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
Jk. They can be used for the experimental detection of entanglement in a system of spin-
21 particles in which the spins cannot be individually addressed. We present various sets of inequalities that can detect all entangled states that can be detected based on the knowledge of (i) the mean values and variances of
Jk in three orthogonal directions, or (ii) the variances of
Jk in three orthogonal directions, or (iii) the mean values of
Jk2 in three orthogonal directions, or (iv) the mean values and variances of
Jk in arbitrary directions. We compare our inequalities to known spin-squeezing entanglement criteria and discuss to which extent spin squeezing is related to entanglement in the reduced two-qubit states. Finally, we apply our criteria for the detection of entanglement in spin models, showing that they can be used to detect bound entanglement in these systems.
Coherent and squeezed photon states have attracted a lot attetion in long time ago, since these states can generate in laboratory. These states are satisfying in minimum uncertainty relation. In recently, states have generates with electrons by Bose-Einstein condensations and particles oscillations. Also,this states are satisfying in minimum uncertainty relation, with this difference that parameters in this states are the first and second moments of soin operators instead of position and momentum operators.The similarity phenomenon about squeezing photon is exist for spin with that distance. The source of spin squeezing in multi-qubit states is entanglement. One applecations of spin squeezing is to detect quantum entanglement which plays a key role in both the foundations of quantum physics and quantum computation processing. In recent years, spin squeezing stsate parameters have close relation with entanglement measure, concurrence, that we can characterize entanglement for a class of many-body spin- states. In reality, spin squeezing parameters are witnesse for many bode entanglement. In this paper; we study relation betweenspin squeezed states and entanglement. Then; we stuy the squeezing spin for -mode and -mode entangled coherent states.
We show that the two definitions of spin squeezing extensively used in the literature [M. Kitagawa and M. Ueda, Phys. Rev. A 47, 5138 (1993) and D.J. Wineland et al., Phys. Rev. A 50, 67 (1994)] give different predictions of entanglement in the two-atom Dicke system. We analyze differences between the definitions and show that the spin squeezing parameter of Kitagawa and Ueda is a better measure of entanglement than the commonly used spectroscopic spin squeezing parameter. We illustrate this relation by examining different examples of a driven two-atom Dicke system in which spin squeezing and entanglement arise dynamically. We give an explanation of the source of the difference using the negativity criterion for entanglement.
This paper reviews quantum spin squeezing, which characterizes the sensitivity of a state with respect to SU(2) rotations, and is significant for both entanglement detection and high-precision metrology. We first present various definitions of spin squeezing parameters, explain their origin and properties for typical states, and then discuss spin-squeezed states produced with nonlinear twisting Hamiltonians. Afterwards, we explain pairwise correlations and entanglement in spin-squeezed states, as well as the relations between spin squeezing and quantum Fisher information, where the latter plays a central role in quantum metrology. We also review the applications of spin squeezing for detecting quantum chaos and quantum phase transitions, as well as the influence of decoherence on spin squeezing. Finally, we review several experimental realizations of spin squeezing, as well as their corresponding theoretical backgrounds, including: producing spin-squeezed states via particle collisions in Bose-Einstein condensates, transferring photon squeezing to atomic ensembles, and generating spin squeezing via quantum non-demolition measurements.