Based on a special controlled-NOT gate, a multi-photon state encoded in polarizations of photons could be transformed into the corresponding single photon qudit encoded in spatial mode. It will make the processing on multi-photon change into the operation on a single-photon, if the inverse transformation from a single photon qudit back to a multi-photon state could be realized also. Associated with linear optical multi-port interferometer for single-photon unitary operation, the positive-operator value measurement and the universal unitary operation for multi-photon state are realized. This approach is more efficient than the previous one with decomposition into two-qubit gates in the circuit-based quantum computation, and it is feasible with using the current experimental technology.
Based on a special controlled-NOT gate, a multi-photon state encoded in polarizations of photons could be transformed into the corresponding single photon qudit encoded in spatial mode. It will make the processing on multi-photon change into the operation on a single-photon, if the inverse transformation from a single photon qudit back to a multi-photon state could be realized also. Associated with linear optical multi-port interferometer for single-photon unitary operation, the positive-operator value measurement and the universal unitary operation for multi-photon state are realized. This approach is more efficient than the previous one with decomposition into two-qubit gates in the circuit-based quantum computation, and it is feasible with using the current experimental technology.
How to manipulate (operate or measure) single photons efficiently and simply is the basic problem in optical quantum information processing. We first present an efficient scheme to transform a biphoton polarization state to a corresponding single-photon state encoded by its polarization and spatial modes. This single-photon state carries both the information of the controlled and target photons. It will make the realization of bipartite positive-operator-valued measurements efficiently and simply. Moreover, the inverse transformation from the single-photon state back to the corresponding biphoton polarization state is also proposed. Using both the transformations, the realization of the arbitrary two-qubit unitary operation is simple with an M-Z interferometer. All the schemes are feasible with the current experimental technology.
How to generate and manipulate high dimensional quantum state is a hot topic in the area of quantum information processing. In the optical system, based on the technique of linear optics and cross phase modulation, we consider the realization of universal unitary operation of single partite polarization encoded qudit. Firstly, we introduce the spatially encoded qudit as ancilla, and the entangler of polarization encoded qudit and spatially encoded qudit as core element. After that, the realization of a special unitary operation for single qutrit is discussed by one entangler and the Fourier transformation performed on the spatially encoded qutrit by a linear optical multi-port interferometer (LOMI). The corresponding success probability could be high, but this scheme is only available for a special type of unitary operations and cannot be developed to realize higher dimensional unitary operation. For general qudit universal unitary operation realization, we use qutrit unitary operation as example. The polarization encoded qutrit could be transformed to spatially encoded qutrit by one entangler and the measurement of polarization encoded qutrit, associated with the measurement results are used to control the transmission factors of mirrors placed on the spatial modes of spatially encoded qutrit. Then the desired universal unitary operation is performed on spatially encoded qutrit by a LOMI. Finally, one more entangler, a LOMI implementing Fourier transformation to spatially encoded qutrit, the measurement of spatially encoded qutrit and the phase shifts controlled by the measurement results through classical feed-forward will complete the realization of qutrit unitary operation. This approach could be developed for general case. By two entanglers, one LOMI for Fourier transformation of spatially encoded qudit and the measurement of polarization encoded qudit associated with its results are used to control the transmission factors of mirrors, the bi-directional mapping between polarization and spatially encoded qudits could be realized. Therefore, the universal unitary operation for general qudit could be realized by one more LOMI performed on the ancilla spatially encoded qutrit. In principle, our scheme is available for general single partite polarization encoded qudit and is feasible with the current experimental technology.
Qutrits, the triple level quantum systems in various forms, have been proposed for quantum information processing recently. By the methods presented in this paper, a biphotonic qutrit, which is encoded with the polarizations of two photons in the same spatial-temporal mode, can be mapped to a single-photon qutrit in spatial modes. It will make arbitrary unitary operation on such biphotonic qutrit possible if we can also realize the inverse map to polarization space. Among the two schemes proposed in this paper, the one based only on linear optics realizes an arbitrary U(3) operation with a very small success probability. However, if added with weak nonlinearity, the success probability can be greatly improved. These schemes are feasible with the current experimental technology.
Multiphoton states are widely applied in quantum information technology. By the methods presented in this paper, the structure of a multiphoton state in the form of multiple single-photon qubit products can be mapped to a single-photon qudit, which could also be in a separable product with other photons. This makes possible the manipulation of such multiphoton states by processing single-photon states. The optical realization of unknown qubit discrimination [B. He, J. A. Bergou, and Y.-H. Ren, Phys. Rev. A 76, 032301 (2007)] is simplified with the transformation methods. Another application is the construction of quantum logic gates, where the inverse transformations back to the input state spaces are also necessary. We especially show that the modified setups to implement the transformations can realize the deterministic multicontrol gates (including Toffoli gate) operating directly on the products of single-photon qubits.
Qutrits, the triple level quantum systems in various forms, have been proposed for quantum information processing recently. By the methods presented in this paper a bi-photonic qutrit, which is encoded with the polarizations of two photons in the same spatial-temporal mode, can be mapped to a single photon qutrit in spatial modes. It will make arbitrary unitary operation on such bi-photonic qutrit possible if we can also realize the inverse map to polarization space. Among the two schemes proposed in this paper, the one based only on linear optics realizes an arbitrary U(3) operation with a very small success probability. However, if added with weak nonlinearity, the success probability can be greatly improved. These schemes are feasible with the current experimental technology.
The information-carrying capacity of a single photon can be vastly expanded by exploiting its multiple degrees of freedom: spatial, temporal, and polarization. Although multiple qubits can be encoded per photon, to date only two-qubit single-photon quantum operations have been realized. Here, we report an experimental demonstration of three-qubit single-photon, linear, deterministic quantum gates that exploit photon polarization and the two-dimensional spatial-parity-symmetry of the transverse single-photon field. These gates are implemented using a polarization-sensitive spatial light modulator that provides a robust, non-interferometric, versatile platform for implementing controlled unitary gates. Polarization here represents the control qubit for either separable or entangling unitary operations on the two spatial-parity target qubits. Such gates help generate maximally entangled three-qubit Greenberger-Horne-Zeilinger and W states, which is confirmed by tomographical reconstruction of single-photon density matrices. This strategy provides access to a wide range of three-qubit states and operations for use in few-qubit quantum information processing protocols.Photons are essential for quantum information processing, but to date only two-qubit single-photon operations have been realized. Here the authors demonstrate experimentally a three-qubit single-photon linear deterministic quantum gate by exploiting polarization along with spatial-parity symmetry.