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Chinese Control Conference (CCC)

More entanglement, less reliability

Hongting Song, Zairong Xi

Published Jan 1, 2011• 1 citation
OpenAlex

Abstract

Entanglement of quantum states is a very important resource in quantum communication systems. For many special tasks, entanglement is found to be helpful. But it is still a problem how to find the relationship between the amount of entanglement and the effect of doing the task. In this work, we consider a particular task—trying to send a single classical bit as effective as possible through a noisy quantum channel and two transmissions through the channel are available as a resource. For two special channels—amplitude damping channel and two-Pauli channel, we separately establish the quantitative connections, and try to find whether the relationship is always monotonous, i.e., the states with the larger entanglement necessarily result in the better effect. Unfortunately, this is not true. At the same time, we can get the optimal codes for the task using this method.

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Entanglement of quantum states is a very important resource in quantum communication systems. For many special tasks, entanglement is found to be helpful. But it is still a problem how to find the relationship between the amount of entanglement and the effect of doing the task. In this work, we consider a particular task—trying to send a single classical bit as effective as possible through a noisy quantum channel and two transmissions through the channel are available as a resource. For two special channels—amplitude damping channel and two-Pauli channel, we separately establish the quantitative connections, and try to find whether the relationship is always monotonous, i.e., the states with the larger entanglement necessarily result in the better effect. Unfortunately, this is not true. At the same time, we can get the optimal codes for the task using this method.
Entanglement is an important resource for various applications of quantum computation. Another important endeavor is to establish the role of entanglement in practical implementation where system of interest is affected by various kinds of noisy channels. Here, a single classical bit is used to send information under the influence of a noisy quantum channel. The entanglement content of quantum states is computed under noisy channels such as amplitude damping, phase damping, squeesed generalised amplitude damping, Pauli channels and various collective noise models on the protocols of quantum key distribution.
The problem of sending a single classical bit through a generalized amplitude damping channel is considered. When two transmissions through the channel are available as a resource, we find that two entangled transmissions can enhance the capability of receiver's judging information correctly under certain conditions compared with two product-state transmissions. In addition, we find a special case in which the two entangled transmissions can always make a classical bit more effectively disable the noise influence.
We study the effects of quantum entanglement on the performance of two classical zero-error communication tasks among multiple parties. Both tasks are generalizations of the two-party zero-error channel-coding problem, where a sender and a receiver want to perfectly communicate messages through a one-way classical noisy channel. If the two parties are allowed to share entanglement, there are several positive results that show the existence of channels for which they can communicate strictly more than what they could do with classical resources. In the first task, one sender wants to communicate a common message to multiple receivers. We show that if the number of receivers is greater than a certain threshold then entanglement does not allow for an improvement in the communication for any finite number of uses of the channel. On the other hand, when the number of receivers is fixed, we exhibit a class of channels for which entanglement gives an advantage. The second problem we consider features multiple collaborating senders and one receiver. Classically, cooperation among the senders might allow them to communicate on average more messages than the sum of their individual possibilities. We show that whenever a channel allows single-sender entanglement-assisted advantage, then the gain extends also to the multisender case. Furthermore, we show that entanglement allows for a peculiar amplification of information which cannot happen classically, for a fixed number of uses of the channels.
Shared entanglement is a resource available to parties communicating over a quantum channel, much akin to public coins in classical communication protocols. Whereas shared randomness does not help in the transmission of information, or significantly reduce the classical complexity of computing functions (as compared to private-coin protocols), shared entanglement leads to startling phenomena such as "quantum teleportation" and "superdense coding."The problem of characterising the power of prior entanglement has puzzled many researchers. In this paper, we revisit the problem of transmitting classical bits over an entanglement-assisted quantum channel. We derive a new, optimal bound on the number of quantum bits required for this task, for any given probability of error. All known lower bounds in the setting of bounded error entanglement-assisted communication are based on sophisticated information theoretic arguments. In contrast, our result is derived from first principles, using a simple linear algebraic technique.
Shared entanglement is a resource available to parties communicating over a quantum channel, much akin to public coins in classical communication protocols. Whereas shared randomness does not help in the transmission of information, or significantly reduce the classical complexity of computing functions (as compared to private-coin protocols), shared entanglement leads to startling phenomena such as "quantum teleportation" and "superdense coding."The problem of characterising the power of prior entanglement has puzzled many researchers. In this paper, we revisit the problem of transmitting classical bits over an entanglement-assisted quantum channel. We derive a new, optimal bound on the number of quantum bits required for this task, for any given probability of error. All known lower bounds in the setting of bounded error entanglement-assisted communication are based on sophisticated information theoretic arguments. In contrast, our result is derived from first principles, using a simple linear algebraic technique.