Reversible computation and the causal structure of space-time

TL;DR

This paper explores how the fundamental causal structure of spacetime constrains the set of reversible quantum operations, revealing that anti-linear anti-unitary gates are forbidden due to causal principles beyond relativity.

Contribution

It demonstrates that the prohibition of anti-unitary gates in quantum mechanics arises from fundamental spacetime causal constraints, linking quantum reversibility to spacetime structure.

Findings

Anti-unitary gates violate a fundamental causal primitive.

Spacetime causal structure constrains quantum reversible operations.

The restriction is distinct from relativistic causality principles.

Abstract

Reversible algorithms play a crucial role both in classical and quantum computation. While for a classical bit the only nontrivial reversible operation is the bit-flip, nature is far more versatile in what it allows to do to a quantum bit. The reversible operations that a quantum computer can perform on a qubit are group of linear unitary transformations. However, laws of quantum mechanics prohibit implementation of anti-linear anti-unitary gates, even though they are perfectly reversible. Here we show that such a restriction on possible set of reversible operations is, remarkably, a fundamental constraint of spacetime structure. In particular, it will be shown that construction of any anti-linear anti-unitary gate will lead to violation of a fundamental causal primitive which, as we shall argue, is fundamentally different from the principle of relativistic causality.