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arXiv:1201.6624

Remote State Preparation of Mental Information

Patrizio Emmanuele Tressoldi, Andrei Yu. Khrennikov

Published Jan 31, 2012• 0 citations
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Abstract

The aim of this paper is to define in theoretical terms and summarise the available experimental evidence that physical and mental "objects", if considered "information units", may present similar classical and quantum models of communication beyond their specific characteristics. Starting with the Remote State Preparation protocol, a variant of the Teleportation protocol, for which formal models and experimental evidence are already available in quantum mechanics, we outline a formal model applied to mental information we defined Remote State Preparation of Mental Information (RSPMI), and we summarise the experimental evidence supporting the feasibility of a RSPMI protocol. The available experimental evidence offers strong support to the possibility of real communication at distance of mental information promoting the integration between disciplines that have as their object of knowledge different aspects of reality, both physical and the mental, leading to a significant paradigm shift in cognitive and information science.

DOI
10.48550/arxiv.1201.6624

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The aim of this paper is to define in theoretical terms and summarise the available experimental evidence that physical and mental "objects", if considered "information units", may present similar classical and quantum models of communication beyond their specific characteristics. Starting with the Remote State Preparation protocol, a variant of the Teleportation protocol, for which formal models and experimental evidence are already available in quantum mechanics, we outline a formal model applied to mental information we defined Remote State Preparation of Mental Information (RSPMI), and we summarise the experimental evidence supporting the feasibility of a RSPMI protocol. The available experimental evidence offers strong support to the possibility of real communication at distance of mental information promoting the integration between disciplines that have as their object of knowledge different aspects of reality, both physical and the mental, leading to a significant paradigm shift in cognitive and information science.
Quantum communication as an important part of quantum information processing has been widely investigated. Different from classical communication,quantum information may be transferred without physical transportation of quantum media. Quantum teleportation is the first typical example. As an improved quantum transport protocol,quantum remote preparation may be used to balance the quantum measurement and classical communication complexity. However,studies have shown that this balance is unsuitable for all quantum states. It greatly depends on the spactial algebraic or geometric structure of space in which the information may be transmitted. Recently,it seems that the restriction can be partially overcome by using information splitting. This paper aims to summarize theoretical remote preparations and presents primitive examples. It is desired that with this article,researchers without fundamental knowledges may be familiar with these schemes. Meanwhile,it provides some suggestions for further research.
Quantum information theory has revolutionized the way in which information is processed using quantum resources such as entangled states, local operations and classical communications. Two important protocols in quantum communications are quantum teleportation and remote state preparation. In quantum teleportation neither the sender nor the receiver know the identity of a state. In remote state preparation the sender knows the state which is to be remotely prepared without ever physically sending the object or the complete classical description of it. Using one unit of entanglement and one classical bit Alice can remotely prepare a photon (from special ensemble) of her choice at Bob's laboratory. In remote state measurement Alice asks Bob to simulate any single particle measurement statistics on an arbitrary photon. In this talk we will present these ideas and discuss the latest developments and future open problems.
Abstract—Remote state preparation is the variant of quantum state teleportation in which the sender knows the quantum state to be communicated. The original paper introducing teleportation established minimal requirements for classical communication and entanglement but the corresponding limits for remote state preparation have remained unknown until now: previous work has shown, however, that it not only requires less classical communication but also gives rise to a tradeoff between these two resources in the appropriate setting. We discuss this problem from first principles, including the various choices one may follow in the definitions of the actual resources. Our main result is a general method of remote state preparation for arbitrary states of many qubits, at a cost of 1 bit of classical communication and 1 bit of entanglement per qubit sent. In this “universal ” formulation, these ebit and cbit requirements are shown to be simultaneously optimal by exhibiting a dichotomy. Our protocol then yields the exact tradeoff curve for memoryless sources of pure states (including the case of incomplete knowledge of the ensemble probabilities), based on the recently established quantum-classical tradeoff for visible quantum data compression. A variation of that method allows us to solve the even more general problem of preparing entangled states between sender and receiver (i.e., purifications of mixed state ensembles). The paper includes an extensive discussion of our results, including the impact of the choice of model on the resources, the topic of obliviousness, and an application to private quantum channels and quantum data hiding. Index Terms—Cryptography, entanglement, large deviations, teleportation, tradeoff. I.
The hitherto unexplored nonlocality of quantum correlations in the information transfer protocol of remote state preparation (RSP) is investigated in terms of a unified nonlocality argument formulated for teleportation as well as for two distinct RSP schemes. The argument differs only in the respective types of local measurements used in each scenario. One of the RSP schemes uses single particle projective measurements, while the other uses joint Bell-basis measurements. Interestingly, the quantum mechanical violations of the Bell-CHSH type inequalities formulated for each of the RSP setups, while being equal to each other, also turn out to be equal to that of the corresponding Bell-CHSH type local realist inequality for teleportation, using the common resource of non-maximally entangled state. This reveals that for such a resource state, the maximum amount of extractable nonlocality of correlations involved in the transfer of information is the same for the standard teleportation protocol and the two RSP schemes considered here, thereby implying that the essential difference between teleportation and remote state preparation lies in the amount of classical information required to be exchanged between parties, and not in the nonlocality of underlying correlations.
In quantum teleportation, neither Alice nor Bob acquires any classical knowledge on teleported states. The teleportation protocol is said to be oblivious to both parties. In remote state preparation (RSP), it is assumed that Alice is given complete classical knowledge on the state that is to be prepared by Bob. Recently, Leung and Shor [e-print quant-ph/0201008] showed that the same amount of classical information as that in teleportation needs to be transmitted in any exact and deterministic RSP protocol that is oblivious to Bob. Assuming that the dimension of subsystems in the prior-entangled state is the same as the dimension of the input space, we study similar RSP protocols, but not necessarily oblivious to Bob. We show that in this case Bob's quantum operation can be safely assumed to be a unitary transformation. We then derive an equation that is a necessary and sufficient condition for such a protocol to exist. By studying this equation, we show that one-qubit RSP requires two classical bits of communication, which is the same amount as in teleportation, even if the protocol is not assumed oblivious to Bob. For higher dimensions, it is still an open question whether the amount of classical communication can be reduced by abandoning oblivious conditions.
Remote state preparation is the variant of quantum state teleportation in which the sender knows the quantum state to be communicated. The original paper introducing teleportation established minimal requirements for classical communication and entanglement but the corresponding limits for remote state preparation have remained unknown until now: previous work has shown, however, that it not only requires less classical communication but also gives rise to a tradeoff between these two resources in the appropriate setting. We discuss this problem from first principles, including the various choices one may follow in the definitions of the actual resources. Our main result is a general method of remote state preparation for arbitrary states of many qubits, at a cost of 1 bit of classical communication and 1 bit of entanglement per qubit sent. In this "universal" formulation, these ebit and cbit requirements are shown to be simultaneously optimal by exhibiting a dichotomy. Our protocol then yields the exact tradeoff curve for memoryless sources of pure states (including the case of incomplete knowledge of the ensemble probabilities), based on the recently established quantum-classical tradeoff for visible quantum data compression. A variation of that method allows us to solve the even more general problem of preparing entangled states between sender and receiver (i.e., purifications of mixed state ensembles). The paper includes an extensive discussion of our results, including the impact of the choice of model on the resources, the topic of obliviousness, and an application to private quantum channels and quantum data hiding.