© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Journal of Optics B Quantum and Semiclassical Optics

Spin squeezing, entanglement and correlations

Swarnamala Sirsi

Published Sep 16, 2004• 3 citations

Abstract

Spin- s assemblies are classified into two mutually exclusive classes: oriented and non-oriented systems. The density matrix ρ, describing oriented systems, can assume diagonal form in the angular momentum basis ( ) defined with respect to the axis of quantization, whereas the eigenstates of ρ for the non-oriented assembly cannot all be identified with states. A new scheme for constructing a mixed, non-oriented spin- s state using s (2 s +1) spinors all pointing in different directions in space and 2 s weights is discussed. Such a construction takes its inspiration from Schwinger's idea of realizing an state as being made up of ( s + m ) 'up' spinors and ( s − m ) 'down' spinors, all defined with respect to a single axis in space. Since the oriented systems are never squeezed, non-oriented spin-1 assemblies which can be prepared in the laboratory with the available NQR technology are examined for signatures of squeezing using our scheme in a frame of reference where the Heisenberg–Robertson uncertainty relation has the same form as the Schrödinger uncertainty relation. It is shown that unlike in the case of the pure spin-1 state where squeezing is synonymous with non-orientedness, a non-oriented spin-1 system need not be squeezed and the existence of entanglement is a necessary but not sufficient condition for the system to be squeezed.

DOI: 10.1088/1464-4266/6/11/002

Related papers

Squeezing and non-oriented spin states

K. S. Mallesh, Swarnamala Sirsi, Mahmoud A A Sbaih +2 more

We classify the pure states of a spin- s system into oriented and non-oriented states. A pure state is said to be non-oriented if it is not an eigenstate of S 2 and S z with respect to any axis of quantization. If it is an eigenstate it is oriented. In this paper, we discuss the notion of spin squeezing in these states. Our analysis shows that the oriented states are not squeezed while non-oriented states exhibit squeezing. We also present a new scheme for the construction of spin- s states using 2 s spinors oriented along different axes. Taking the case of s = 1, we show that `non-oriented' nature and hence squeezing arise from the intrinsic quantum correlations that exist among the spinors in the coupled state.

Journal of Physics A Mathematical and General•Jan 24, 2000•12 citations

Mixed state entanglement and generalized Schwinger model

Veena Adiga, Swarnamala Sirsi

: A new scheme for constructing a mixed spin density matrix has already been introduced to study spin squeezing in some states of practical interest. Such a construction takes its inspiration from Schwinger's idea of realising a state as being made of (j+m) “up spinors” and (j-m) “down spinors”, all defined with respect to a single axis in space. The new scheme is employed here to study some of the well known entanglement measures which characterise the quantumness of a state. Some well known states are considered for an in depth analysis

•Jun 26, 2009•0 citations

Spin squeezing of mixed systems

K. S. Mallesh, Sirsi, S, Sbaih, M A A +2 more

Abstract. The notion of spin squeezing has been discussed in this paper using the density matrix formalism. Extending the definition of squeezing for pure states given by Kitagawa and Ueda in an appropriate manner and employing the spherical tensor representation, we show that mixed spin states which are non-oriented and possess vector polarization indeed exhibit squeezing. We construct a mixed state of a spin 1 system using two spin 1/2 states and study its squeezing behaviour as a function of the individual polarizations of the two spinors.

•Jan 1, 2000•3 citations

Spin squeezing of mixed systems

K S Mallesh, Swarnamala Sirsi, Mahmoud A A Sbaih +2 more

The notion of spin squeezing has been discussed in this paper using the density matrix formalism. Extending the definition of squeezing for pure states given by Kitagawa and Ueda in an appropriate manner and employing the spherical tensor representation, we show that mixed spin states which are non-oriented and possess vector polarization indeed exhibit squeezing. We construct a mixed state of a spin 1 system using two spin ½ states and study its squeezing behaviour as a function of the individual polarizations of the two spinors.

arXiv:quant-ph/0010088•Journal of Physics A Mathematical and General•Apr 5, 2001•6 citations

Spin Squeezing and Quantum Correlations

A. R. Usha Devi, Sudha

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 phenomena arising due to superpositions in the multiparticle Hilbert space. Here, we outline different quantitative measures of spin squeezing and discuss the intrinsic relation of spin squeezing with quantum entanglement in multiqubit systems.

arXiv:1101.0308•Dec 31, 2010•0 citations

Squeezing of a coupled state of two spinors

A. R. Usha Devi, K. S. Mallesh, Mahmoud A A Sbaih +2 more

The notion of spin squeezing involves reduction in the uncertainty of a component of the spin vector below a certain limit. This aspect has been studied earlier for pure and mixed states of definite spin. In this paper, this study has been extended to coupled spin states which do not possess sharp spin value. A general squeezing criterion has been obtained by requiring that a direct product state for two spinors is not squeezed. The squeezing aspect of entangled states is studied in relation to their spin- spin correlations.

arXiv:quant-ph/0204019•Journal of Physics A Mathematical and General•Apr 29, 2003•12 citations

Spin- s assemblies are classified into two mutually exclusive classes: oriented and non-oriented systems. The density matrix ρ, describing oriented systems, can assume diagonal form in the angular momentum basis ( ) defined with respect to the axis of quantization, whereas the eigenstates of ρ for the non-oriented assembly cannot all be identified with states. A new scheme for constructing a mixed, non-oriented spin- s state using s (2 s +1) spinors all pointing in different directions in space and 2 s weights is discussed. Such a construction takes its inspiration from Schwinger's idea of realizing an state as being made up of ( s + m ) 'up' spinors and ( s − m ) 'down' spinors, all defined with respect to a single axis in space. Since the oriented systems are never squeezed, non-oriented spin-1 assemblies which can be prepared in the laboratory with the available NQR technology are examined for signatures of squeezing using our scheme in a frame of reference where the Heisenberg–Robertson uncertainty relation has the same form as the Schrödinger uncertainty relation. It is shown that unlike in the case of the pure spin-1 state where squeezing is synonymous with non-orientedness, a non-oriented spin-1 system need not be squeezed and the existence of entanglement is a necessary but not sufficient condition for the system to be squeezed.

We classify the pure states of a spin- s system into oriented and non-oriented states. A pure state is said to be non-oriented if it is not an eigenstate of S 2 and S z with respect to any axis of quantization. If it is an eigenstate it is oriented. In this paper, we discuss the notion of spin squeezing in these states. Our analysis shows that the oriented states are not squeezed while non-oriented states exhibit squeezing. We also present a new scheme for the construction of spin- s states using 2 s spinors oriented along different axes. Taking the case of s = 1, we show that `non-oriented' nature and hence squeezing arise from the intrinsic quantum correlations that exist among the spinors in the coupled state.

: A new scheme for constructing a mixed spin density matrix has already been introduced to study spin squeezing in some states of practical interest. Such a construction takes its inspiration from Schwinger's idea of realising a state as being made of (j+m) “up spinors” and (j-m) “down spinors”, all defined with respect to a single axis in space. The new scheme is employed here to study some of the well known entanglement measures which characterise the quantumness of a state. Some well known states are considered for an in depth analysis

Abstract. The notion of spin squeezing has been discussed in this paper using the density matrix formalism. Extending the definition of squeezing for pure states given by Kitagawa and Ueda in an appropriate manner and employing the spherical tensor representation, we show that mixed spin states which are non-oriented and possess vector polarization indeed exhibit squeezing. We construct a mixed state of a spin 1 system using two spin 1/2 states and study its squeezing behaviour as a function of the individual polarizations of the two spinors.

The notion of spin squeezing has been discussed in this paper using the density matrix formalism. Extending the definition of squeezing for pure states given by Kitagawa and Ueda in an appropriate manner and employing the spherical tensor representation, we show that mixed spin states which are non-oriented and possess vector polarization indeed exhibit squeezing. We construct a mixed state of a spin 1 system using two spin ½ states and study its squeezing behaviour as a function of the individual polarizations of the two spinors.

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 phenomena arising due to superpositions in the multiparticle Hilbert space. Here, we outline different quantitative measures of spin squeezing and discuss the intrinsic relation of spin squeezing with quantum entanglement in multiqubit systems.

The notion of spin squeezing involves reduction in the uncertainty of a component of the spin vector below a certain limit. This aspect has been studied earlier for pure and mixed states of definite spin. In this paper, this study has been extended to coupled spin states which do not possess sharp spin value. A general squeezing criterion has been obtained by requiring that a direct product state for two spinors is not squeezed. The squeezing aspect of entangled states is studied in relation to their spin- spin correlations.