Optical setup for teleportation of the XOR function using coherent state qubits

1. Optical setup for teleportation of the XOR function using coherent state qubits João B. R. Silva George A. P. Thé Rubens V. Ramos giq@deti.ufc.br

2. Outline • Short review of coherent state quantum information processing (CSQIP) • Protocol of teleportation of the xor function between two classical bits • Optical setup for probabilistic generation of the tripartite state • Optical setup for teleportation of the xor function • Entanglement generation under decoherence caused by lossy devices • Conclusions

3. 1. Review of CSQIP • Coherent states: • Qubit: 0L=- and 1L= • Orthogonality: • 012=-2=exp(-42)1.11254x10-7 (≥2) • Balanced beam splitter (BS): • Phase modulator (PM): •  =is aNOT gate .

4. 2. Protocol for teleportation of the xor function GHZ state: Measurements (M1, M2 and M3): • {110, 101, 000, 011}DEC  K=R • {100, 111, 010, 001}DEC  KR Initial state: Final state: Where |=(|0|1)/21/2

5. 3. Optical setup for probabilistic generation of the tripartite state GHZ state: GHZ generator based teleportation: • Hadamard gate needs a teleportation that, sometimes, requires a Z gate that, by its turn, is implemented realizing a teleportation. • It has a low efficiency. • Depends on  (lossless).

6. 3. Optical setup for probabilistic generation of the tripartite state GHZ generator without teleportation: =N(-+)/21/2

7. 3. Optical setup for probabilistic generation of the tripartite state Final state before HD: u is the useless part that contains the situations in which detection happens in both detectors, D1 and D2.

8. 4. Optical setup for teleportation of the xor function Input state: [2-1(-,-,+-,,+,-,+,,-)135]K2R4 ; K,R {-,}.

9. 4. Optical setup for teleportation of the xor function The total quantum state just before the measurers : M1/M2: presence (bit 1) or absence (bit 0) of the light. Measurements (M1, M2 and M3): • {110, 101, 000, 011}DEC  K=R • {100, 111, 010, 001}DEC  KR

10. 5. Entanglement generation under decoherence caused by lossy devices Losses are modeled by ideal beam splitters (BSL) at the inputs with transmissivity,  .

11. 5. Entanglement generation under decoherence caused by lossy devices The total state before homodyne detection in the optical system: • ≥ 2 -1/2(orthogonality) • New logical states: 0L-1/2 and 1L1/2 • =(1-)1/2

12. 5. Entanglement generation under decoherence caused by lossy devices Without taking into account the state uL, the valid output state, with probability ½, is • And its density matrix is

13. Having =1 and  =1/2 where =exp[-42(1-)], tracing out the “lost” modes (qubits 5-8), the useful tripartite output state is 5. Entanglement generation under decoherence caused by lossy devices where U=IIX and The total probability of success is /2.

14. 5. Entanglement generation under decoherence caused by lossy devices Probability of success /2 versus BSL transmissivity .

15. 5. Entanglement generation under decoherence caused by lossy devices Entangler with teleportation versus Entangler without teleportation *S. Glancy, H. Vasconcelos and T.C. Ralph, Phys.Rev.A, 70, 22317 (2004).

16. Conclusions • It was proposed a setup for probabilistic generation of the tripartite state. • It was presented a proposal for the realization of the quantum teleportation protocol of the xor function, for coherent state qubit, using only linear optical devices. • The efficiency of the proposed (lossless) teleporter setup is 1/2. • An advantage of our setups is the absence of single-qubit gates based on teleportation, that are common in quantum information processing with coherent states. • It was analyzed the decoherence effects caused by lossy devices in the entangled state generator. It was observed that, in order to guarantee a probability of success upper than 0.25, the transmissivity  should not be lower than 0.96, implying that even low losses can be harmful for the efficiency of the setup.

17. Acknowledgements • Useful discussions with Hilma Vasconcelos are gratefully acknowledged. • The authors thank the Department of Teleinformatic Engineering (Federal University of Ceara - Brazil) and the Brazilian Agency for Research CNPq.