Can one certify the preparation of a coherent, many-body quantum state by measurements with bounded accuracy in the presence of noise and decoherence? Here, we introduce a criterion to assess the fragility of large-scale quantum states which is based on the distinguishability of orthogonal states after the action of very small amounts of noise. States which do not pass this criterion are called asymptotically incertifiable. We show that, if a coherent quantum state is asymptotically incertifiable, there exists an incoherent mixture (with entropy at least log 2) which is experimentally indistinguishable from the initial state. The Greenberger-Horne-Zeilinger states are examples of such asymptotically incertifiable states. More generally, we prove that any so-called macroscopic superposition state is asymptotically incertifiable. We also provide examples of quantum states that are experimentally indistinguishable from highly incoherent mixtures, i.e., with an almost-linear entropy in the number of qubits. Finally we show that all unique ground states of local gapped Hamiltonians (in any dimension) are certifiable.Can one certify the preparation of a coherent, many-body quantum state by measurements with bounded accuracy in the presence of noise and decoherence? Here, we introduce a criterion to assess the fragility of large-scale quantum states which is based on the distinguishability of orthogonal states after the action of very small amounts of noise. States which do not pass this criterion are called asymptotically incertifiable. We show that, if a coherent quantum state is asymptotically incertifiable, there exists an incoherent mixture (with entropy at least log 2) which is experimentally indistinguishable from the initial state. The Greenberger-Horne-Zeilinger states are examples of such asymptotically incertifiable states. More generally, we prove that any so-called macroscopic superposition state is asymptotically incertifiable. We also provide examples of quantum states that are experimentally indistinguishable from highly incoherent mixtures, i.e., with an almost-linear entropy in the number of qubits. Finally we show that all unique ground states of local gapped Hamiltonians (in any dimension) are certifiable.

Jun 3, 20130 citations

Stable Macroscopic Quantum Superpositions

Florian Fröwis, Wolfgang Dür

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 setups.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 setups.

arXiv:1012.4472Physical Review LettersMar 16, 2011100 citations

High-dimensional entanglement certification: bounding relative entropy of entanglement in $2d+1$ experiment-friendly measurementsHigh-dimensional entanglement certification: bounding relative entropy of entanglement in $2d+1$ experiment-friendly measurements

Alexandria J. Moore, Andrew M. Weiner

Entanglement -- the coherent correlations between parties in a joint quantum system -- is well-understood and quantifiable in the two-dimensional, two-party case. Higher (>2)-dimensional entangled systems hold promise in extending the capabilities of various quantum information applications. Despite the utility of such systems, methods for quantifying high-dimensional entanglement are more limited and experimentally challenging. We review entanglement certification approaches and the large number of -- often difficult -- measurements required to apply them. We present a novel certification method whose measurement requirements scale linearly with subsystem dimension (scaling with the square-root of the system dimension) and which requires only a single complex measurement. The certification method places a lower-bound on the relative entropy of entanglement of any maximally correlated state thereby certifying system entanglement. A lower bound is also shown for any maximally correlated state in the presence of noise -- the expected experimental case. We discuss experimental realization of all required measurements.Entanglement -- the coherent correlations between parties in a joint quantum system -- is well-understood and quantifiable in the two-dimensional, two-party case. Higher (>2)-dimensional entangled systems hold promise in extending the capabilities of various quantum information applications. Despite the utility of such systems, methods for quantifying high-dimensional entanglement are more limited and experimentally challenging. We review entanglement certification approaches and the large number of -- often difficult -- measurements required to apply them. We present a novel certification method whose measurement requirements scale linearly with subsystem dimension (scaling with the square-root of the system dimension) and which requires only a single complex measurement. The certification method places a lower-bound on the relative entropy of entanglement of any maximally correlated state thereby certifying system entanglement. A lower bound is also shown for any maximally correlated state in the presence of noise -- the expected experimental case. We discuss experimental realization of all required measurements.

arXiv:2210.10717Oct 19, 20220 citations

Equilibration and the eigenstate thermalization hypothesis as limits to observing macroscopic quantum superpositions

Gabriel Dias Carvalho, Pedro S. Correia, Thiago R. de Oliveira

Macroscopic quantum superpositions are widely believed to be unobservable because large systems cannot be perfectly isolated from their environments. Here, we show that even under perfect isolation, intrinsic unitary dynamics in generic many-body systems, as analyzed through the eigenstate thermalization hypothesis and random matrix theory, can suppress the observable signatures of macroscopic coherence. Using the Greenberger-Horne-Zeilinger (GHZ) state as a representative example, we demonstrate that while fully correlated measurements can initially distinguish a macroscopic superposition from its corresponding classical mixture, generic many-body evolution renders them operationally indistinguishable for most times. By analyzing both distinguishability measures and established quantifiers of macroscopic quantumness, we find that equilibration not only hides coherence from accessible observables but also suppresses the corresponding signatures of macroscopic quantumness, in particular within the additive-local framework considered here. These results identify unitary thermalization, independent of environmental decoherence, as a fundamental mechanism that limits the observation of macroscopic quantum effects.Macroscopic quantum superpositions are widely believed to be unobservable because large systems cannot be perfectly isolated from their environments. Here, we show that even under perfect isolation, intrinsic unitary dynamics in generic many-body systems, as analyzed through the eigenstate thermalization hypothesis and random matrix theory, can suppress the observable signatures of macroscopic coherence. Using the Greenberger-Horne-Zeilinger (GHZ) state as a representative example, we demonstrate that while fully correlated measurements can initially distinguish a macroscopic superposition from its corresponding classical mixture, generic many-body evolution renders them operationally indistinguishable for most times. By analyzing both distinguishability measures and established quantifiers of macroscopic quantumness, we find that equilibration not only hides coherence from accessible observables but also suppresses the corresponding signatures of macroscopic quantumness, in particular within the additive-local framework considered here. These results identify unitary thermalization, independent of environmental decoherence, as a fundamental mechanism that limits the observation of macroscopic quantum effects.

quant-pharXiv:2512.11522Physical Review ADec 15, 20250 citations

Partial separability and entanglement criteria for multiqubit quantum states

Michael Seevinck, Jos Uffink

We explore the subtle relationships between partial separability and entanglement of subsystems in multiqubit quantum states and give experimentally accessible conditions that distinguish between various classes and levels of partial separability in a hierarchical order. These conditions take the form of bounds on the correlations of locally orthogonal observables. Violations of such inequalities give strong sufficient criteria for various forms of partial inseparability and multiqubit entanglement. The strength of these criteria is illustrated by showing that they are stronger than several other well-known entanglement criteria (the fidelity criterion, violation of Mermin-type separability inequalities, the Laskowski-\ifmmode \dot{Z}\else \.{Z}\fi{}ukowski criterion, and the D\"ur-Cirac criterion) and also by showing their great noise robustness for a variety of multiqubit states, including $N$ -qubit Greenberger-Horne-Zeilinger states and Dicke states. Furthermore, for $N\ensuremath{\geqslant}3$ they can detect bound entangled states. For all these states, the required number of measurement settings for implementation of the entanglement criteria is shown to be only $N+1$ . If one chooses the familiar Pauli matrices as single-qubit observables, the inequalities take the form of bounds on the antidiagonal matrix elements of a state in terms of its diagonal matrix elements.We explore the subtle relationships between partial separability and entanglement of subsystems in multiqubit quantum states and give experimentally accessible conditions that distinguish between various classes and levels of partial separability in a hierarchical order. These conditions take the form of bounds on the correlations of locally orthogonal observables. Violations of such inequalities give strong sufficient criteria for various forms of partial inseparability and multiqubit entanglement. The strength of these criteria is illustrated by showing that they are stronger than several other well-known entanglement criteria (the fidelity criterion, violation of Mermin-type separability inequalities, the Laskowski-\ifmmode \dot{Z}\else \.{Z}\fi{}ukowski criterion, and the D\"ur-Cirac criterion) and also by showing their great noise robustness for a variety of multiqubit states, including $N$-qubit Greenberger-Horne-Zeilinger states and Dicke states. Furthermore, for $N\ensuremath{\geqslant}3$ they can detect bound entangled states. For all these states, the required number of measurement settings for implementation of the entanglement criteria is shown to be only $N+1$. If one chooses the familiar Pauli matrices as single-qubit observables, the inequalities take the form of bounds on the antidiagonal matrix elements of a state in terms of its diagonal matrix elements.

arXiv:0710.5326Physical Review ASep 2, 2008110 citations

Entanglement and Decoherence: Fragile and Robust Entanglement

Jaroslav Novotný, G. Alber, Igor Jex

The destruction of entanglement of open quantum systems by decoherence is investigated in the asymptotic long-time limit. For this purpose a general and analytically solvable decoherence model is presented which does not involve any weak-coupling or Markovian assumption. It is shown that two fundamentally different classes of entangled states can be distinguished and that they can be influenced significantly by two important environmental properties, namely, its initially prepared state and its size. Quantum states of the first class are fragile against decoherence so that they can be disentangled asymptotically even if coherences between pointer states are still present. Quantum states of the second type are robust against decoherence. Asymptotically they can be disentangled only if also decoherence is perfect. A simple criterion for identifying these two classes on the basis of two-qubit entanglement is presented.The destruction of entanglement of open quantum systems by decoherence is investigated in the asymptotic long-time limit. For this purpose a general and analytically solvable decoherence model is presented which does not involve any weak-coupling or Markovian assumption. It is shown that two fundamentally different classes of entangled states can be distinguished and that they can be influenced significantly by two important environmental properties, namely, its initially prepared state and its size. Quantum states of the first class are fragile against decoherence so that they can be disentangled asymptotically even if coherences between pointer states are still present. Quantum states of the second type are robust against decoherence. Asymptotically they can be disentangled only if also decoherence is perfect. A simple criterion for identifying these two classes on the basis of two-qubit entanglement is presented.

arXiv:1103.3318Physical Review LettersAug 23, 201120 citations

High-dimensional entanglement certification: bounding relative entropy of entanglement in

2d+1

experiment-friendly measurements

N

-qubit Greenberger-Horne-Zeilinger states and Dicke states. Furthermore, for $N\ensuremath{\geqslant}3$ they can detect bound entangled states. For all these states, the required number of measurement settings for implementation of the entanglement criteria is shown to be only

N+1

. If one chooses the familiar Pauli matrices as single-qubit observables, the inequalities take the form of bounds on the antidiagonal matrix elements of a state in terms of its diagonal matrix elements.