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arXiv:1304.0283

Fidelity of remote state preparation can be enhanced by local operation

Congyi Hua, Sheng-Wen Li, Yixin Chen

Published Apr 1, 2013• 1 citation
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Abstract

Remote state preparation (RSP) is a quantum information protocol which allows preparing a quantum state at a distant location with the help of a preshared nonclassical resource state and a classical channel. The efficiency of successfully doing this task can be represented by the RSP-fidelity of the resource state. In this paper, we study the influence on the RSP-fidelity by applying certain local operations on the resource state. We prove that RSP-fidelity does not increase for any unital local operation. However, for nonunital local operation, such as local amplitude damping channel, we find that some resource states can be enhanced to increase the RSP-fidelity. We give the optimal parameter of symmetric local amplitude damping channel for enhancing Bell-diagonal resource states. In addition, we show RSP-fidelity can suddenly change or even vanish at instant under local decoherence.

DOI
10.48550/arxiv.1304.0283

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Remote state preparation (RSP) is a quantum information protocol which allows preparing a quantum state at a distant location with the help of a preshared nonclassical resource state and a classical channel. The efficiency of successfully doing this task can be represented by the RSP-fidelity of the resource state. In this paper, we study the influence on the RSP-fidelity by applying certain local operations on the resource state. We prove that RSP-fidelity does not increase for any unital local operation. However, for nonunital local operation, such as local amplitude damping channel, we find that some resource states can be enhanced to increase the RSP-fidelity. We give the optimal parameter of symmetric local amplitude damping channel for enhancing Bell-diagonal resource states. In addition, we show RSP-fidelity can suddenly change or even vanish at instant under local decoherence.
Transmission efficiency (TE) of remote state preparation (RSP) with a shared quantum state and one bit of classical communication is considered. Following Daki\ifmmode \acute{c}\else \'{c}\fi{} et al. [Nat. Phys. 8, 666 (2012)], the encoding and decoding operators of the protocol are restricted to the physically relevant classes of projective measurements and unitary operators, respectively. It is shown that contrary to the previous arguments, the quadratic fidelity as well as the linear fidelity could be a valid figure of merit to quantify the TE of RSP. Then, the TE of the protocol in terms of both linear and quadratic fidelities is evaluated in a fully optimized scenario which includes the maximization over the encoding parameters as well as a meaningful maximization over the decoding parameters. The results show that, in this scenario, the TE scales with the sum of the two largest eigenvalues of the squared correlation matrix of the resource state that is zero only for product states. This approach successfully quantifies the performance of the protocol in terms of the resource state parameters and provides a means to compare the usefulness of any two resource states for RSP.
We propose a scheme for deterministic remote preparation of an arbitrary two-qubit state via a relay node. Afterwards, we investigate how the scheme is influenced by the noise type, the initial state to be remotely prepared, and the decoherence rate. We find that the fidelity is symmetrical with the line (λb-f=λp-f=0.5) in bit-flip and phase-flip channels. In addition, the fidelity decreases with the increase of decoherence rate in the amplitude-damping and phase-damping channels. We also compare it with other RSP schemes. Since only Bell pairs work as the quantum channels, it makes our RSP scheme more available and feasible.
Remote state preparation (RSP) is the act of preparing a quantum state at a remote location without actually transmitting the state itself. Using at most two classical bits and a single shared maximally entangled state, one can in theory remotely prepare any qubit state with certainty and with perfect fidelity. However, in any experimental implementation the average fidelity between the target and output states cannot be perfect. In order for an RSP experiment to demonstrate genuine quantum advantages, it must surpass the optimal threshold of a comparable classical protocol. Here we study the fidelity achievable by RSP protocols lacking shared entanglement and determine the optimal value for the average fidelity in several different cases. We implement an experimental scheme for deterministic remote preparation of arbitrary photon polarization qubits, preparing 178178178 different pure and mixed qubit states with an average fidelity of 0.9950.9950.995. Our experimentally achieved average fidelities surpass our derived classical thresholds whenever the classical protocol does not trivially allow for perfect RSP.
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.
Quantum networks typically comprise quantum channels, repeaters, and end nodes. Remote state preparation (RSP) allows one end node to prepare the states of the other end nodes remotely. While quantum discord has recently been recognized as necessary for RSP, it does not guarantee the practical implementation of RSP in quantum networks surpasses any classical method. Herein, we theoretically introduce and experimentally study a quantum resource that we call the RSP capability. This resource validates all the static and dynamic elements required to enable genuine quantum networks where the RSP’s implementation can outperform any classical emulation of entanglement- and qubit-unitaries-free strategies, including the static resources of Einstein-Podolsky-Rosen pairs and the dynamic resources of quantum channels and repeaters. Our experiment measures the RSP capability to demonstrate the transition between classical and nonclassical RSP depending on the photon-pair qualities. It shows that quantum discord does not confirm a nonclassical RSP, but the RSP capability does. These results help reveal the quantum advantages that emerge when networking RSP is in play. The authors introduce and experimentally study a quantum resource called the remote state preparation capability. This resource validates all static and dynamic elements required to enable quantum networks where the implementation of remote state preparation can outperform any classical emulation of entanglement- and qubit-unitaries-free strategies.
In recent years, exploration of the possible use of separable states as a resource to achieve quantum information processing (QIP) tasks has been gaining increasing significance. In this context, a particularly important demonstration has been that nonvanishing discord is the necessary condition for separable states to be used as a resource for remotely preparing any arbitrary pure target state [Nat. Phys. 8, 666 (2012)]. The present work stems from our observation that not only can resource states with the same discord imply different efficiencies (in terms of average fidelity) of the remote state preparation (RSP) protocol, but also states with higher discord can imply lower RSP efficiency. Therefore, this necessitates identification of the relevant feature of quantum correlations that can appropriately quantify the effectiveness of the resource state for the RSP protocol. To this end, for the two-qubit Bell-diagonal states, we show that an appropriate measure of simultaneous correlations in three mutually unbiased bases can serve to quantify the usefulness of the resource for the RSP task using entangled as well as separable states, including nondiscordant states as a resource. In particular, it is revealed that zero-discord states with such a nonvanishing measure can be useful for remotely preparing a subset of pure target states. Thus, this work shows that, using separable states, an effective resource for QIP tasks such as RSP can be provided by simultaneous correlations in mutually unbiased bases.