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arXiv:1504.05147 · New Journal of Physics

Hyperdense coding and superadditivity of classical capacities in hypersphere theories

Serge Massar, Stefano Pironio, Damián Pitalúa-García

Published Oct 26, 2015• 14 citations

Abstract

In quantum superdense coding, two parties previously sharing entanglement can communicate a two bit message by sending a single qubit.We study this feature in the broader framework of general probabilistic theories.We consider a particular class of theories in which the local state space of the communicating parties corresponds to Euclidian hyperballs of dimension n (the case n = 3 corresponds to the Bloch ball of quantum theory).We show that a single n-ball can encode at most one bit of information, independently of n.We introduce a bipartite extension of such theories for which there exist dense coding protocols such that n log 1 2 + ( ) bits are communicated if entanglement is previously shared by the communicating parties.For n 3, > these protocols are more powerful than the quantum one, because more than two bits are communicated by transmission of a system that locally encodes at most one bit.We call this phenomenon hyperdense coding (HDC).Our HDC protocols imply superadditive classical capacities: two entangled systems can encode n log 1 2 2 + > ( ) bits, even though each system individually encodes at most one bit.In our examples, HDC and superadditivity of classical capacities come at the expense of violating tomographic locality or dynamical continuous reversibility.

DOI: 10.1088/1367-2630/17/11/113002

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In quantum superdense coding, two parties previously sharing entanglement can communicate a two bit message by sending a single qubit.We study this feature in the broader framework of general probabilistic theories.We consider a particular class of theories in which the local state space of the communicating parties corresponds to Euclidian hyperballs of dimension n (the case n = 3 corresponds to the Bloch ball of quantum theory).We show that a single n-ball can encode at most one bit of information, independently of n.We introduce a bipartite extension of such theories for which there exist dense coding protocols such that n log 1 2 + ( ) bits are communicated if entanglement is previously shared by the communicating parties.For n 3, > these protocols are more powerful than the quantum one, because more than two bits are communicated by transmission of a system that locally encodes at most one bit.We call this phenomenon hyperdense coding (HDC).Our HDC protocols imply superadditive classical capacities: two entangled systems can encode n log 1 2 2 + > ( ) bits, even though each system individually encodes at most one bit.In our examples, HDC and superadditivity of classical capacities come at the expense of violating tomographic locality or dynamical continuous reversibility.

Superdense coding proved that entanglement-assisted quantum communications can improve the data transmission rates compared to classical systems. It allows sending 2 classical bits between the parties in exchange of 1 quantum bit and a pre-shared entangled Bell pair. This paper introduces a new protocol which is intended for distributed communication. Using a pre-shared entangled Bell pair and 1 classical bit 2,5 classical bits can be transmitted in average. This means not only valuable increase in capacity but the two-way distributed operation opens new fields of investigation.

The famous superdense coding protocol of Bennett and Wiesner demonstrates that it is possible to communicate two bits of classical information by sending only one qubit and using a shared EPR pair. Our first result is that an arbitrary protocol for achieving this task (where there are no assumptions on the sender’s encoding operations or the dimension of the shared entangled state) is locally equivalent to the canonical Bennett-Wiesner protocol. In other words, the superdense coding task is rigid . In particular, we show that the sender and receiver only use additional entanglement (beyond the EPR pair) as a source of classical randomness. We also investigate several questions about higher-dimensional superdense coding, where the goal is to communicate one of d 2 possible messages by sending a d -dimensional quantum state, for general dimensions d . Unlike the d =2 case (i.e., sending a single qubit), there can be inequivalent superdense coding protocols for higher d . We present concrete constructions of inequivalent protocols, based on constructions of inequivalent orthogonal unitary bases for all d > 2. Finally, we analyze the performance of superdense coding protocols where the encoding operators are independently sampled from the Haar measure on the unitary group. Our analysis involves bounding the distinguishability of random maximally entangled states, which may be of independent interest.

We present a method, known as hyperdense coding, which uses photons hyperentangled in polarization and temporal mode to transmit up to 2.81 bits/photon of classical information over a two-qubit quantum channel. Furthermore, the hyperentangled photons used in this approach are much less susceptible to the influences of turbulence than spatial qubits, allowing for turbulence-resistant communication. We compare this technique to previously implemented hyperentanglement-enhanced superdense coding implementations which have a maximum theoretical channel capacity of 2 bits/photon.

Quantum dense coding is a foundational protocol in quantum communication, allowing two classical bits to be transmitted by sending a single qubit when a maximally entangled pair is shared. In this work, we consider Embedded Dense Coding (EDC)-a generalization of deterministic dense coding that embeds one subsystem into a higher-dimensional Hilbert space. To assess the operational advantage of EDC compared to standard dense coding, we consider the probability of transmission error when fixing the rate of entanglement consumed per classical message sent. We first demonstrate that EDC enables a smaller one-shot transmission error compared to standard dense coding when using quantum channels with nonzero rates of dephasing and loss. We then demonstrate that even with noiseless communication channels, EDC leads to smaller overall errors when the sender and receiver have noisy local processors. This advantage is shown through concrete implementations of EDC on IBM's Heron processor.

Abstract Superdense coding uses entanglement as a resource to communicate classical information efficiently through quantum channels. A superdense coding method is optimal when its capacity reaches Holevo bound. We show that for optimality, maximal entanglement is a necessity across the bipartition of Alice and Bob, but neither absolute nor genuine multipartite entanglement is required. Unlike the previous schemes, which can transmit either even or odd bits of information, we demonstrate a generalized dense coding protocol using the genuine multipartite entangled GHZ state to send arbitrary information bits. Expressed in the eigenbasis of different Pauli operators, GHZ state is characterized by a unique parity pattern which enables us to formulate a security checking technique to ensure absolute security of the protocol. We show this method is better applicable in a scenario, where the initial information is distributed among spatially separated parties. Finally, optimizing the number of qubit(s) sent to Bob, we construct a distributed dense coding method, which completely depicts absolutely secure quantum communication between many to one party.

In quantum information theory, superdense coding allows two network entities to exchange two classical bits via a quantum channel using a single quantum bit (qubit) transmission, provided they have pre-shared an entangled qubit. An attacker intercepting the qubit during transmission cannot extract meaningful data without the other entangled qubit from the pair. However, an attacker can disrupt the communication by introducing its own qubit to the receiver. To enhance the security of superdense coding, we propose an authentication mechanism through a classical communication channel.