Abstract Wigner’s seminal work on the Poincaré group revealed one of the fundamental principles of quantum theory: symmetry groups are projectively represented. The condensed-matter counterparts of the Poincaré group could be the spacetime groups of periodically driven crystals or spacetime crystals featuring spacetime periodicity. In this study, we establish the general theory of projective spacetime symmetry algebras of spacetime crystals and reveal their intrinsic connections to gauge structures. As important applications, we exhaustively classify (1,1)D projective symmetry algebras and systematically construct spacetime lattice models for them all. Additionally, we present three consequences of projective spacetime symmetry that surpass ordinary theory: the electric Floquet-Bloch theorem, Kramers-like degeneracy of spinless Floquet crystals, and symmetry-enforced crossings in the Hamiltonian spectral flows. Our work provides both theoretical and experimental foundations to explore novel physics protected by projective spacetime symmetry of spacetime crystals.Abstract Wigner’s seminal work on the Poincaré group revealed one of the fundamental principles of quantum theory: symmetry groups are projectively represented. The condensed-matter counterparts of the Poincaré group could be the spacetime groups of periodically driven crystals or spacetime crystals featuring spacetime periodicity. In this study, we establish the general theory of projective spacetime symmetry algebras of spacetime crystals and reveal their intrinsic connections to gauge structures. As important applications, we exhaustively classify (1,1)D projective symmetry algebras and systematically construct spacetime lattice models for them all. Additionally, we present three consequences of projective spacetime symmetry that surpass ordinary theory: the electric Floquet-Bloch theorem, Kramers-like degeneracy of spinless Floquet crystals, and symmetry-enforced crossings in the Hamiltonian spectral flows. Our work provides both theoretical and experimental foundations to explore novel physics protected by projective spacetime symmetry of spacetime crystals.

arXiv:2310.09577Communications PhysicsNov 14, 20233 citations

Quantum Adaptive Spacetime Geometry

Jincheng Zhang

This paper explores the potential of quantum self-adaptive spacetime geometry – a novel computational framework leveraging quantum entanglement to dynamically adjust spacetime parameters and enable precise spacetime modeling. Traditional approaches to spacetime simulation rely on manually designed geometries, limiting their adaptability. We propose a mechanism that dynamically adjusts spacetime geometry based on learned data and environmental information, automating the process through a specialized spacetime geometry calculation algorithm. The core claim is that this framework offers a significant advancement in spacetime simulation, enabling more accurate and flexible modeling compared to conventional methods. This work introduces a dynamic spacetime geometry parameter adjustment system, demonstrating its potential for enhanced simulation fidelity and computational efficiency.This paper explores the potential of quantum self-adaptive spacetime geometry – a novel computational framework leveraging quantum entanglement to dynamically adjust spacetime parameters and enable precise spacetime modeling. Traditional approaches to spacetime simulation rely on manually designed geometries, limiting their adaptability. We propose a mechanism that dynamically adjusts spacetime geometry based on learned data and environmental information, automating the process through a specialized spacetime geometry calculation algorithm. The core claim is that this framework offers a significant advancement in spacetime simulation, enabling more accurate and flexible modeling compared to conventional methods. This work introduces a dynamic spacetime geometry parameter adjustment system, demonstrating its potential for enhanced simulation fidelity and computational efficiency.

Aug 31, 20260 citations

Space-Time Counterfactuals

J. Finkelstein

arXiv:quant-ph/9811057SyntheseJun 1, 199912 citations

Physics without time

Carlo Rovelli C, Francesca Vidotto

Cambridge University Press eBooksNov 13, 20140 citations

Spacetime-constrained oblivious transfer

Damián Pitalúa-García

In 1-out-of-2 oblivious transfer (OT), Alice inputs numbers ${x}_{0},{x}_{1}$ , Bob inputs a bit $b$ and outputs ${x}_{b}$ . Secure OT requires that Alice and Bob learn nothing about $b$ and ${x}_{\overline{b}}$ , respectively. We define spacetime-constrained oblivious transfer (SCOT) as OT in Minkowski spacetime in which Bob must output ${x}_{b}$ within ${R}_{b}$ , where ${R}_{0}$ and ${R}_{1}$ are fixed spacelike separated spacetime regions. We show that unconditionally secure SCOT is impossible with classical protocols in Minkowski (or Galilean) spacetime, or with quantum protocols in Galilean spacetime. We describe a quantum SCOT protocol in Minkowski spacetime, and we show it unconditionally secure.In 1-out-of-2 oblivious transfer (OT), Alice inputs numbers ${x}_{0},{x}_{1}$, Bob inputs a bit $b$ and outputs ${x}_{b}$. Secure OT requires that Alice and Bob learn nothing about $b$ and ${x}_{\overline{b}}$, respectively. We define spacetime-constrained oblivious transfer (SCOT) as OT in Minkowski spacetime in which Bob must output ${x}_{b}$ within ${R}_{b}$, where ${R}_{0}$ and ${R}_{1}$ are fixed spacelike separated spacetime regions. We show that unconditionally secure SCOT is impossible with classical protocols in Minkowski (or Galilean) spacetime, or with quantum protocols in Galilean spacetime. We describe a quantum SCOT protocol in Minkowski spacetime, and we show it unconditionally secure.

arXiv:1512.05649Physical Review AJun 29, 201628 citations

In 1-out-of-2 oblivious transfer (OT), Alice inputs numbers

{x}_{0},{x}_{1}

, Bob inputs a bit

b

and outputs

{x}_{b}

. Secure OT requires that Alice and Bob learn nothing about

b

and

{x}_{\overline{b}}

, respectively. We define spacetime-constrained oblivious transfer (SCOT) as OT in Minkowski spacetime in which Bob must output

{x}_{b}

within

{R}_{b}

, where

{R}_{0}

and

{R}_{1}

are fixed spacelike separated spacetime regions. We show that unconditionally secure SCOT is impossible with classical protocols in Minkowski (or Galilean) spacetime, or with quantum protocols in Galilean spacetime. We describe a quantum SCOT protocol in Minkowski spacetime, and we show it unconditionally secure.