

We present a scalable method for the tomography of large multiqubit quantum
registers. It acquires information about the permutationally invariant part of
the density operator, which is a good approximation to the true state in many,
relevant cases. Our method gives the best measurement strategy to minimize the
experimental effort as well as the un...

We study squeezing of the spin uncertainties by quantum non-demolition (QND) measurement in non-polarized spin ensembles. Unlike the case of polarized ensembles, the QND measurements can be performed with negligible back-action, which allows, in principle, perfect spin squeezing as quantified by [G. Toth et al., Phys. Rev. Lett. 99, 250405 (2007)]....

Photon sources for multi-photon entanglement experiments are commonly based on the process of spontaneous parametric down conversion. Due to the probabilistic photon production, such experiments suffer from low multiphoton count rates. To increase this count rate, we present a novel SPDC pump source based on a femtosecond UV enhancement cavity that...

We study the separability of symmetric bipartite quantum states and show that a single correlation measurement is sufficient to detect the entanglement of any bipartite symmetric state with a non-positive partial transpose. We also discuss entanglement conditions and entanglement witnesses for states with a positive partial transpose. Comment: 5 pa...

We present general numerical methods to construct witness operators for entanglement detection and estimation of the fidelity. Our methods are applied to detecting entanglement in the vicinity of a six-qubit Dicke state with three excitations and also to further entangled symmetric states. All our witnesses are designed to keep the measurement effo...

We consider a number operator-annihilation operator uncertainty as a well behaved alternative to the number-phase uncertainty relation, and examine its properties. We find a formulation in which the bound on the product of uncertainties depends on the expectation value of the particle number. Thus, while the bound is not a constant, it is a quantit...

What is the relation between spin squeezing and entanglement? To clarify this, we derive the full set of generalized spin squeezing inequalities for the detection of entanglement. These are inequalities for the mean values and variances of the collective angular momentum components. They can be used for the experimental detection of entanglement in...

How can one prove that a given quantum state is entangled? In this paper we review different methods that have been proposed for entanglement detection. We first explain the basic elements of entanglement theory for two or more particles and then entanglement verification procedures such as Bell inequalities, entanglement witnesses, the determinati...

We report on the experimental observation and characterization of a six-photon entangled Dicke state. We obtain a fidelity as high as 0.654$\pm$0.024 and prove genuine six-photon entanglement by, amongst others, a two-setting witness yielding -0.422$\pm$0.148. This state has remarkable properties; e.g., it allows obtaining inequivalent entangled st...

We study the separability of permutationally symmetric quantum states. We show that for bipartite symmetric systems most of the relevant entanglement criteria coincide. However, we provide a method to generate examples of bound entangled states in symmetric systems, for the bipartite and the multipartite case. These states shed some new light on th...