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Journal of Optics B Quantum and Semiclassical Optics

Controlled sign gate through mode entangled states

Sergey A. Podoshvedov

Published Oct 30, 2004• 3 citations
Publisher

Abstract

We propose a model to perform controlled sign (CS) gate flip in two stages that is free of the use of detectors discriminating between one- and two-photon number states. The CS gate with mode entangled qubits and two-photon quantum channel is used at the first stage to produce a more perfect four-photon quantum channel. A two-photon quantum channel can be constructed using a spontaneous parametric down converter and methods of linear optics. We describe the CS gate performance with the help of a four-photon quantum channel at the second stage. The success probability of the CS gate performance with both two- and four-photon quantum channels is 1/4. The use of usual detectors at the first stage leads to the appearance of a noisy quantum channel that is shown not to have influence on the valid CS gate flip at the second stage whose outcome is characterized by fourfold coincidence registration of photons. The success probability of such a CS gate in two stages is 1/16.

DOI
10.1088/1464-4266/6/12/010

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We propose a model to perform controlled sign (CS) gate flip in two stages that is free of the use of detectors discriminating between one- and two-photon number states. The CS gate with mode entangled qubits and two-photon quantum channel is used at the first stage to produce a more perfect four-photon quantum channel. A two-photon quantum channel can be constructed using a spontaneous parametric down converter and methods of linear optics. We describe the CS gate performance with the help of a four-photon quantum channel at the second stage. The success probability of the CS gate performance with both two- and four-photon quantum channels is 1/4. The use of usual detectors at the first stage leads to the appearance of a noisy quantum channel that is shown not to have influence on the valid CS gate flip at the second stage whose outcome is characterized by fourfold coincidence registration of photons. The success probability of such a CS gate in two stages is 1/16.
We present a model to realize a probabilistic conditional sign flip gate using only linear optics. The gate operates in the space of number-state qubits and is obtained by a nonconventional use of the teleportation protocol. Both a destructive and a nondestructive version of the gate are presented. In the former case an Hadamard gate on the control qubit is combined with a projective teleportation scheme mixing control and target. The success probability is 1∕21∕21∕2. In the latter case we need a quantum encoder realized via the interaction of the control qubit with an ancillary state composed of two maximally entangled photons. The success probability is 1∕41∕41∕4.
We propose a simple experimental scheme of preparing a four-photon entangled state, which is a useful resource for two-qubit quantum operations, e.g., the controlled-NOT gate. The scheme can successfully postselect the events of the desired four-photon entangled state in the coincidence basis and can be constructed with four photons from parametric down conversion, linear optical devices, and conventional photon detectors, all of which are available in current technology. We also show an experimental scheme for a controlled-NOT gate based on teleportation with the prepared four-photon state.
We propose a linear optical scheme to implement the nondeterministic two-qubit controlled phase gate with the certain success probability. The proposed setup involves simple linear optical elements, a pair of the two-photon polarization entangled states, and the conventional photon detectors that only distinguish the vacuum and nonvacuum Fock number states. A sophisticated single-photon detector distinguishing one or two photon states is unnecessary. This can greatly simplify the experimental realization of a linear optical quantum computer.
We present a model to realise a probabilistic quantum teleportation of two-particle mode entangled state through the four-photon quantum channel. Four modes of the two-photon mode entangled state are directly transferred to other spatial four modes of the quantum channel with success probability of 50%. The quantum protocol operates in space of photon number states. A Bell state measurement with four beam splitters and four pairs of detectors in the teleportation protocol is accomplished in the fourfold coincidence basis.
As demonstrated by E. Knill et al. [Nature 409 , 46 (2001)], quantum teleportation and quantum logic gates with a success probability close to one can be implemented using only linear optical elements, additional photons, and post-selection. To do this, it is desirable to have special quantum channels in sight before quantum teleportation performance. Here, we propose an experimental arrangement to generate a two-photon KLM state different from the well-known Bell states. This two-photon KLM state can be used to enhance the success probability of the quantum teleportation of a one-mode quantum qubit from 0.5 up to 2/3.