It has previously been shown that probabilistic quantum logic operations can be performed using linear optical elements, additional photons (ancilla), and post-selection based on the output of single-photon detectors. Here we describe the operation of several quantum logic operations of an elementary nature, including a quantum parity check and a quantum encoder, and we show how they can be combined to implement a controlled-NOT (CNOT) gate. All of these gates can be constructed using polarizing beam splitters that completely transmit one state of polarization and totally reflect the orthogonal state of polarization, which allows a simple explanation of each operation. We also describe a polarizing beam splitter implementation of a CNOT gate that is closely analogous to the quantum teleportation technique previously suggested by Gottesman and Chuang [Nature 402, p.390 (1999)]. Finally, our approach has the interesting feature that it makes practical use of a quantum-eraser technique.
In this paper we propose a scheme to model the phonon analog of optical elements, including a polarizing beam splitter, a half- wave plate, and a quarter- wave plate, as well as an implementation of CNOT and Pauli gates, by using two atoms confined in a 2D plane. The internal states of the atoms are taken to be Rydberg circular states. Using this model we can manipulate the motional state of the atom, with possible applications in optomechanical integrated circuits for quantum information processing and quantum simulation. Towards this aim, we study the interaction of two trapped atoms with tw…
A spin-polarizing electron beam splitter is described which relies on an arrangement of linearly polarized laser waves of nonrelativistic intensity. An incident electron beam is first coherently scattered off a bichromatic laser field, splitting the beam into two portions, with electron spin and momentum being entangled. Afterwards, the partial beams are coherently superposed in an interferometric setup formed by standing laser waves. As a result, the outgoing electron beam is separated into its spin components along the laser magnetic field, which is shown by both analytical and numerical sol…
We discuss a device capable of filtering out two-mode states of light with mode populations differing by more than a certain threshold, while not revealing which mode is more populated. It would allow engineering of macroscopic quantum states of light in a way which is preserving specific superpositions. As a result, it would enhance optical phase estimation with these states as well as distinguishability of "macroscopic" qubits. We propose an optical scheme, which is a relatively simple, albeit non-ideal, operational implementation of such a filter. It uses tapping of the original polarizatio…
We propose an experimentally feasible scheme to generate nonmaximal entanglement between two atomic ensembles. The degree of entanglement is readily tunable. The scheme involves laser manipulation of atomic ensembles, adjustable quarter- and half-wave plates, beam splitter, polarizing beam splitters, and single-photon detectors, and well fits the status of the current experimental technology. Finally we use the nonmaximally entangled state of ensembles to demonstrate quantum nonlocality by detecting the Clauser-Horne-Shimony-Holt inequality.
We put forward an effective amplification protocol for protecting the single-photon entangled state of the time-bin qubit. The protocol only requires one pair of the single-photon entangled state and some auxiliary single photons. With the help of the 50:50 beam splitters, variable beam splitters with the transmission of $t$ and the polarizing beam splitters, we can increase the fidelity of the single-photon entangled state under $t<\frac{1}{2}$. Moreover, the encoded time-bin information can be perfectly contained. Our protocol is quite simple and economical. More importantly, it can be reali…
We present the realization of a physical quantum random number generator based on the process of splitting a beam of photons on a beam splitter, a quantum mechanical source of true randomness. By utilizing either a beam splitter or a polarizing beam splitter, single photon detectors and high speed electronics the presented devices are capable of generating a binary random signal with an autocorrelation time of 11.8 ns and a continuous stream of random numbers at a rate of 1 Mbit/s. The randomness of the generated signals and numbers is shown by running a series of tests upon data samples. The …
We put forward an effective amplification protocol for protecting the single-photon multi-mode W state of the time-bin qubit. The protocol only relies on linear optical elements, such as the $50:50$ beam splitters, variable beam splitters with the transmission of $t$ and the polarizing beam splitters. Only one pair of the single-photon multi-mode W state and some auxiliary single photons are required, and the fidelity of the single-photon multi-mode W state can be increased under $t<\frac{1}{2}$. The encoded time-bin information can be perfectly contained. Our protocol is quite simple and econ…
We present a faithful qubit transmission scheme with linear optics against collective noise, not resorting to ancillary qubits. Its set-up is composed of three unbalanced polarization interferometers, based on a polarizing beam splitter, a beam splitter and a half-wave plate, which makes this scheme more feasible than others with present technology. The fidelity of successful transmission is 1, independent of the parameters of the collective noise, and the success probability for obtaining an uncorrupted state can be improved to 100% with some time delayers. Moreover, this scheme has some good…
We demonstrate an atomic Faraday dichroic beam splitter suitable to spatially separate signal and idler fields from pump degenerate four-wave mixing in an atomic source. By rotating the plane of polarization of one mode $90^{\circ}$ with respect to the other, a subsequent polarizing beam splitter separates the two frequencies, which differ by only 13.6 GHz, and achieves a suppression of $(-26.3\pm0.1)$ and $(-21.2\pm0.1)$ dB in the two outputs, with a corresponding transmission of 97 and 99 %. This technique avoids the need to use spatial separation of four-wave mixing modes and thus opens the…
We report the first direct experimental characterization of continuous variable quantum Stokes parameters. We generate a continuous wave light beam with more than 3 dB of simultaneous squeezing in three of the four Stokes parameters. The polarization squeezed beam is produced by mixing two quadrature squeezed beams on a polarizing beam splitter. Depending on the squeezed quadrature of these two beams the quantum uncertainty volume on the Poincaré sphere became a `cigar' or `pancake'-like ellipsoid.
We show a systematic construction for implementing general measurements on a single qubit, including both strong (or projection) and weak measurements. We mainly focus on linear optical qubits. The present approach is composed of simple and feasible elements, i.e., beam splitters, wave plates, and polarizing beam splitters. We show how the parameters characterizing the measurement operators are controlled by the linear optical elements. We also propose a method for the implementation of general measurements in solid-state qubits.
We show how to create practical, efficient, quantum repeaters, employing double-photon guns, for long-distance optical quantum communication. The guns create polarization-entangled photon pairs on demand. One such source might be a semiconducter quantum dot, which has the distinct advantage over parametric down-conversion that the probability of creating a photon pair is close to one, while the probability of creating multiple pairs vanishes. The swapping and purifying components are implemented by polarizing beam splitters and probabilistic optical CNOT gates.
Bias-preserving cat-cat CNOT gate via vacuum-conditional beam-splitter
Amazon Center for Quantum Computing（亚马逊量子计算中心）；Institute for Quantum Information and Matter, California Institute of Technology（加州理工学院量子信息与物质研究所）；Thomas J. Watson, Sr., Laboratory of Applied Physics, California Institute of Technology（加州理工学院托马斯·J·沃森Sr.应用物理实验室）；NVIDIA Corporation（英伟达公司）
We propose a technique for performing quantum state tomography of photonic polarization-encoded multi-qubit states. Our method uses a single rotating wave plate, a polarizing beam splitter and two photon-counting detectors per photon mode. As the wave plate rotates, the photon counters measure a pseudo-continuous signal which is then Fourier transformed. The density matrix of the state is reconstructed using the relationship between the Fourier coefficients of the signal and the Stokes' parameters that represent the state. The experimental complexity, i.e. different wave plate rotation frequen…
Knill, Laflamme, and Milburn (KLM) proved that it is possible to build a scalable universal quantum computer using only linear-optics elements and conditional dynamics [Nature (London) {\bf 409}, 46 (2001)\cite{Knill}]. However, the practical realization of the quantum logic gate for the scheme is still technically difficult. A major difficulty is the requirement for sub-wavelength level stabilization of the interlocking interferometers. Following our recent experimental work[Phys. Rev. Lett.{\bf 92}, 017902 (2004)\cite{Sanaka2}], we describe a more feasible scheme to implement the gate that g…
We present an economical setup for faithful entanglement sharing against collective noise. It is composed of polarizing beam splitters, half wave plates, polarization independent wavelength division multiplexers, and frequency shifters. An arbitrary qubit error on the polarization state of each photon in a multi-photon system caused by the noisy channel can be rejected, without resorting to additional qubits, fast polarization modulators, and nondestructive quantum nondemolition detectors. Its success probability is in principle 100%, which is independent of the noise parameters, and it can be…
We report the first experimental demonstration of an optical quantum controlled-NOT gate without any path interference, where the two interacting path interferometers of the original proposals (Phys. Rev. A {\bf 66}, 024308 (2001), Phys. Rev. A {\bf 65}, 012314 (2002)) have been replaced by three partially polarizing beam splitters with suitable polarization dependent transmittances and reflectances. The performance of the device is evaluated using a recently proposed method (Phys. Rev. Lett. {\bf 94}, 160504 (2005)), by which the quantum process fidelity and the entanglement capability can be…
We aim to analytically arrive at a beam splitter formulation for electron waves. The electron beam splitter is an essential component of quantum logical devices. To arrive at the beam splitter structure, the electrons are treated as waves, i.e. we assume the transport to be ballistic. Ballistic electrons are electrons that travel over such short distances that their phase coherence is maintained. For mesoscopic devices with size smaller than the mean free path, the phase relaxation length and the Fermi wavelength of electrons in the medium, the transport can be considered to be coherent and he…
We experimentally demonstrate a programmable single-qubit quantum gate. This device applies a unitary phase shift operation to a data qubit with the value of the phase shift being fully determined by the state of a program qubit. Our linear optical implementation is based on the encoding of qubits into polarization states of single photons, two-photon interference on a polarizing beam splitter, and measurement on the output program qubit. We fully characterize the programmable gate by quantum process tomography. The achieved average quantum process fidelity exceeding 97% illustrates very good …
An interesting aspect of multipartite entanglement is that for perfect teleportation and superdense coding, not the maximally entangled W states but a special class of non-maximally entangled W-like states are required. Therefore, efficient preparation of such W-like states is of great importance in quantum communications, which has not been studied as much as the preparation of W states. In this letter, we propose a simple optical scheme for efficient preparation of large-scale polarization based entangled W-like states by fusing two W-like states or expanding a W-like state with an ancilla p…
We describe a feasible logic Bell-state analysis protocol by employing the logic entanglement to be the robust concatenated Greenberger-Horne-Zeilinger (C-GHZ) state. This protocol only uses polarization beam splitters and half-wave plates, which are available in current experimental technology. We can conveniently identify two of the logic Bell states. This protocol can be easily generalized to the arbitrary C-GHZ state analysis. We can also distinguish two $N$-logic-qubit C-GHZ states. As the previous theory and experiment both showed that the C-GHZ state has the robustness feature, this log…
A systematic method for simulating small-scale quantum circuits by use of linear optical devices is presented. It relies on the representation of several quantum bits by a single photon, and on the implementation of universal quantum gates using simple optical components (beam splitters, phase shifters, etc.). This suggests that the optical realization of small quantum networks is reasonable given the present technology in quantum optics, and could be a useful technique for testing simple quantum algorithms or error-correction schemes. The optical circuit for quantum teleportation is presented…
We describe and discuss a solid state proposal for quantum computation with mobile spin qubits in one-dimensional systems, based on recent advances in spintronics. Static electric fields are used to implement a universal set of quantum gates, via the spin-orbit and exchange couplings. Initialization and measurement can be performed either by spin injection from/to ferromagnets, or by using spin filters and mesoscopic spin polarizing beam-splitters. The vulnerability of this proposal to various sources of error is estimated by numerical simulations. We also assess the suitability of various mat…
In this paper, we propose a method for building a two-qubit gate with the Jaynes-Cummings model (JCM). In our scheme, we construct a qubit from a pair of optical paths where a photon is running. Generating Knill, Laflamme and Milburn's nonlinear sign-shift gate by the JCM, we construct the conditional sign-flip gate, which works with small error probability in principle. We also discuss two experimental setups for realizing our scheme. In the first experimental setup, we make use of coherent lights to examine whether or not our scheme works. In the second experimental setup, an optical loop ci…
We present a systematic comparison of different methods of fidelity estimation of a linear optical quantum controlled-Z gate implemented by two-photon interference on a partially polarizing beam splitter. We have utilized a linear fidelity estimator based on the Monte Carlo sampling technique as well as a non-linear estimator based on maximum likelihood reconstruction of a full quantum process matrix. In addition, we have also evaluated lower bound on quantum gate fidelity determined by average quantum state fidelities for two mutually unbiased bases. In order to probe various regimes of opera…
We investigate quantum entanglement of three photons performing discrete-time quantum walk (DTQW) on the nearest-neighbor sites of a square lattice. Such a DTQW setup has already been proposed to be realizable using linear optical elements. Each lattice site corresponds to the sequential action of a half-wave plate and a polarizing beam splitter. Two-dimensional DTQW can be mapped to an effective one-dimensional DTQW with a four-sided coin that depends on the polarization and direction of motion of the photons. It is known that such a system is capable to spatially entangle two photons, prepar…
The so-called NOON states are quantum optical resources known to be useful especially for quantum lithography and metrology. At the same time, they are known to be very sensitive to photon losses and rather hard to produce experimentally. Concerning the former, here we present a scheme where NOON states are the elementary resources for building quantum error correction codes against photon losses, thus demonstrating that such resources can also be useful to suppress the effect of loss. Our NOON-code is an exact code that can be systematically extended from one-photon to higher-number losses. I…
Quantum logic gates are important for quantum computations and quantum information processing in numerous physical systems. While time-bin qubits are suited for quantum communications over optical fiber, many essential quantum logic gates for them have not yet been realized. Here, we demonstrated a controlled-phase (C-Phase) gate for time-bin qubits that uses a 2x2 optical switch based on an electro-optic modulator. A Hong-Ou-Mandel interference measurement showed that the switch could work as a time-dependent beam splitter with a variable spitting ratio. We confirmed that two independent time…
We present a realization of two-qubit controlled-phase gate, based on the linear and nonlinear properties of the probe and signal optical pulses in an asymmetric GaAs/AlGaAs double quantum wells. It is shown that, in the presence of cross-phase modulation, a giant cross-Kerr nonlinearity and mutually matched group velocities of the probe and signal optical pulses can be achieved while realizing the suppression of linear and self-Kerr optical absorption synchronously. These characteristics serve to exhibit an all-optical two-qubit controlled-phase gate within efficiently controllable photon-pho…
Linear optics quantum logic gates are the best tool to generate multi-photon entanglement. Simplifying a recent approach [Phys. Rev. A 65, 062324; Phys. Rev. A 66, 024308] we were able to implement the conditional phase gate with only one second order interference at a polarization dependent beam splitter, thereby significantly increasing its stability. The improved quality of the gate is evaluated by analysing its entangling capability and by performing full process tomography. The achieved results ensure that this device is well suited for implementation in various multi photon quantum infor…
Integrated photonic circuits have a strong potential to perform quantum information processing. Indeed, the ability to manipulate quantum states of light by integrated devices may open new perspectives both for fundamental tests of quantum mechanics and for novel technological applications. However, the technology for handling polarization encoded qubits, the most commonly adopted approach, is still missing in quantum optical circuits. Here we demonstrate the first integrated photonic Controlled-NOT (CNOT) gate for polarization encoded qubits. This result has been enabled by the integration, b…
Continuous-variable cluster states allow for fault-tolerant measurement-based quantum computing when used in tandem with the Gottesman-Kitaev-Preskill (GKP) encoding of a qubit into a bosonic mode. For quad-rail-lattice macronode cluster states, whose construction is defined by a fixed, low-depth beam splitter network, we show that a Clifford gate and GKP error correction can be simultaneously implemented in a single teleportation step. We give explicit recipes to realize the Clifford generating set, and we calculate the logical gate-error rates given finite squeezing in the cluster-state and …
Single photon interference due to passage through a periodic grating is considered in a novel proposal for processing D-dimensional quantum systems (quDits) encoded in the spatial degrees of freedom of light. We show that free space propagation naturally implements basic single quDit gates by means of the Talbot effect: an intricate time-space carpet of light in the near field diffraction regime. Adding a diagonal phase gate, we show that a complete set of single quDit gates can be implemented. We then introduce a spatially-dependent beam splitter that allows implementation of controlled opera…
It has been proved that surface plasmon polariton (SPP) can well conserve and transmit the quantum nature of entangled photons. Therefore, further utilization and manipulation of such quantum nature of SPP in a plasmonic chip will be the next task for scientists in this field. In quantum logic circuits, the controlled-NOT (CNOT) gate is the key building block. Here, we implement the first plasmonic quantum CNOT gate with several-micrometer footprint by utilizing a single polarization-dependent beam-splitter (PDBS) fabricated on the dielectric-loaded SPP waveguide (DLSPPW). The quantum logic fu…
Conditional quantum optical processes enable a wide range of technologies from generation of highly non-classical states to implementation of quantum logic operations. The process fidelity that can be achieved in a realistic implementation depends on a number of system parameters. Here we experimentally examine Fock-state filtration, a canonical example of a broad class of conditional quantum operations acting on a single optical field mode. This operation is based upon interference of the mode to be manipulated with an auxiliary single-photon state at a beam splitter, resulting in the entangl…
