No-Summoning Theorem: A Quantum Constraint in Relativistic Frameworks

In the article titled “A No-summoning theorem in Relativistic Quantum Theory” published in 2011, the authors investigate a fundamental limitation in the manipulation and transfer of quantum states within the framework of relativistic quantum theory. They consider a scenario where Alice gives Bob an unknown quantum state at a spacetime point (P). Later, at some point (Q) in the causal future of (P), Alice requests the return of that state. While Bob knows he will be summoned to return the state at (Q), he does not know the exact location or timing of (Q) until the request is made. The authors demonstrate that unlike in classical Minkowski spacetime or Galilean quantum mechanics—where such a summons can be fulfilled with negligible delay—Bob cannot, in general, return the unknown quantum state in a relativistic quantum setting. This limitation arises not merely from the no-signalling principle (which forbids faster-than-light communication) or the no-cloning theorem (which prohibits copying unknown quantum states) individually, but from their combination manifested in relativistic contexts. Hence, the no-summoning theorem signifies a unique, intrinsic feature of relativistic quantum theory, placing stringent constraints on how quantum information is transmitted and controlled when relativistic causality is respected (Kent, 2011).

From a quantum governance perspective, these findings highlight critical considerations for managing quantum information protocols across spacetime in a way consistent with relativistic constraints. The no-summoning theorem implies that in distributed quantum networks, especially those spanning large distances or involving relativistic effects, it is fundamentally impossible to guarantee instantaneous retrieval of an unknown quantum state at arbitrarily specified future spacetime points. Governance frameworks for quantum communication and computing must thus incorporate mechanisms acknowledging this intrinsic limitation, such as pre-agreed retrieval points or carefully designed quantum memory management consistent with causal structure. Moreover, safeguarding quantum information necessitates adherence to the no-signalling and no-cloning principles, underscoring that governance models must ensure privacy and security protocols cannot violate these fundamental constraints. Policies regulating quantum networks might leverage the no-summoning concept to prevent unauthorized duplication or repositioning of quantum states, thereby strengthening security assurances. Therefore, this theorem provides a rigorous scientific basis for crafting robust and physically grounded quantum governance policies that address the unique challenges posed by relativistic quantum phenomena.

Reference: Kent, A. (2011). A No-summoning theorem in Relativistic Quantum Theory. arXiv preprint arXiv:1101.4612.