Quantum discord in the ground and thermal states of spin clusters

Quantum discord (QD) is a general measure of bipartite quantum correlations with a potential role in quantum information processing tasks. Spin clusters serve as ideal candidates for the implementation of some of the associated protocols. In this paper, we consider a symmetric spin trimer and a tetramer which describe a number of known molecular magnets and compute the QD in the ground and thermal states of the clusters. The variations of the QD as a function of an anisotropy parameter, magnetic field and temperature are investigated. We obtain a number of interesting results such as a finite value of the QD in the trimer ground state for which the pairwise entanglement is known to be zero, differences in the nature of some of the variations in the ferromagnetic and antiferromagnetic cases, and discontinuous jumps in the magnitude of the QD at first-order quantum phase transition points. A remarkable feature that is observed is that the QD completely vanishes only in the asymptotic limit of temperature T → ∞. We further study the dynamics of the QD and the pairwise entanglement at T = 0 under the effect of a dephasing channel describing the interaction of the reduced spin cluster state with independent local environments. The QD is found to vanish asymptotically as t → ∞. In the case of the spin trimer, the pairwise entanglement has a zero value at all times and reaches a zero value in a finite time in the case of the tetramer.Quantum discord (QD) is a general measure of bipartite quantum correlations with a potential role in quantum information processing tasks. Spin clusters serve as ideal candidates for the implementation of some of the associated protocols. In this paper, we consider a symmetric spin trimer and a tetramer which describe a number of known molecular magnets and compute the QD in the ground and thermal states of the clusters. The variations of the QD as a function of an anisotropy parameter, magnetic field and temperature are investigated. We obtain a number of interesting results such as a finite value of the QD in the trimer ground state for which the pairwise entanglement is known to be zero, differences in the nature of some of the variations in the ferromagnetic and antiferromagnetic cases, and discontinuous jumps in the magnitude of the QD at first-order quantum phase transition points. A remarkable feature that is observed is that the QD completely vanishes only in the asymptotic limit of temperature T → ∞. We further study the dynamics of the QD and the pairwise entanglement at T = 0 under the effect of a dephasing channel describing the interaction of the reduced spin cluster state with independent local environments. The QD is found to vanish asymptotically as t → ∞. In the case of the spin trimer, the pairwise entanglement has a zero value at all times and reaches a zero value in a finite time in the case of the tetramer.

arXiv:1012.0650Journal of Physics B Atomic Molecular and Optical PhysicsFeb 1, 201127 citations

Thermal and magnetic quantum discord in Heisenberg models

T. Werlang, Gustavo Rigolin

We investigate how quantum correlations [quantum discord (QD)] of a two-qubit one-dimensional $\mathit{XYZ}$ Heisenberg chain in thermal equilibrium depend on the temperature $T$ of the bath and also on an external magnetic field $B$ . We show that the behavior of thermal QD differs in many unexpected ways from thermal entanglement. For example, we show situations where QD increases with $T$ when entanglement decreases, cases where QD increases with $T$ even in regions with zero entanglement, and that QD signals a quantum phase transition even at finite $T$ . We also show that by properly tuning $B$ or the interaction between the qubits we get nonzero QD for any $T$ and we present an effect not seen for entanglement, the ``regrowth'' of thermal QD.We investigate how quantum correlations [quantum discord (QD)] of a two-qubit one-dimensional $\mathit{XYZ}$ Heisenberg chain in thermal equilibrium depend on the temperature $T$ of the bath and also on an external magnetic field $B$. We show that the behavior of thermal QD differs in many unexpected ways from thermal entanglement. For example, we show situations where QD increases with $T$ when entanglement decreases, cases where QD increases with $T$ even in regions with zero entanglement, and that QD signals a quantum phase transition even at finite $T$. We also show that by properly tuning $B$ or the interaction between the qubits we get nonzero QD for any $T$ and we present an effect not seen for entanglement, the ``regrowth'' of thermal QD.

arXiv:0911.3903Physical Review AApr 1, 2010259 citations

THERMAL DISCORD AND NEGATIVITY IN A TWO-SPIN-QUTRIT SYSTEM UNDER DIFFERENT MAGNETIC FIELDS

XIAO-JING LI, Huihui Ji, Xi-Wen Hou

The characterization of quantum discord (QD) has been well understood only for two-qubit states and is little known for mixed states beyond qubits. In this work, thermal quantum discord is studied for a qutrit system in different magnetic fields, where classical correlation and entanglement negativity are calculated for comparison. It is shown that the discord is more robust against temperature than the negativity. For a suitable region of magnetic field and its direction, the discord is non-zero while the negativity is zero. When the system is at a lower temperature, these three quantities, however, display a similar behavior for the varied field and direction, and their discontinuities come from crossovers between different ground states in the system. Moreover, the inequality between the quantum and classical correlations depends upon the system parameters as well as the temperature. In particular, both correlations are equal at a suitable field, direction, and temperature. Remarkably, such an equality remains for a strong field in the antiparallel direction, while both correlations in two-qubit systems are identical for any antiparallel field and temperature. These are useful for quantum information and understanding quantum correlations in qutrit mixed states.The characterization of quantum discord (QD) has been well understood only for two-qubit states and is little known for mixed states beyond qubits. In this work, thermal quantum discord is studied for a qutrit system in different magnetic fields, where classical correlation and entanglement negativity are calculated for comparison. It is shown that the discord is more robust against temperature than the negativity. For a suitable region of magnetic field and its direction, the discord is non-zero while the negativity is zero. When the system is at a lower temperature, these three quantities, however, display a similar behavior for the varied field and direction, and their discontinuities come from crossovers between different ground states in the system. Moreover, the inequality between the quantum and classical correlations depends upon the system parameters as well as the temperature. In particular, both correlations are equal at a suitable field, direction, and temperature. Remarkably, such an equality remains for a strong field in the antiparallel direction, while both correlations in two-qubit systems are identical for any antiparallel field and temperature. These are useful for quantum information and understanding quantum correlations in qutrit mixed states.

International Journal of Quantum InformationDec 1, 20138 citations

Quantum and classical thermal correlations in the XY spin- 1 2 chain

Jonas Maziero, H. C. Guzman, Lucas C. Céleri +2 more

We investigate pairwise quantum correlation as measured by the quantum discord as well as its classical counterpart in the thermodynamic limit of anisotropic $\mathit{XY}$ spin- $1/2$ chains in a transverse magnetic field for both zero and finite temperatures. Analytical expressions for both classical and quantum correlations are obtained for spin pairs at any distance. In the case of zero temperature, it is shown that the quantum discord for spin pairs farther than second neighbors is able to characterize a quantum phase transition, even though pairwise entanglement is absent for such distances. For finite temperatures, we show that quantum correlations can be increased with temperature in the presence of a magnetic field. Moreover, in the $\mathit{XX}$ limit, thermal quantum discord is found to be dominant over classical correlation while the opposite scenario takes place for the transverse field Ising model limit.We investigate pairwise quantum correlation as measured by the quantum discord as well as its classical counterpart in the thermodynamic limit of anisotropic $\mathit{XY}$ spin-$1/2$ chains in a transverse magnetic field for both zero and finite temperatures. Analytical expressions for both classical and quantum correlations are obtained for spin pairs at any distance. In the case of zero temperature, it is shown that the quantum discord for spin pairs farther than second neighbors is able to characterize a quantum phase transition, even though pairwise entanglement is absent for such distances. For finite temperatures, we show that quantum correlations can be increased with temperature in the presence of a magnetic field. Moreover, in the $\mathit{XX}$ limit, thermal quantum discord is found to be dominant over classical correlation while the opposite scenario takes place for the transverse field Ising model limit.

arXiv:1002.3906Physical Review AJul 22, 2010228 citations

Thermal entanglement properties of small spin clusters

Indrani Bose, Amit Tribedi

Exchange interactions in spin systems can give rise to quantum entanglement in the ground and thermal states of the systems. We consider a spin tetramer, with spins of magnitude $\frac{1}{2}$ , in which the spins interact via nearest-neighbor, diagonal, and four-spin interactions of strength ${J}_{1}$ , ${J}_{2}$ , and $K$ , respectively. The ground- and thermal-state entanglement properties of the tetramer are calculated analytically in the various limiting cases. Both bipartite and multipartite entanglements are considered and a signature of the quantum phase transition (QPT), in terms of the entanglement ratio, is identified. The first-order QPT is accompanied by discontinuities in the nearest-neighbor and diagonal concurrences. The magnetic properties of a $S=\frac{1}{2}$ antiferromagnetic polyoxovanadate compound V12 are well explained by tetramers, with ${J}_{2}=0$ , $K=0$ , in which the spins interact via the isotropic Heisenberg exchange interaction Hamiltonian. Treating the magnetic susceptibility $\ensuremath{\chi}$ as an entanglement witness (EW), an estimate of the lower bound of the critical entanglement temperature ${T}_{c}$ below which entanglement is present in the experimental compound, is determined. Two other cases considered include the symmetric tetramer---i.e., tetrahedron $({J}_{1}={J}_{2},K=0)$ ---and the symmetric trimer. In both the cases, there is no entanglement between a pair of spins in the thermal state but multipartite entanglement is present. A second EW based on energy provides an estimate of the entanglement temperature ${T}_{E}$ below which the thermal state is definitely entangled. This EW detects bipartite entanglement in the case of the tetramer describing a square of spins (the case of V12 ) and multipartite entanglement in the cases of the tetrahedron and symmetric trimer.Exchange interactions in spin systems can give rise to quantum entanglement in the ground and thermal states of the systems. We consider a spin tetramer, with spins of magnitude $\frac{1}{2}$, in which the spins interact via nearest-neighbor, diagonal, and four-spin interactions of strength ${J}_{1}$, ${J}_{2}$, and $K$, respectively. The ground- and thermal-state entanglement properties of the tetramer are calculated analytically in the various limiting cases. Both bipartite and multipartite entanglements are considered and a signature of the quantum phase transition (QPT), in terms of the entanglement ratio, is identified. The first-order QPT is accompanied by discontinuities in the nearest-neighbor and diagonal concurrences. The magnetic properties of a $S=\frac{1}{2}$ antiferromagnetic polyoxovanadate compound V12 are well explained by tetramers, with ${J}_{2}=0$, $K=0$, in which the spins interact via the isotropic Heisenberg exchange interaction Hamiltonian. Treating the magnetic susceptibility $\ensuremath{\chi}$ as an entanglement witness (EW), an estimate of the lower bound of the critical entanglement temperature ${T}_{c}$ below which entanglement is present in the experimental compound, is determined. Two other cases considered include the symmetric tetramer---i.e., tetrahedron $({J}_{1}={J}_{2},K=0)$---and the symmetric trimer. In both the cases, there is no entanglement between a pair of spins in the thermal state but multipartite entanglement is present. A second EW based on energy provides an estimate of the entanglement temperature ${T}_{E}$ below which the thermal state is definitely entangled. This EW detects bipartite entanglement in the case of the tetramer describing a square of spins (the case of V12 ) and multipartite entanglement in the cases of the tetrahedron and symmetric trimer.

arXiv:cond-mat/0503170Physical Review AAug 15, 200557 citations

QUANTUM DISCORD IN THE GROUND STATE OF SPIN CHAINS

M. S. Sarandy, THIAGO R. DE OLIVEIRA, Luigi Amico A

The ground state of a quantum spin chain is a natural playground for investigating correlations. Nevertheless, not all correlations are genuinely of quantum nature. Here we review the recent progress to quantify the "quantumness" of the correlations throughout the phase diagram of quantum spin systems. Focusing to one spatial dimension, we discuss the behavior of quantum discord (QD) close to quantum phase transitions (QPT). In contrast to the two-spin entanglement, pairwise discord is effectively long-ranged in critical regimes. Besides the features of QPT, QD is especially feasible to explore the factorization phenomenon, giving rise to nontrivial ground classical states in quantum systems. The effects of spontaneous symmetry breaking are also discussed as well as the identification of quantum critical points through correlation witnesses.The ground state of a quantum spin chain is a natural playground for investigating correlations. Nevertheless, not all correlations are genuinely of quantum nature. Here we review the recent progress to quantify the "quantumness" of the correlations throughout the phase diagram of quantum spin systems. Focusing to one spatial dimension, we discuss the behavior of quantum discord (QD) close to quantum phase transitions (QPT). In contrast to the two-spin entanglement, pairwise discord is effectively long-ranged in critical regimes. Besides the features of QPT, QD is especially feasible to explore the factorization phenomenon, giving rise to nontrivial ground classical states in quantum systems. The effects of spontaneous symmetry breaking are also discussed as well as the identification of quantum critical points through correlation witnesses.

arXiv:1208.4817International Journal of Modern Physics BNov 1, 201248 citations

We investigate how quantum correlations [quantum discord (QD)] of a two-qubit one-dimensional

\mathit{XYZ}

Heisenberg chain in thermal equilibrium depend on the temperature

T

of the bath and also on an external magnetic field

B

. We show that the behavior of thermal QD differs in many unexpected ways from thermal entanglement. For example, we show situations where QD increases with

T

when entanglement decreases, cases where QD increases with

T

even in regions with zero entanglement, and that QD signals a quantum phase transition even at finite

T

. We also show that by properly tuning

B

or the interaction between the qubits we get nonzero QD for any

T

and we present an effect not seen for entanglement, the ``regrowth'' of thermal QD.

We investigate pairwise quantum correlation as measured by the quantum discord as well as its classical counterpart in the thermodynamic limit of anisotropic

\mathit{XY}

spin-

1/2

chains in a transverse magnetic field for both zero and finite temperatures. Analytical expressions for both classical and quantum correlations are obtained for spin pairs at any distance. In the case of zero temperature, it is shown that the quantum discord for spin pairs farther than second neighbors is able to characterize a quantum phase transition, even though pairwise entanglement is absent for such distances. For finite temperatures, we show that quantum correlations can be increased with temperature in the presence of a magnetic field. Moreover, in the

\mathit{XX}

limit, thermal quantum discord is found to be dominant over classical correlation while the opposite scenario takes place for the transverse field Ising model limit.

Exchange interactions in spin systems can give rise to quantum entanglement in the ground and thermal states of the systems. We consider a spin tetramer, with spins of magnitude

\frac{1}{2}

, in which the spins interact via nearest-neighbor, diagonal, and four-spin interactions of strength

{J}_{1}

{J}_{2}

, and

K

, respectively. The ground- and thermal-state entanglement properties of the tetramer are calculated analytically in the various limiting cases. Both bipartite and multipartite entanglements are considered and a signature of the quantum phase transition (QPT), in terms of the entanglement ratio, is identified. The first-order QPT is accompanied by discontinuities in the nearest-neighbor and diagonal concurrences. The magnetic properties of a

S=\frac{1}{2}

antiferromagnetic polyoxovanadate compound V12 are well explained by tetramers, with

{J}_{2}=0

K=0

, in which the spins interact via the isotropic Heisenberg exchange interaction Hamiltonian. Treating the magnetic susceptibility $\ensuremath{\chi}$ as an entanglement witness (EW), an estimate of the lower bound of the critical entanglement temperature

{T}_{c}

below which entanglement is present in the experimental compound, is determined. Two other cases considered include the symmetric tetramer---i.e., tetrahedron

({J}_{1}={J}_{2},K=0)

---and the symmetric trimer. In both the cases, there is no entanglement between a pair of spins in the thermal state but multipartite entanglement is present. A second EW based on energy provides an estimate of the entanglement temperature

{T}_{E}

below which the thermal state is definitely entangled. This EW detects bipartite entanglement in the case of the tetramer describing a square of spins (the case of V12 ) and multipartite entanglement in the cases of the tetrahedron and symmetric trimer.