DeepAI AI Chat
Log In Sign Up

On the Entanglement Cost of One-Shot Compression

by   Shima Bab Hadiashar, et al.
University of Waterloo

We revisit the task of compressing an ensemble of quantum states in the one-shot setting. The protocols achieving the best compression use shared entanglement that may be much larger than the original message, while others (with potentially larger communication cost) have entanglement cost bounded by the message length. This motivates the question as to whether entanglement is truly necessary for compression, and if so, how much of it is needed. Motivated by questions in communication complexity, we lift certain restrictions imposed on compression protocols in tasks such as state-splitting and channel simulation. We show that an ensemble constructed by Jain, Radhakrishnan, and Sen (ICALP'03) saturates the known bounds on the sum of communication and entanglement costs, even with the relaxed compression protocols we study. The ensemble and the associated one-way communication protocol have several remarkable properties. The ensemble is incompressible by more than a constant number of qubits without entanglement, even when constant error is allowed. Moreover, in the presence of entanglement, the communication cost of compression can be arbitrarily smaller than the entanglement cost. The quantum information cost of the protocol can thus be arbitrarily smaller than the cost of compression without entanglement. The ensemble can also be used to show the impossibility of reducing, via compression, the entanglement used in two-party protocols for computing Boolean functions.


Trade-offs between Entanglement and Communication

We study the advantages of quantum communication models over classical c...

Matching upper bounds on symmetric predicates in quantum communication complexity

In this paper, we focus on the quantum communication complexity of funct...

SoK on Performance Bounds in Anonymous Communication

Communicating anonymously comes at a cost - and large communities have b...

Communication Complexity of One-Shot Remote State Preparation

Quantum teleportation uses prior shared entanglement and classical commu...

Compact Neural Networks based on the Multiscale Entanglement Renormalization Ansatz

The goal of this paper is to demonstrate a method for tensorizing neural...

A Boolean Functions Theoretic Approach to Quantum Hypergraph States and Entanglement

We establish an one-to-one correspondence between the Boolean functions ...