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Superdense coding of quantum states

Aram Harrow, Patrick Hayden, Debbie Leung

TL;DR

This work describes a method for nonobliviously communicating a 2l-qubit quantum state by physically transmitting l+o(l) qubits, and by consuming l ebits of entanglement plus some shared random bits.

Abstract

We describe a method to non-obliviously communicate a 2l-qubit quantum state by physically transmitting l+o(l) qubits of communication, and by consuming l ebits of entanglement and some shared random bits. In the non-oblivious scenario, the sender has a classical description of the state to be communicated. Our method can be used to communicate states that are pure or entangled with the sender's system; l+o(l) and 3l+o(l) shared random bits are sufficient respectively.

Superdense coding of quantum states

TL;DR

This work describes a method for nonobliviously communicating a 2l-qubit quantum state by physically transmitting l+o(l) qubits, and by consuming l ebits of entanglement plus some shared random bits.

Abstract

We describe a method to non-obliviously communicate a 2l-qubit quantum state by physically transmitting l+o(l) qubits of communication, and by consuming l ebits of entanglement and some shared random bits. In the non-oblivious scenario, the sender has a classical description of the state to be communicated. Our method can be used to communicate states that are pure or entangled with the sender's system; l+o(l) and 3l+o(l) shared random bits are sufficient respectively.

Paper Structure

This paper contains 2 sections, 2 theorems, 32 equations.

Table of Contents

  1. Proof of Lemma \ref{['lem:pure']}
  2. Extension of lemma \ref{['lem:pure']} for sharing entangled states

Key Result

Lemma 1

Let $0 < \epsilon \leq 1$. If $d \geq \hbox{$\frac{10}{\epsilon}$}$, there exists a set of isometries $\{U_k\}_{k=1}^{n}$, where $n = \hbox{$\frac{120 \ln 2}{\epsilon^3}$} \, d \log d$, such that Here, each $U_k$ takes $d^2$-dimensional states into a Hilbert space ${\cal H}_A \otimes {\cal H}_B$, where $\dim({\cal H}_A) = \hbox{$\frac{112 \ln 2}{\epsilon^2}$} \, d \log d$ and $\dim({\cal H}_B) =

Theorems & Definitions (2)

  • Lemma 1
  • Lemma 2