# Quantum Entanglement in Time

## TL;DR

This paper introduces the concept of quantum entanglement in time within the framework of entangled consistent histories, exploring its properties, bounds, and implications for temporal quantum correlations.

## Contribution

It presents a novel theoretical framework for quantum entanglement in time and analyzes its properties and bounds using tools from spatial quantum states.

## Key findings

- Quantum entanglement in time exhibits monogamy similar to spatial entanglement.
- Derived the Tsirelson bound for Leggett-Garg inequalities based on entangled histories.
- Established bounds on temporal correlations in quantum systems.

## Abstract

In this paper we present a concept of quantum entanglement in time in a context of entangled consistent histories. These considerations are supported by presentation of necessary tools closely related to those acting on a space of spatial multipartite quantum states. We show that in similarity to monogamy of quantum entanglement in space, quantum entanglement in time is also endowed with this property for a particular history. Basing on these observations, we discuss further bounding of temporal correlations and derive analytically the Tsirelson bound implied by entangled histories for the Leggett-Garg inequalities.