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arXiv:quant-ph/0404139 · Physical Review A

Conditional sign flip via teleportation

Gian Luca Giorgi, FERDINANDO DE PASQUALE, Simone Paganelli

Published Aug 26, 2004• 6 citations
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Abstract

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 $1∕2$. 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 $1∕4$.

DOI
10.1103/physreva.70.022319

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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.
Reliable entangling gates for qubits encoded in single-photon states represent a major challenge on the road to scalable quantum computing architectures based on linear optics. In this work, we present two approaches to develop high-fidelity, near-deterministic controlled-sign-shift gates based on the techniques of quantum gate teleportation. On the one hand, teleportation in a discrete-variable setting, i.e., for qubits, offers unit-fidelity operations but suffers from low success probabilities. Here, we apply recent results on advanced linear optical Bell measurements to reach a near-deterministic regime. On the other hand, in the setting of continuous variables, associated with coherent states, squeezing, and, typically, Gaussian states, teleportation can be performed in a deterministic fashion, but the finite amount of squeezing implies an inevitable deformation of a teleported single-mode state. Using a new generalized form of the nonlinear-sign-shift gate for gate teleportation, we are able to achieve fidelities of the resulting controlled-sign gate above 9090%90. A special focus is also put on a comparison of the two approaches, not only with respect to fidelity and success probability, but also in terms of resource consumption.
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 consider novel implementation of quantum teleportation protocol of unknown qubit by superposition of displacement operators with equal modulo but opposite in sign amplitudes. Entangled hybrid state with coherent components of small amplitude is used as quantum channel. Coherent components of the quantum channel displace the teleported qubit at the same absolute but opposite in sign values, so that any information about amount by which the qubit is displaced is lost despite the fact that one of these events has definitely occurred. Alice unambiguously distinguishes her measurement outcomes and Bob obtains at his disposal two states of a single photon in superposition state of two modes. The superposition of the displacement operators is nonunitary, so success probability of the protocol depends on the amplitude parameters of the teleported qubit. Remarkably, the success probability of the teleportation can be made arbitrary high for some amplitude values of the teleported state by means of initial amplitude modulation of unknown qubit and bits of classical information for Bob to identify the states. The scheme is realized by linear optics methods and works without photon number resolving measurement.
In this paper a new scheme for teleporting an unknown entangled state of two particles is proposed. To weaken the requirement for the quantum channel, without loss of generality, two communicators only share a non-maximally entangled two-particle state. Teleportation can be probabilistically realized if sender performs Bell-state measurements and Hadamard transformation and receiver introduces two auxiliary particles, operates C -not operation, single-qubit measurements and appropriate unitary transformations. The probability of successful teleportation is determined by the smaller one among the coefficients' absolute values of the quantum channel.
Qubits are realized as polarization state of photons or as superpositions of the spin states of electrons. In this paper we propose a scheme to probabilistically teleport an unknown arbitrary two-qubit state using a non-maximally entangled GHZ- like state and a non-maximally Bell state simultaneously as quantum channels. We also discuss the success probability of our scheme. We perform POVM in the protocol which is operationally advantageous. In our scheme we show that the non-maximal quantum resources perform better than maximal resources.
This paper outlines a linear-optical protocol for the teleportation of bipartite entangled coherent states (ECSs) using maximally ECSs as quantum channels. The scheme relies on symmetric beam splitters, phase shifters, photon-number-resolved measurements, and conditional local phase operations. Successful teleportation is achieved probabilistically with a constant success rate of 50%, independent of the coherent-state amplitude [Formula: see text], and governed by the parity of the measurement outcomes. The absence of nonlinear optical processes or direct photon interactions renders the protocol experimentally feasible and scalable, making it suitable for applications in continuous-variable quantum communication, quantum information processing, and coherent-state entanglement distribution.