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Research in Optical Sciences

Joining the quantum state of two photons into one

Chiara Vitelli, Nicolò Spagnolo, Fabio Sciarrino, Enrico Santamato, Lorenzo Marrucci

Published Jan 1, 2014• 2 citations
Publisher

Abstract

We introduce and demonstrate experimentally a physical process, named quantum joining, in which the two-dimensional quantum states (qubits) of two input photons are combined into a single output photon, within a four-dimensional Hilbert space.
DOI
10.1364/qim.2014.qw3b.2

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A photonic process called quantum-state joining has been recently experimentally demonstrated [Vitelli et al., Nat. Photonics 7, 521 (2013)] that corresponds to the transfer of the internal two-dimensional quantum states of two input photons, i.e., two photonic qubits, into the four-dimensional quantum state of a single photon, i.e., a photonic ququart. A scheme for the inverse process, namely, quantum state splitting, has also been proposed. Both processes can be iterated in a cascaded layout, to obtain the joining and/or splitting of more than two qubits, thus leading to a general scheme for varying the number of photons in the system while preserving its total quantum state, or quantum information content. Here, we revisit these processes from a theoretical point of view. After casting the theory of the joining and splitting processes in the more general occupation number notation, we introduce some modified schemes that are in principle unitary [not considering the implementation of the controlled-not (cnot) gates] and do not require projection and feed-forward steps. This can be particularly important in the quantum state splitting case, to obtain a scheme that does not rely on postselection. Moreover, we formally prove that the quantum joining of two photon states with linear optics requires the use of at least one ancilla photon. This is somewhat unexpected, given that the demonstrated joining scheme involves the sequential application of two cnot quantum gates, for which a linear optical scheme with just two photons and postselection is known to exist. Finally we explore the relationship between the joining scheme and the generation of clusters of multiparticle entangled states involving more than one qubit per particle.
Quantum state joining has been recently experimentally demonstrated [C. Vitelli et al., Nat. Photon. 7, 521 (2013)] which can transfer two input photonic qubits into a photonic ququart. Here, we revisit these processes from a hybrid point of view. By exploring the giant optical circular birefringence induced by quantum-dot spins in one-sided optical microcavities, we introduce some deterministic joining schemes including two quantum-dot spin joining, hybrid photon and quantum-dot spin joining, and two-photon joining. The input quantum information is represented by one photon with polarization and spatial mode degrees of freedom (DOFs). These schemes are also adapted to the inverse processes called quantum state splitting because all the joining procedures are unitary and do not require projection and feed-forward steps. The fused photon is convenient for realizing elementary logic gates such as the controlled-not (cnot) gate, swap gate, and Toffoli gate. These hybrid fusion and splitting schemes provide flexible synthesis of the quantum-dot spin and photon in quantum applications. The transmission superiority of photons and storage superiority of the quantum-dot spin may be combined for quantum network communication or quantum computations.
Abstract Optimizing the physical realization of quantum gates is important to build a quantum computer. The controlled-SWAP gate, also named Fredkin gate, can be widely applicable in various quantum information processing schemes. In the present research, we propose and experimentally implement quantum Fredkin gate in a single-photon hybrid-degrees-of-freedom system. Polarization is used as the control qubit, and SWAP operation is achieved in a four-dimensional Hilbert space spanned by photonic orbital angular momentum. The effective conversion rate P of the quantum Fredkin gate in our experiment is (95.4 ± 2.6)%. Besides, we find that a kind of Greenberger–Horne–Zeilinger-like states can be prepared by using our quantum Fredkin gate, and these nonseparale states can show its quantum contextual characteristic by the violation of Mermin inequality. Our experimental design and coding method are useful for quantum computing and quantum fundamental study in high-dimensional and hybrid coding quantum systems.