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Locking classical correlation in quantum states

David DiVincenzo, Michal Horodecki, Debbie Leung, John Smolin, Barbara Terhal

TL;DR

There are (2n+1)-qubit states for which a one-bit message doubles the optimal classical mutual information between measurement results on the subsystems, from n/2 bits to n bits.

Abstract

We show that there exist bipartite quantum states which contain large hidden classical correlation that can be unlocked by a disproportionately small amount of classical communication. In particular, there are $(2n+1)$-qubit states for which a one bit message doubles the optimal classical mutual information between measurement results on the subsystems, from $n/2$ bits to $n$ bits. States exhibiting this behavior need not be entangled. We study the range of states exhibiting this phenomenon and bound its magnitude.

Locking classical correlation in quantum states

TL;DR

There are (2n+1)-qubit states for which a one-bit message doubles the optimal classical mutual information between measurement results on the subsystems, from n/2 bits to n bits.

Abstract

We show that there exist bipartite quantum states which contain large hidden classical correlation that can be unlocked by a disproportionately small amount of classical communication. In particular, there are -qubit states for which a one bit message doubles the optimal classical mutual information between measurement results on the subsystems, from bits to bits. States exhibiting this behavior need not be entangled. We study the range of states exhibiting this phenomenon and bound its magnitude.

Paper Structure

This paper contains 3 sections, 1 theorem, 35 equations.

Table of Contents

  1. Appendix
  2. Locking with more bases
  3. Small initial correlation

Key Result

Lemma 1

If $\rho$ is a bipartite state on $C^{d} \otimes C^d$, then where $d' < 2d$ is a prime power no less than $d$.

Theorems & Definitions (1)

  • Lemma 1