We show that spin squeezing implies pairwise entanglement for arbitrary symmetric multiqubit states. If the squeezing parameter is less than or equal to 1, we demonstrate a quantitative relation between the squeezing parameter and the concurrence for the even and odd states. We prove that the even states generated from the initial state with all qubits being spin down, via the one-axis twisting Hamiltonian, are spin squeezed if and only if they are pairwise entangled. For the states generated via the one-axis twisting Hamiltonian with an external transverse field for any number of qubits greater than 1 or via the two-axis counter-twisting Hamiltonian for any even number of qubits, the numerical results suggest that such states are spin squeezed if and only if they are pairwise entangled.
Quantum entanglement reflects itself through non-local correlations among the subsystems of a quantum system. This thesis focuses on constructing a complete set of local invariants characterizing symmetric two qubit systems and analyzing the pairwise entanglement properties like collective spin squeezing - exhibited by multiqubits - in terms of two qubit entanglement invariants. Further, the collective pairwise entanglement properties of symmetric multiqubit states are shown to be captured entirely by the off diagonal block of the covariance matrix.
Majorana geometric representation of pure N-qubit states obeying exchange symmetry is em- ployed to explore spin squeezing properties in the family of states with two distinct spinors. Dicke states are characterized by two orthogonal spinors and belong to this family - but they are not spin squeezed. On the otherhand, those constituted by two non-orthogonal spinors exhibit spin squeezing.
Recent years have witnessed revolutionary improvement in the production, manipulation, characterization and quantification of multiatom (multiqubit) states - because of their promising applications in high precision atomic clocks, atomic interferrometry, quantum metrology and quantum information protocols. In the characterization and quantification of non-classical atomic correlations, two concepts namely, spin squeezing and quantum entanglement emerge. While spin squeezing originates from the uncertainty relation between atomic collective angular momentum operators, entanglement is a peculiar…
Keeping in view the exchange symmetry aspects in studies on spin squeezing of multiqubit states, we show that Ising type Hamiltonian does not retain the exchange symmetry of initially symmetric multiqubit states. Specifically, we show that all N-qubit states (N greater than or equal to 5) obeying permutation symmetry lose their symmetry after evolution with one dimensional Ising chain with nearest neighbor interactions. Among 4-qubit symmetric pure states, only W type states retain their symmetry under time evolution with Ising Hamiltonian.
The pairwise entanglement of an arbitrary atomic pair randomly extracted from a laser-driven dense multiqubit sample in the presence of quantum dissipation due to spontaneous emission is considered. The dipole-dipole interaction between the particles shifts the laser-qubit resonance frequency and consequently modifies the quantum entanglement. By means of an appropriate tuning of the laser frequency, one can optimize the entanglement in this system. For large ensembles, the maximum entanglement occurs near the laser parameters where the steady-state sample exhibits phase transition phenomena.
We investigate the nonlocality distributions among multiqubit systems based on the maximal violations of the Clauser-Horne-Shimony-Holt (CHSH) inequality of reduced pairwise qubit systems. We present a trade-off relation satisfied by these maximal violations, which gives rise to restrictions on the distribution of nonlocality among the subqubit systems. For a three-qubit system, it is impossible that all pairs of qubits violate the CHSH inequality, and once a pair of qubits violates the CHSH inequality maximally, the other two pairs of qubits must both obey the CHSH inequality. Detailed exampl…
A recursive approach to determine the Hilbert-Schmidt measure of pairwise quantum discord in a special class of symmetric states of $k$ qubits is presented. We especially focus on the reduced states of $k$ qubits obtained from a balanced superposition of symmetric $n$-qubit states (multiqubit Schrödinger cat states) by tracing out $n-k$ particles $(k=2,3, \cdots ,n-1)$. Two pairing schemes are considered. In the first one, the geometric discord measuring the correlation between one qubit and the party grouping $(k-1)$ qubits is explicitly derived. This uses recursive relations between the Fano…
We study the multipartite correlations of the multi-atom dark states, which are characterized by the atomic squeezing beyond the pairwise entanglement. It is shown that, in the photon storage process with atomic ensemble via electromagnetically induced transparency (EIT) mechanism, the atomic squeezing and the pairwise entanglement can be created by adiabatically manipulating the Rabi frequency of the classical light field on the atomic ensemble. We also consider the sudden death for the atomic squeezing and the pairwise entanglement under various decoherence channels. An optimal time for gene…
In order to witness multipartite correlations beyond pairwise entanglement, spin-squeezing parameters are analytically calculated for a spin ensemble in a collective initial state under three different decoherence channels. It is shown that, in analogy to pairwise entanglement, the spin squeezing described by different parameters can suddenly become zero at different vanishing times. This finding shows the general occurrence of sudden vanishing phenomena of quantum correlations in many-body systems, which here is referred to as spin-squeezing sudden death (SSSD). It is shown that the SSSD usua…
Pairwise entanglement properties of a symmetric multi-qubit system are analyzed through a complete set of two-qubit local invariants. Collective features of entanglement, such as spin squeezing, are expressed in terms of invariants and a classifcation scheme for pairwise entanglement is proposed. The invariant criteria given here are shown to be related to the recently proposed (Phys. Rev. Lett. 95, 120502 (2005)) generalized spin squeezing inequalities for pairwise entanglement in symmetric multi-qubit states.
We explore the dynamics of entanglement in classically chaotic systems by considering a multiqubit system that behaves collectively as a spin system obeying the dynamics of the quantum kicked top. In the classical limit, the kicked top exhibits both regular and chaotic dynamics depending on the strength of the chaoticity parameter $κ$ in the Hamiltonian. We show that the entanglement of the multiqubit system, considered for both bipartite and pairwise entanglement, yields a signature of quantum chaos. Whereas bipartite entanglement is enhanced in the chaotic region, pairwise entanglement is su…
We study the relations between spin squeezing and concurrence, and find that they are qualitatively equivalent for an ensemble of spin-1/2 particles with exchange symmetry and parity, if we adopt the spin squeezing criterion given by the recent work (G. Toth et al. Phys. Rev. Lett. 99, 250405 (2007)). This suggests that the spin squeezing has more intimate relations with pairwise entanglement. We exemplify the result by considering a superposition of two Dicke states.
We study spin squeezing, negative correlations, and concurrence in the quantum kicked top model. We prove that the spin squeezing and negative correlations are equivalent for spin systems with only symmetric Dicke states populated. We numerically analyze spin squeezing parameters and concurrence in this model, and find that the maximal spin squeezing direction, which refers to the minimal pairwise correlation direction, is strongly influenced by quantum chaos. Entanglement (spin squeezing) sudden death and sudden birth occur alternatively for the periodic and quasi-periodic cases, while only e…
Quantum spin squeezing is an important resource for quantum information processing, but its squeezing degree is not easy to preserve in an open system with decoherence. Here, we propose a scheme to implement single-photon-triggered spin squeezing with decoherence reduction in an open system. In our system, a Dicke model (DM) is introduced into the quadratic optomechanics, which can be equivalent to an effective DM manipulated by the photon number. Besides, the phonon mode of the optomechanical system is coupled to a squeezed vacuum reservoir with a phase matching, resulting in that the thermal…
We derive necessary and sufficient inseparability conditions imposed on the variance matrix of symmetric qubits. These constraints are identified by examining a structural parallelism between continuous variable states and two qubit states. Pairwise entangled symmetric multiqubit states are shown here to obey these constraints. We also bring out an elegant local invariant structure exhibited by our constraints.
Monogamy relations place restrictions on the shareability of quantum corellations in multipartite states. Being an intrinsic quantum feature, monogamy property throws light on {\emph{residual}} entanglement, an entanglement which is not accounted for by the pairwise entanglement in the state. Expressed in terms of suitable pairwise entanglement measures such as concurrence, the monogamy inequality leads to the evaluation of {\emph{tangle}}, a measure of residual entanglement. In this work, we explore monogamy relations in pure symmetric multiqubit states constituted by two distinct spinors, th…
Collective spin operators for symmetric multi-quDit (namely, identical $D$-level atom) systems generate a U$(D)$ symmetry. We explore generalizations to arbitrary $D$ of SU(2)-spin coherent states and their adaptation to parity (multicomponent Schrödinger cats), together with multi-mode extensions of NOON states. We write level, one- and two-quDit reduced density matrices of symmetric $N$-quDit states, expressed in the last two cases in terms of collective U$(D)$-spin operator expectation values. Then we evaluate level and particle entanglement for symmetric multi-quDit states with linear and …
We calculate Nielsen's circuit complexity of coherent spin state operators. An expression for the complexity is obtained by using the small angle approximation of the Euler angle parametrisation of a general $SO(3)$ rotation. This is then extended to arbitrary times for systems whose time evolutions are generated by couplings to an external field, as well as non-linearly interacting Hamiltonians. In particular, we show how the Nielsen complexity relates to squeezing parameters of the one-axis twisted Hamiltonians in a transverse field, thus indicating its relation with pairwise entanglement. W…
