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Exchange-free computation on an unknown qubit at a distance

H Salih, Jonte R. Hance, W McCutcheon, T Rudolph, JG Rarity

Published Jan 19, 2021• 0 citations
Publisher

Abstract

We present a way of directly manipulating an arbitrary qubit, without the exchange of any particles. This includes as an application the exchange-free preparation of an arbitrary quantum state at Alice by a remote classical Bob. As a result, we are able to propose a protocol that allows one party to directly enact, by means of a suitable program, any computation exchange-free on a remote second party's unknown qubit. Further, we show how to use this for the exchange-free control of a universal two-qubit gate, thus opening the possibility of directly enacting any desired algorithm remotely on a programmable quantum circuit.

DOI
10.25405/ncl.34496418

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We present a way of directly manipulating an arbitrary qubit, without the exchange of any particles. This includes as an application the exchange-free preparation of an arbitrary quantum state at Alice by a remote classical Bob. As a result, we are able to propose a protocol that allows one party to directly enact, by means of a suitable program, any computation exchange-free on a remote second party's unknown qubit. Further, we show how to use this for the exchange-free control of a universal two-qubit gate, thus opening the possibility of directly enacting any desired algorithm remotely on a programmable quantum circuit.
Abstract We present a way of directly manipulating an arbitrary qubit, without the exchange of any particles. This includes as an application the exchange-free preparation of an arbitrary quantum state at Alice by a remote classical Bob. As a result, we are able to propose a protocol that allows one party to directly enact, by means of a suitable program, any computation exchange-free on a remote second party's unknown qubit. Further, we show how to use this for the exchange-free control of a universal two-qubit gate, thus opening the possibility of directly enacting any desired algorithm remotely on a programmable quantum circuit.
We propose a protocol for the remote implementation of an arbitrary two-qubit unitary operation using pre-shared entanglement. In our protocol, Bob possesses an unknown two-qubit state, while Alice implements the required operations using calibrated black-box devices. Alice does not need to know the parameters of these operations, and Bob's unknown state never leaves his laboratory. The protocol is based on the Euler decomposition of single-qubit unitary operations and the Cartan decomposition of two-qubit unitary operations. First, we construct protocols for the remote implementation of the single-qubit operation U=Rz(γ)Rx(β)Rz(α)U = R_z(γ)R_x(β)R_z(α)U=Rz​(γ)Rx​(β)Rz​(α) using pre-shared Bell states. We then construct a protocol for the two-qubit operation Rzz(θ)R_{zz}(θ)Rzz​(θ) using a single pre-shared Bell state and extend it to Rxx(θ)R_{xx}(θ)Rxx​(θ) and Ryy(θ)R_{yy}(θ)Ryy​(θ) through local unitary transformations. These elementary protocols are finally combined to implement an arbitrary two-qubit unitary operation. A third party, Charlie, determines the required decomposition and provides Alice with the corresponding black-box devices before the protocol begins. Thus, neither Alice nor Bob requires the classical description of the unitary operation.
Teleportation is a cornerstone of quantum technologies, and has played a key role in the development of quantum information theory. Pushing the limits of teleportation is therefore of particular importance. Here, we apply a different aspect of quantumness to teleportation---namely exchange-free, or counterfactual, computation at a distance. We propose a universal controlled-phase gate, where no particles are exchanged between control and target. This allows the full repertoire of quantum computation to me made exchange-free, including both complete Bell detection among two remote parties and so teleportation and telecloning. Further, we show that this gate, and the protocols based on it, is experimentally feasible, simulating the fidelity of our exchange-free teleportation and telecloning protocols for realistic bit-errors.
Teleportation is a cornerstone of quantum technologies, and has played a key role in the development of quantum information theory. Pushing the limits of teleportation is therefore of particular importance. Here, we apply a different aspect of quantumness to teleportation---namely exchange-free, or counterfactual, computation at a distance. We propose a universal controlled-phase gate, where no particles are exchanged between control and target. This allows the full repertoire of quantum computation to me made exchange-free, including both complete Bell detection among two remote parties and so teleportation and telecloning. Further, we show that this gate, and the protocols based on it, is experimentally feasible, simulating the fidelity of our exchange-free teleportation and telecloning protocols for realistic bit-errors.
Abstract Teleportation is a cornerstone of quantum technologies, and has played a key role in the development of quantum information theory. Pushing the limits of teleportation is therefore of particular importance. Here, we apply a different aspect of quantumness to teleportation—namely exchange-free, or counterfactual, computation at a distance. We propose a universal controlled-phase gate, where no particles are exchanged between control and target. This allows the full repertoire of quantum computation to me made exchange-free, including both complete Bell detection among two remote parties and so teleportation and telecloning. Further, we show that this gate, and the protocols based on it, is experimentally feasible, simulating the fidelity of our exchange-free teleportation and telecloning protocols for realistic bit-errors.