arXiv:1611.06064 · Physical Review A

Absolutely classical spin states

Fabian Bohnet-Waldraff, O. Giraud, Daniel Braun

Published Jan 19, 2017• 15 citations

Abstract

We introduce the concept of ``absolutely classical'' spin states, in analogy to absolutely separable states of bipartite quantum systems. Absolutely classical states are states that remain classical (i.e., a convex sum of projectors on coherent states of a spin $j$) under any unitary transformation applied to them. We investigate the maximal size of the ball of absolutely classical states centered on the maximally mixed state and derive a lower bound for its radius as a function of the total spin quantum number. We also obtain a numerical estimate of this maximal radius and compare it to the case of absolutely separable states.

DOI: 10.1103/physreva.95.012318

Related papers

Maximally entangled mixed symmetric states of two qubits

Eduardo Serrano-Ensástiga, John Martin

Jan 1, 20210 citations

Maximum entanglement of mixed symmetric states under unitary transformations

Eduardo Serrano-Ensástiga, John Martin

arXiv:2112.05102SciPost PhysicsSep 28, 20236 citations

On the maximum purity of absolutely separable bipartite states

Hoàng Phi Dũng, Vu The Khoi

arXiv:2510.19508Oct 22, 20250 citations

Classicality of spin states

Olivier Giraud, Petr A. Braun, Daniel Braun

arXiv:0805.2592Physical Review AOct 27, 200898 citations

Absolutely entangled sets of pure states for bipartitions and multipartitions

Baichu Yu, Pooja Jayachandran, Adam Burchardt +3 more

arXiv:2106.16216Physical Review ASep 17, 20210 citations

Total, quantum, and classical measures of anticoherence for mixed spin states

Jérôme Denis, Tara Lacaille, John Martin +1 more

quant-pharXiv:2605.29436May 29, 20260 citations

arXiv:1611.06064 · Physical Review A

Absolutely classical spin states

Fabian Bohnet-Waldraff, O. Giraud, Daniel Braun

Published Jan 19, 2017• 15 citations

arXiv HTML PDF

Abstract

j

) under any unitary transformation applied to them. We investigate the maximal size of the ball of absolutely classical states centered on the maximally mixed state and derive a lower bound for its radius as a function of the total spin quantum number. We also obtain a numerical estimate of this maximal radius and compare it to the case of absolutely separable states.

DOI: 10.1103/physreva.95.012318

Related papers

Maximally entangled mixed symmetric states of two qubits

Eduardo Serrano-Ensástiga, John Martin

In this work, a variation of the problem originally solved by Verstraete, Audenaert, and De Moor [Phys. Rev. A 64, 012316 (2001)] on what is the maximum entanglement that can be created in a two-qubit system by a global unitary transformation is considered and solved when permutation invariance in the state is imposed. The additional constraint of permutation symmetry appears naturally in the context of bosonic systems or spin states. We also characterise symmetric two-qubit states that remain separable after any global unitary transformation, called symmetric absolutely separable states (SAS), or absolutely classical for spin states. This allows us to determine the maximal radius of a ball of SAS states around the maximally mixed state in the symmetric sector, and the minimal radius of a ball that includes the set of SAS states. For three-qubit systems, a necessary condition for absolute separability of symmetric states is given, which leads us to upper bounds on the ball radii similar to those studied for the two-qubit system.In this work, a variation of the problem originally solved by Verstraete, Audenaert, and De Moor [Phys. Rev. A 64, 012316 (2001)] on what is the maximum entanglement that can be created in a two-qubit system by a global unitary transformation is considered and solved when permutation invariance in the state is imposed. The additional constraint of permutation symmetry appears naturally in the context of bosonic systems or spin states. We also characterise symmetric two-qubit states that remain separable after any global unitary transformation, called symmetric absolutely separable states (SAS), or absolutely classical for spin states. This allows us to determine the maximal radius of a ball of SAS states around the maximally mixed state in the symmetric sector, and the minimal radius of a ball that includes the set of SAS states. For three-qubit systems, a necessary condition for absolute separability of symmetric states is given, which leads us to upper bounds on the ball radii similar to those studied for the two-qubit system.

Jan 1, 20210 citations

Maximum entanglement of mixed symmetric states under unitary transformations

Eduardo Serrano-Ensástiga, John Martin

We study the maximum entanglement that can be produced by a global unitary transformation for systems of two and three qubits constrained to the fully symmetric states. This restriction to the symmetric subspace appears naturally in the context of bosonic or collective spin systems. We also study the symmetric states that remain separable after any global unitary transformation, called symmetric absolutely separable (SAS) states, or absolutely classical for spin states. The results for the two-qubit system are deduced analytically. In particular, we determine the maximal radius of a ball of SAS states around the maximally mixed state in the symmetric sector, and the minimal radius of a ball that contains the set of SAS states. As an application of our results, we also analyse the temperature dependence of the maximum entanglement that can be obtained from the thermal state of a spin-1 system with a spin-squeezing Hamiltonian. For the symmetric three-qubit case, our results are mostly numerical, and we conjecture a 3-parameter family of states that achieves the maximum negativity in the unitary orbit of any mixed state. In addition, we derive upper bounds, apparently tight, on the radii of balls containing only/all SAS states.We study the maximum entanglement that can be produced by a global unitary transformation for systems of two and three qubits constrained to the fully symmetric states. This restriction to the symmetric subspace appears naturally in the context of bosonic or collective spin systems. We also study the symmetric states that remain separable after any global unitary transformation, called symmetric absolutely separable (SAS) states, or absolutely classical for spin states. The results for the two-qubit system are deduced analytically. In particular, we determine the maximal radius of a ball of SAS states around the maximally mixed state in the symmetric sector, and the minimal radius of a ball that contains the set of SAS states. As an application of our results, we also analyse the temperature dependence of the maximum entanglement that can be obtained from the thermal state of a spin-1 system with a spin-squeezing Hamiltonian. For the symmetric three-qubit case, our results are mostly numerical, and we conjecture a 3-parameter family of states that achieves the maximum negativity in the unitary orbit of any mixed state. In addition, we derive upper bounds, apparently tight, on the radii of balls containing only/all SAS states.

arXiv:2112.05102SciPost PhysicsSep 28, 20236 citations

On the maximum purity of absolutely separable bipartite states

Hoàng Phi Dũng, Vu The Khoi

In this study, we investigate the problem of determining the maximum purity for absolutely separable and absolutely PPT quantum states. From the geometric viewpoint, this problem is equivalent to asking for the exact Euclidean radius of the smallest ball around the maximally mixed state that encompasses the set of all absolutely separable or absolutely PPT states. Our results provide an analytic solution for two qubit states. Based on numerical computation, we propose a conjectured maximum purity for absolutely separable qubit-qudit states and absolutely PPT qutrit-qudit states.In this study, we investigate the problem of determining the maximum purity for absolutely separable and absolutely PPT quantum states. From the geometric viewpoint, this problem is equivalent to asking for the exact Euclidean radius of the smallest ball around the maximally mixed state that encompasses the set of all absolutely separable or absolutely PPT states. Our results provide an analytic solution for two qubit states. Based on numerical computation, we propose a conjectured maximum purity for absolutely separable qubit-qudit states and absolutely PPT qutrit-qudit states.

arXiv:2510.19508Oct 22, 20250 citations

Classicality of spin states

Olivier Giraud, Petr A. Braun, Daniel Braun

We extend the concept of classicality in quantum optics to spin states. We call a state ``classical'' if its density matrix can be decomposed as a weighted sum of angular momentum coherent states with positive weights. Classical spin states form a convex set $\mathcal{C}$ , which we fully characterize for a spin $1∕2$ and a spin 1. For arbitrary spin, we provide ``nonclassicality witnesses.'' For bipartite systems, $\mathcal{C}$ forms a subset of all separable states. A state of two spins $1∕2$ belongs to $\mathcal{C}$ if and only if it is separable, whereas for a spin $1∕2$ coupled to a spin 1, there are separable states which do not belong to $\mathcal{C}$ . We show that in general the question whether a state is in $\mathcal{C}$ can be answered by a linear programming algorithm.We extend the concept of classicality in quantum optics to spin states. We call a state ``classical'' if its density matrix can be decomposed as a weighted sum of angular momentum coherent states with positive weights. Classical spin states form a convex set $\mathcal{C}$, which we fully characterize for a spin $1∕2$ and a spin 1. For arbitrary spin, we provide ``nonclassicality witnesses.'' For bipartite systems, $\mathcal{C}$ forms a subset of all separable states. A state of two spins $1∕2$ belongs to $\mathcal{C}$ if and only if it is separable, whereas for a spin $1∕2$ coupled to a spin 1, there are separable states which do not belong to $\mathcal{C}$. We show that in general the question whether a state is in $\mathcal{C}$ can be answered by a linear programming algorithm.

arXiv:0805.2592Physical Review AOct 27, 200898 citations

Absolutely entangled sets of pure states for bipartitions and multipartitions

Baichu Yu, Pooja Jayachandran, Adam Burchardt +3 more

A set of quantum states is said to be absolutely entangled when at least one state in the set remains entangled for any definition of subsystems, i.e., for any choice of the global reference frame. In this work we investigate the properties of absolutely entangled sets (AESs) of pure quantum states. For the case of a two-qubit system, we present a sufficient condition to detect an AES, and use it to construct families of $N$ states such that $N\ensuremath{-}3$ (the maximal possible number) remain entangled for any definition of subsystems. For a general bipartition $d={d}_{1}{d}_{2}$ , we prove that sets of $N>\ensuremath{\lfloor}({d}_{1}+1)({d}_{2}+1)/2\ensuremath{\rfloor}$ states are AESs with Haar measure 1. Then, we define AESs for multipartitions. We derive a general lower bound on the number of states in an AES for a given multipartition, and also construct explicit examples. In particular, we exhibit an AES with respect to any possible multipartitioning of the total system.A set of quantum states is said to be absolutely entangled when at least one state in the set remains entangled for any definition of subsystems, i.e., for any choice of the global reference frame. In this work we investigate the properties of absolutely entangled sets (AESs) of pure quantum states. For the case of a two-qubit system, we present a sufficient condition to detect an AES, and use it to construct families of $N$ states such that $N\ensuremath{-}3$ (the maximal possible number) remain entangled for any definition of subsystems. For a general bipartition $d={d}_{1}{d}_{2}$, we prove that sets of $N>\ensuremath{\lfloor}({d}_{1}+1)({d}_{2}+1)/2\ensuremath{\rfloor}$ states are AESs with Haar measure 1. Then, we define AESs for multipartitions. We derive a general lower bound on the number of states in an AES for a given multipartition, and also construct explicit examples. In particular, we exhibit an AES with respect to any possible multipartitioning of the total system.

arXiv:2106.16216Physical Review ASep 17, 20210 citations

Total, quantum, and classical measures of anticoherence for mixed spin states

Jérôme Denis, Tara Lacaille, John Martin +1 more

Anticoherent spin states have isotropic low-order spin moments and are relevant to direction-independent metrology and quantum reference-frame alignment. In contrast to pure states, for mixed states such isotropy may originate either from genuine quantum correlations or from classical statistical mixing. We introduce an axiomatic framework for mixed-state $t$ -anticoherence based on the symmetric qubit embedding. We distinguish total $t$ -anticoherence, non-decreasing under SU(2)-covariant channels, from quantum $t$ -anticoherence, defined as a resource monotone relative to a chosen total measure and constrained to coincide with it on pure states. This yields a classical contribution as their difference. We construct total measures based on reduced-state purity, Hilbert-Schmidt distance, and cumulative multipoles, and we discuss fidelity-based total candidates. We construct quantum counterparts via convex-roof extensions of pure-state functionals tied to bipartite entanglement in the symmetric sector. We provide explicit mixed-state examples, identify states with maximal quantum anticoherence supported on anticoherent subspaces, study robustness under particle loss for different types of states, and characterize the trade-off between purity and the maximal achievable anticoherence order.Anticoherent spin states have isotropic low-order spin moments and are relevant to direction-independent metrology and quantum reference-frame alignment. In contrast to pure states, for mixed states such isotropy may originate either from genuine quantum correlations or from classical statistical mixing. We introduce an axiomatic framework for mixed-state $t$-anticoherence based on the symmetric qubit embedding. We distinguish total $t$-anticoherence, non-decreasing under SU(2)-covariant channels, from quantum $t$-anticoherence, defined as a resource monotone relative to a chosen total measure and constrained to coincide with it on pure states. This yields a classical contribution as their difference. We construct total measures based on reduced-state purity, Hilbert-Schmidt distance, and cumulative multipoles, and we discuss fidelity-based total candidates. We construct quantum counterparts via convex-roof extensions of pure-state functionals tied to bipartite entanglement in the symmetric sector. We provide explicit mixed-state examples, identify states with maximal quantum anticoherence supported on anticoherent subspaces, study robustness under particle loss for different types of states, and characterize the trade-off between purity and the maximal achievable anticoherence order.

quant-pharXiv:2605.29436May 29, 20260 citations

j

\mathcal{C}

, which we fully characterize for a spin

1∕2

and a spin 1. For arbitrary spin, we provide ``nonclassicality witnesses.'' For bipartite systems,

\mathcal{C}

forms a subset of all separable states. A state of two spins

1∕2

belongs to

\mathcal{C}

if and only if it is separable, whereas for a spin

1∕2

coupled to a spin 1, there are separable states which do not belong to

\mathcal{C}

. We show that in general the question whether a state is in

\mathcal{C}

can be answered by a linear programming algorithm.

N

states such that $N\ensuremath{-}3$ (the maximal possible number) remain entangled for any definition of subsystems. For a general bipartition

d={d}_{1}{d}_{2}

, we prove that sets of $N>\ensuremath{\lfloor}({d}_{1}+1)({d}_{2}+1)/2\ensuremath{\rfloor}$ states are AESs with Haar measure 1. Then, we define AESs for multipartitions. We derive a general lower bound on the number of states in an AES for a given multipartition, and also construct explicit examples. In particular, we exhibit an AES with respect to any possible multipartitioning of the total system.

t

-anticoherence based on the symmetric qubit embedding. We distinguish total

t

-anticoherence, non-decreasing under SU(2)-covariant channels, from quantum

t

-anticoherence, defined as a resource monotone relative to a chosen total measure and constrained to coincide with it on pure states. This yields a classical contribution as their difference. We construct total measures based on reduced-state purity, Hilbert-Schmidt distance, and cumulative multipoles, and we discuss fidelity-based total candidates. We construct quantum counterparts via convex-roof extensions of pure-state functionals tied to bipartite entanglement in the symmetric sector. We provide explicit mixed-state examples, identify states with maximal quantum anticoherence supported on anticoherent subspaces, study robustness under particle loss for different types of states, and characterize the trade-off between purity and the maximal achievable anticoherence order.