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arXiv:0909.3970

Simulation of quantum gates by postselection of interference experiments in multi-port beam-splitter (BS) configurations

Y. Ben-Aryeh

Published Sep 22, 2009• 0 citations

Abstract

Using multiport beam-splitter (BS) configurations eight input operators a(0),a(1),a(2) a(3),a(4) a(5),a(6), a(7) are mixed by 12 BS's to produce the output operators b(0), b(1), b(2), b(3), b(4), b(5), b(6), b(7). A single photon entering into, or exiting from, one port of a BS is considered as the |0> state while that in the second port of the BS is considered as the |1> state. Two single photons are inserted into two of the BS's simulating two input qubit-states by operators a(0), a(1),a(2), a(3) . In order to simulate the two-qubit gates we exclude by postselection all the cases in which one or two photons exit through output ports b(4), b(5), b(6), b(7) so that only 25% of the experiments are taken into account. The method simulates explicitly the CNOT and SWAP gates but similar methods can be used for other gates.

DOI: 10.48550/arxiv.0909.3970

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Using multiport beam-splitter (BS) configurations eight input operators a(0),a(1),a(2) a(3),a(4) a(5),a(6), a(7) are mixed by 12 BS's to produce the output operators b(0), b(1), b(2), b(3), b(4), b(5), b(6), b(7). A single photon entering into, or exiting from, one port of a BS is considered as the |0> state while that in the second port of the BS is considered as the |1> state. Two single photons are inserted into two of the BS's simulating two input qubit-states by operators a(0), a(1),a(2), a(3) . In order to simulate the two-qubit gates we exclude by postselection all the cases in which one or two photons exit through output ports b(4), b(5), b(6), b(7) so that only 25% of the experiments are taken into account. The method simulates explicitly the CNOT and SWAP gates but similar methods can be used for other gates.

We investigate the photon statistics at the outputs of a four-port beam splitter, when a strong coherent field is incident on one input port and various other fields enter at the second inner port. Some non-classical interference effects are encountered. In particular, there is a large difference between the cases when a one photon field enters at input port 2 and when a field in a coherent state with an average of one photon enters at port 2. In the former case the probability P(m) of the difference m between the detected photons at output ports 3 and 4 has a minimum at m = 0 whenever the quantum efficiency exceeds one third. As the quantum efficiency falls from one to zero, the form of the probability distribution P(m/1) changes drastically.

Multiphoton entanglement is an important resource for linear optics quantum computing. Here we show that a wide range of highly entangled multiphoton states, including

W

-states, can be prepared by interfering single photons inside a Bell multiport beam splitter and using postselection. A successful state preparation is indicated by the collection of one photon per output port. An advantage of the Bell multiport beam splitter is that it redirects the photons without changing their inner degrees of freedom. The described setup can therefore be used to generate polarization, time-bin, and frequency multiphoton entanglement, even when using only a single photon source.

Quantum theory predicts that two indistinguishable photons incident on a beam-splitter interferometer exit together (the pair emerges randomly from one port or the other). We use a special photon-number-resolving energy detector for a direct observation of this quantum-interference phenomenon. Simultaneous measurements from two such detectors, one at each beam-splitter-interferometer output port, confirm the absence of cross coincidences. Photon-number-resolving detectors are expected to find use in other quantum-optics and quantum-information-processing experiments.

A new method based on quantum encoders is developed for implementing quantum computational gates, especially the CNOT gate. Photonic qubits are used where ∣0> and ∣1> represent horizontal ∣H> and vertical ∣V> polarized photons, respectively. By the use of polarizing beam splitters (PBSs) and entangled two-photon states in a certain experimental scheme, each input qubit state is copied, with a certain probability of success, into four equivalent input qubit states. The present method concentrates on the special case where the initial two-qubit state is separable. The CNOT gate (multiplied by 2) is decomposed into a summation of four unitary matrices each of dimension 4×4 and where each of these unitary matrices operates on a corresponding copy of the input two-qubit state. By adding the amplitudes of the four two-qubit states, which is obtained in a decoding interference experiment, the CNOT gate is implemented.

Hong-Ou-Mandel interference is one of the clearest signatures of quantum behaviour: two identical photons meeting at a beam splitter always leave together. Here we demonstrate that this symmetry can be broken. Using a programmable integrated photonic processor, we interfere imbalanced two-photon states on a variable beam splitter and show that the output state of quantum interference can be continuously tuned, reaching the extreme case where destructive interference suppresses bunching at one output port. The asymmetry creates a forbidden bunching channel: photons may exit together at one port or separately at both ports, but cannot emerge together at the other port.