The transport of states is a fundamental task in quantum information processing systems, enabling operations such as quantum key distribution and inter-component communication within quantum computers. A straightforward approach to the design of state transfer networks are spatial symmetries such as permutation or reflection symmetry. Instead of strictly confining the design space in this fashion, our work takes a novel path by harnessing photonic networks that lack any conventional spatial symmetries, while nevertheless supporting an efficient transfer of quantum states [1], [2]. Key to this approach are so-called latent symmetries [3], which are embodied exclusively in the spectral properties of the network, thereby remaining hidden in the spatial domain. Two network sites $u$ and $v$ are considered latent-symmetric if there is no permutation symmetry between them, but the two sites are cospectral, i.e. the sets of eigenvalues of the networks obtained upon removal of either site are identical (fig. 1a). One of the hallmark features of latent symmetry is the existence of so-called singlet sites [4] at which these networks can be arbitrarily extended without breaking the latent symmetry (e.g. for sites $a, b, c$ in fig. 1a). Anti-symmetric excitations at the two latent-symmetric sites will always interfere destructively at those singlet sites and hence will never leave the initial network. Latent symmetries significantly improve the flexibility in designing quantum networks and hold great potential for applications in quantum cryptography and secure state transfer.The transport of states is a fundamental task in quantum information processing systems, enabling operations such as quantum key distribution and inter-component communication within quantum computers. A straightforward approach to the design of state transfer networks are spatial symmetries such as permutation or reflection symmetry. Instead of strictly confining the design space in this fashion, our work takes a novel path by harnessing photonic networks that lack any conventional spatial symmetries, while nevertheless supporting an efficient transfer of quantum states [1], [2]. Key to this approach are so-called latent symmetries [3], which are embodied exclusively in the spectral properties of the network, thereby remaining hidden in the spatial domain. Two network sites$u$and$v$are considered latent-symmetric if there is no permutation symmetry between them, but the two sites are cospectral, i.e. the sets of eigenvalues of the networks obtained upon removal of either site are identical (fig. 1a). One of the hallmark features of latent symmetry is the existence of so-called singlet sites [4] at which these networks can be arbitrarily extended without breaking the latent symmetry (e.g. for sites$a, b, c$in fig. 1a). Anti-symmetric excitations at the two latent-symmetric sites will always interfere destructively at those singlet sites and hence will never leave the initial network. Latent symmetries significantly improve the flexibility in designing quantum networks and hold great potential for applications in quantum cryptography and secure state transfer.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)Jun 23, 20250 citations

Generalized uncertainty principle from deformed angular momentum algebra

Ahmad Adel Abutaleb

This work establishes a link between deformed angular momentum operators and modifications of the quantum uncertainty principle. Starting from an algebra in which the standard angular momentum operators are deformed by two parameters, [Formula: see text] and [Formula: see text], we construct the corresponding momentum operators via [Formula: see text] where the radial operator [Formula: see text] is determined by the requirement that the standard momentum operator is recovered in the limit [Formula: see text], [Formula: see text]. The resulting commutation relations take the form [Formula: see text] where [Formula: see text] is a position-dependent deformation matrix. This leads to an uncertainty relation [Formula: see text] which is state-dependent, anisotropic and position-dependent. We use the term Generalized Uncertainty Principle (GUP) in its broad sense referring to any modification of the Heisenberg relation motivated by quantum-gravity ideas. However, the model does not yield a fixed minimal length of the kind familiar from conventional GUP models (e.g. [Formula: see text]). In the isotropic, limit the trace of the deformation matrix simplifies the bound to [Formula: see text] which can be considered as a rescaling of the uncertainty constant. Our work thus provides a geometric origin for modified uncertainty relations from symmetry breaking in the rotation group, and offers a framework in which quantum-gravity effects manifest themselves through state- and direction-dependent measurement limits, without necessarily introducing a universal minimal length.This work establishes a link between deformed angular momentum operators and modifications of the quantum uncertainty principle. Starting from an algebra in which the standard angular momentum operators are deformed by two parameters, [Formula: see text] and [Formula: see text], we construct the corresponding momentum operators via [Formula: see text] where the radial operator [Formula: see text] is determined by the requirement that the standard momentum operator is recovered in the limit [Formula: see text], [Formula: see text]. The resulting commutation relations take the form [Formula: see text] where [Formula: see text] is a position-dependent deformation matrix. This leads to an uncertainty relation [Formula: see text] which is state-dependent, anisotropic and position-dependent. We use the term Generalized Uncertainty Principle (GUP) in its broad sense referring to any modification of the Heisenberg relation motivated by quantum-gravity ideas. However, the model does not yield a fixed minimal length of the kind familiar from conventional GUP models (e.g. [Formula: see text]). In the isotropic, limit the trace of the deformation matrix simplifies the bound to [Formula: see text] which can be considered as a rescaling of the uncertainty constant. Our work thus provides a geometric origin for modified uncertainty relations from symmetry breaking in the rotation group, and offers a framework in which quantum-gravity effects manifest themselves through state- and direction-dependent measurement limits, without necessarily introducing a universal minimal length.

International Journal of Modern Physics DMar 13, 20260 citations

The problem of symmetry in quantum mechanics

H. Weyl

Journal of the Franklin InstituteApr 1, 19293 citations

u

and

v

are considered latent-symmetric if there is no permutation symmetry between them, but the two sites are cospectral, i.e. the sets of eigenvalues of the networks obtained upon removal of either site are identical (fig. 1a). One of the hallmark features of latent symmetry is the existence of so-called singlet sites [4] at which these networks can be arbitrarily extended without breaking the latent symmetry (e.g. for sites

a, b, c

in fig. 1a). Anti-symmetric excitations at the two latent-symmetric sites will always interfere destructively at those singlet sites and hence will never leave the initial network. Latent symmetries significantly improve the flexibility in designing quantum networks and hold great potential for applications in quantum cryptography and secure state transfer.