When a photon with well-defined polarization and momentum passes through a focusing device, these properties are no longer well defined. Their loss is captured by describing polarization by a 3x3 effective density matrix. Here we show that the effective density matrix corresponds to the actual photodetection model and we provide a simple formula to calculate it in terms of classical fields. Moreover, we explore several possible experimental consequences of the "longitudinal" term: limits on single-photon detection efficiency, polarization-dependent atomic transitions rates and the implications on quantum information processing.
Photonic polarization qubits are widely used in quantum computation and quantum communication due to the robustness in transmission and the easy qubit manipulation. An integrated quantum memory for polarization qubits is a fundamental building block for large-scale integrated quantum networks. However, on-demand storing polarization qubits in an integrated quantum memory is a long-standing challenge due to the anisotropic absorption of solids and the polarization-dependent features of microstructures. Here we demonstrate a reliable on-demand quantum memory for polarization qubits, using a depr…
We address the propagation of a single photon pulse with two polarization components, i.e., a polarization qubit, in an inhomogeneously broadened "phaseonium" Λ-type three-level medium. We combine some of the non-trivial propagation effects characteristic for this kind of coherently prepared systems and the controlled reversible inhomogeneous broadening technique to propose several quantum information processing applications, such as a protocol for polarization qubit filtering and sieving as well as a tunable polarization beam splitter. Moreover, we show that, by imposing a spatial variation o…
We present an optical filter that transmits photon pairs only if they share the same horizontal or vertical polarization, without decreasing the quantum coherence between these two possibilities. Various applications for entanglement manipulations and multi-photon qubits are discussed.
Four-qubit cluster states of two photons entangled in polarization and linear momentum have been used to realize a complete set of single qubit rotations and the C-NOT gate for equatorial qubits with high values of fidelity. By the computational equivalence of the two degrees of freedom our result demonstrate the suitability of two photon cluster states for rapid and efficient one-way quantum computing.
We present an efficient arbitrary polarization qubit transmission scheme against channel noise by utilizing frequency degree of freedom, which is more stable in transmission surroundings. The information of quantum state is encoded in frequency state during the transmission and transferred to polarization state later. Both the fidelity of quantum state transmitted and the success probability of this scheme are 1 in principle.
In this work, we present active and passive linear optical setups for error correction in quantum communication systems that employ polarization of single-photon and mesoscopic coherent states. Applications in quantum communication systems are described.
We address the issue of dephasing effects in flying polarization qubits propagating through optical fiber by using the method of dynamical decoupling. The control pulses are implemented with half waveplates suitably placed along the realistic lengths of the single mode optical fiber. The effects of the finite widths of the waveplates on the polarization rotation are modeled using tailored refractive index profiles inside the waveplates. We show that dynamical decoupling is effective in preserving the input qubit state with the fidelity close to one when the polarization qubit is subject to the…
We report an experimental realization of an atomic vapor quantum memory for the photonic po- larization qubit. The performance of the quantum memory for the polarization qubit, realized with electromagnetically-induced transparency in two spatially separated ensembles of warm Rubidium atoms in a single vapor cell, has been characterized with quantum process tomography. The process fidelity better than 0.91 for up to 16 μs of storage time has been achieved.
Polarization-encoded qubits are particularly useful in quantum information tasks due to the easy transportation in a single spatial and temporal mode, the accurate qubit manipulation and the high robustness against decoherence. Reliable storage of polarization-encoded qubits is essential for the construction of large-scale quantum networks. Here we demonstrate a faithful quantum memory for photonic polarization qubits using the noiseless photon echo protocol implemented in a rare-earth-ion doped crystal (151Eu3+:Y2SiO5). Based on a detailed spectroscopic investigation on the 151Eu3+ ions at th…
Non-classical joint measurements can hugely improve the efficiency with which certain figures of merit of quantum systems are measured. We use such a measurement to determine a particular figure of merit, the purity, for a polarization qubit. In the process we highlight some of subtleties involved in common methods for generating decoherence in quantum optics.
Light is an irreplaceable means of communication among various quantum information processing and storage devices. Due to their different physical nature, some of these devices couple more strongly to discrete, and some to continuous degrees of freedom of a quantum optical wave. It is therefore desirable to develop a technological capability to interconvert quantum information encoded in these degrees of freedom. Here we generate and characterize an entangled state between a dual-rail (polarization-encoded) single-photon qubit and a qubit encoded as a superposition of opposite-amplitude cohere…
We study how one-particle correlations transfer to manifest as two-particle correlations in the context of parametric down-conversion (PDC), a process in which a pump photon is annihilated to produce two entangled photons. We work in the polarization degree of freedom and show that for any two-qubit generation process that is both trace-preserving and entropy-nondecreasing, the concurrence $C(ρ)$ of the generated two-qubit state $ρ$ follows an intrinsic upper bound with $C(ρ)\leq (1+P)/2$, where $P$ is the degree of polarization of the pump photon. We also find that for the class of two qubit …
We compare two physical systems: polarization degrees of freedom of a macroscopic light beam and the Josephson junction (JJ) in the "charge qubit regime". The first system obviously cannot carry genuine quantum information and we show that the maximal entanglement which could be encoded into polarization of two light beams scales like 1/(photon number). Two theories of JJ, one leading to the picture of "JJ-qubit" and the other based on the mean-field approach are discussed. The later, which seems to be more appropriate, implies that the JJ system is, essentially, mathematically equivalent to t…
We perform a proof-of-principle demonstration of the measurement-device-independent quantum key distribution (MDI-QKD) protocol using weak coherent states and polarization-encoded qubits over two optical fiber links of 8.5 km each. Each link was independently stabilized against polarization drifts using a full-polarization control system employing two wavelength-multiplexed control channels. A linear-optics-based polarization Bell-state analyzer was built into the intermediate station, Charlie, which is connected to both Alice and Bob via the optical fiber links. Using decoy-states, a lower bo…
Non-deterministic noiseless amplification of a single mode can circumvent the unique challenges to amplifying a quantum signal, such as the no-cloning theorem, and the minimum noise cost for deterministic quantum state amplification. However, existing devices are not suitable for amplifying the fundamental optical quantum information carrier, a qubit coherently encoded across two optical modes. Here, we construct a coherent two-mode amplifier, to demonstrate the first heralded noiseless linear amplification of a qubit encoded in the polarization state of a single photon. In doing so, we increa…
We propose an efficient faithful polarization-state transmission scheme by utilizing frequency degree of freedom besides polarization and an additional qubit prepared in a fixed polarization. An arbitrary single-photon polarization state is protected against the collective noise probabilistically. With the help of frequency beam splitter and frequency shifter, the success probability of our faithful qubit transmission scheme with frequency degree of freedom can be 1/2 in principle.
One of the major challenges in quantum computation has been to preserve the coherence of a quantum system against dephasing effects of the environment. The information stored in photon polarization, for example, is quickly lost due to such dephasing, and it is crucial to preserve the input states when one tries to transmit quantum information encoded in the photons through a communication channel. We propose a dynamical decoupling sequence to protect photonic qubits from dephasing by integrating wave plates into optical fiber at prescribed locations. We simulate random birefringent noise along…
The encoding of quantum information in photonic time-bin qubits is apt for long distance quantum communication schemes. In practice, due to technical constraints such as detector response time, or the speed with which co-polarized time-bins can be switched, other encodings, e.g. polarization, are often preferred for operations like state detection. Here, we present the conversion of qubits between polarization and time-bin encodings using a method that is based on an ultrafast optical Kerr shutter and attain efficiencies of 97% and an average fidelity of 0.827+/-0.003 with shutter speeds near …
We propose a scheme to generate entanglement between a single-photon qubit in the polarization basis and a coherent state of light. The required resources are a superposition of coherent states, a polarization entangled photon pair, beam splitters, the displacement operation, and four photodetectors. Even when realistic detectors with a limited efficiency are used, an arbitrarily high fidelity can be obtained by adjusting a beam-splitter ratio and the displacement amplitude at the price of reducing the success probability. Our analysis shows that high fidelities may be obtained using on-off de…
We report on the quantum storage and retrieval of photonic polarization quantum bits onto and out of a solid state storage device. The qubits are implemented with weak coherent states at the single photon level, and are stored for 500 ns in a praseodymium doped crystal with a storage and retrieval efficiency of 10%, using the atomic frequency comb scheme. We characterize the storage by using quantum state tomography, and find that the average conditional fidelity of the retrieved qubits exceeds 95% for a mean photon number mu=0.4. This is significantly higher than a classical benchmark, taking…
We report on two optical realizations of the $1 \to 2$ asymmetric phase-covariant cloning machines for polarization states of single photons. The experimental setups combine two-photon interference and tunable polarization filtering that enables us to control the asymmetry of the cloners. The first scheme involves a special unbalanced bulk beam splitter exhibiting different splitting ratios for vertical and horizontal polarizations, respectively. The second implemented scheme consists of a balanced fiber coupler where photon bunching occurs, followed by a free-space part with polarization filt…
The pairwise entanglement and local polarization of the ground state are discussed by studying the Heisenberg XX model in finite qubit case. The results show that: the ground state is composed by the micro state with the minimal total spin 0 (for even qubit) or 1/2 (for odd qubit), local polarization (LP) has intimate relation with the probability of the micro state in the ground state, the stronger the LP the smaller the probability, the same LP corresponding to the same probability; the pairwise entanglement of the ground state is the biggest in all the eigenvectors. We find when the qubit i…
We propose a scheme to implement a heralded quantum memory for single-photon polarization qubits with a single atom trapped in an optical cavity. In this scheme, an injected photon only exchanges quantum state with the atom, so that the heralded storage can be achieved by detecting the output photon. We also demonstrate that the scheme can be used for realizing the heralded quantum state transfer, exchange and entanglement distribution between distant nodes. The ability to detect whether the operation has succeeded or not is crucial for practical application.
A scheme based on electromagnetically induced transparency is used to store light in a Bose-Einstein condensate. In this process, a photonic polarization qubit is stored in atomic Zeeman states. The performance of the storage process is characterized and optimized. The average process fidelity is 1.000 +/- 0.004. For long storage times, temporal fluctuations of the magnetic field reduce this value, yielding a lifetime of the fidelity of 1.1 +/- 0.2 ms. The write-read efficiency of the pulse energy can reach 0.53 +/- 0.05.
Aiming the construction of quantum computers and quantum communication systems based on optical devices, in this work we present possible implementations of quantum and classical CNOTs gates, as well an optical setup for generation and distribution of bipartite entangled states, using linear optical devices and photon number quantum non-demolition measurement.
Superpositions of two orthogonal single-photon polarization states are commonly used as optical qubits. If such qubits are sent by continuous variable quantum teleportation, the modifications of the qubit states due to imperfect entanglement cause an increase in the average photon number of the output state. This effect can be interpreted as an accidental quantum cloning of the single photon input. We analyze the output statistics of the single photon teleportation and derive the transfer and cloning fidelities from the equations of the polarization qubit.
The problems associated with practical implementation of the scheme proposed for preparation of arbitrary states of polarization ququarts based on biphotons are discussed. The influence of frequency dispersion effects are considered, and the necessity of group velocities dispersion compensation in the frequency non-degenerate case even for continuous pumping is demonstrated. A method for this compensation is proposed and implemented experimentally. Physical restrictions on the quality of prepared two-photon states are revealed.
We demonstrate a robust implementation of a deterministic linear-optical Controlled-NOT (CNOT) gate for single-photon two-qubit quantum logic. A polarization Sagnac interferometer with an embedded 45$^{\circ}$-oriented dove prism is used to enable the polarization control qubit to act on the momentum (spatial) target qubit of the same photon. The CNOT gate requires no active stabilization because the two spatial modes share a common path, and it is used to entangle the polarization and momentum qubits.
A quantum internet connects remote quantum processors that need interact and exchange quantum signals over a long distance through photonic channels. However, these quantum nodes are usually composed of quantum systems with emitted photons unsuitable for long-distance transmission. Therefore, quantum wavelength conversion to telecom is crucial for long-distance quantum networks based on optical fiber. Here we propose wavelength conversion devices for single-photon polarization qubits using continuous variable quantum teleportation, which can efficiently convert qubits between near-infrared (78…
In the 1987 spin retrodiction puzzle of Vaidman, Aharonov, and Albert one is challenged to ascertain the values of $σ_x$, $σ_y$, and $σ_z$ of a spin-1/2 particle by utilizing entanglement. We report the experimental realization of a quantum-optical version in which the outcome of an intermediate polarization projection is inferred by exploiting single-photon two-qubit quantum gates. The experimental success probability is consistently above the 90.2% threshold of the optimal one-qubit strategy, with an average success probability of 95.6%.
Direct access to the initial polarization of ${}^{13}C$ nuclei by measuring coherence evolution of an nitrogen-vacancy center spin qubit
Institute of Theoretical Physics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology（弗罗茨瓦夫科技大学基础技术学院理论物理研究所）；FZU - Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）
Here we show an ultra-low noise regime of operation in a simple quantum memory in warm Rb atomic vapor. By modelling the quantum dynamics of four-level room temperature atoms, we achieve fidelities >90% for single-photon level polarization qubits, clearly surpassing any classical strategy exploiting the non-unitary memory efficiency. This is the first time such important threshold has been crossed with a room temperature device. Additionally we also show novel experimental techniques capable of producing fidelities close to unity. Our results demonstrate the potential of simple, resource-moder…
Storage of quantum information encoded into true single photons is an essential constituent of long-distance quantum communication based on quantum repeaters and of optical quantum information processing. The storage of photonic polarization qubits is, however, complicated by the fact that many materials are birefringent and have polarization-dependent absorption. Here we present and demonstrate a simple scheme that allows compensating for these polarization effects. The scheme is demonstrated using a solid-state quantum memory implemented with an ensemble of rare-earth ions doped into a biaxi…
A long-lived and multimode quantum memory is a key component needed for the development of quantum communication. Here we present temporally multiplexed storage of 5 photonic polarization qubits encoded onto weak coherent states in a rare-earth-ion doped crystal. Using spin refocusing techniques we can preserve the qubits for more than half a millisecond. The temporal multiplexing allows us to increase the effective rate of the experiment by a factor of 5, which emphasizes the importance of multimode storage for quantum communication. The fidelity upon retrieval is higher than the maximum clas…
Quantum memory for flying optical qubits is a key enabler for a wide range of applications in quantum information science and technology. A critical figure of merit is the overall storage-and-retrieval efficiency. So far, despite the recent achievements of efficient memories for light pulses, the storage of qubits has suffered from limited efficiency. Here we report on a quantum memory for polarization qubits that combines an average conditional fidelity above 99% and an efficiency equal to (68$\pm$ 2)%, thereby demonstrating a reversible qubit mapping where more information is retrieved than …
We present an original self-error-rejecting photonic qubit transmission scheme for both the polarization and spatial states of photon systems transmitted over collective noise channels. In our scheme, we use simple linear-optical elements, including half-wave plates, 50:50 beam splitters, and polarization beam splitters, to convert spatial-polarization modes into different time bins. By using postselection in different time bins, the success probability of obtaining the uncorrupted states approaches 1/4 for single-photon transmission, which is not influenced by the coefficients of noisy channe…
Recent progress in integrated-optics technology has made photonics a promising platform for quantum networks and quantum computation protocols. Integrated optical circuits are characterized by small device footprints and unrivalled intrinsic interferometric stability. Here, we take advantage of femtosecond-laser-written waveguides' ability to process polarization-encoded qubits and present the first implementation of a heralded controlled-NOT gate on chip. We evaluate the gate performance in the computational basis and a superposition basis, showing that the gate can create polarization entang…
We investigate an optical quantum memory scheme with V-type three-level atoms based on the controlled reversible inhomogeneous broadening (CRIB) technique. We theoretically show the possibility to store and retrieve a weak light pulse interacting with the two optical transitions of the system. This scheme implements a quantum memory for a polarization qubit - a single photon in an arbitrary polarization state - without the need of two spatially separated two-level media, thus offering the advantage of experimental compactness overcoming the limitations due to mismatching and unequal efficienci…
Decoherence may significantly affect the polarization state of optical pulses propagating in dispersive media because of the unavoidable presence of more than a single frequency in the envelope of the pulse. Here we report on the suppression of polarization decoherence in a ring cavity obtained by properly retooling for photonic qubits the ``bang-bang'' protection technique already employed for nuclear spins and nuclear-quadrupole qubits. Our results show that bang-bang control can be profitably extended to quantum information processes involving flying polarization qubits.
Building on an earlier proposal for the production of polarization-entangled microwaves by means of intraband transitions in a pair of quantum dots, we show how this device can be used to transfer an unknown single-qubit state from electronic charge to photonic polarization degrees of freedom. No postselection is required, meaning that the quantum state transfer happens deterministically. Decoherence of the charge qubit causes a non-monotonic decay of the fidelity of the transferred state with increasing decoherence rate.
A SWAP operation between different types of qubits of single photons is essential for manipulating hyperentangled photons for a variety of applications. We have implemented an efficient SWAP gate for the momentum and polarization degrees of freedom of single photons. The SWAP gate was utilized in a single-photon two-qubit quantum logic circuit to deterministically transfer momentum entanglement between a pair of down-converted photons to polarization entanglement. The polarization entanglement thus obtained violates Bell's inequality by more than 150 standard deviations.
Logic qubit entanglement, which is also called the concatenated Greenberger-Horne-Zeilinger (C-GHZ) state, is robust in practical noisy environment. In this paper, we will describe an efficient approach to realize the complete polarization Bell-state analysis which is encoded in the logic qubit. We showed that the logic Bell-state can be distinguished in two steps with the help of the parity-check measurement (PCM), which is constructed by the cross-Kerr nonlinearity. We also explain that this approach can be used to distinguish arbitrary C-GHZ state with $N$ logic qubits. This protocol is use…
Systematic errors are inevitable in most measurements performed in real life because of imperfect measurement devices. Reducing systematic errors is crucial to ensuring the accuracy and reliability of measurement results. To this end, delicate error-compensation design is often necessary in addition to device calibration to reduce the dependence of the systematic error on the imperfection of the devices. The art of error-compensation design is well appreciated in nuclear magnetic resonance system by using composite pulses. In contrast, there are few works on reducing systematic errors in quant…
The Solovay-Kitaev theorem allows us to approximate any single-qubit gate to arbitrary accuracy with a finite sequence of fundamental operations from a universal set of gates. Inspired by this decomposition, we present a quantum channel simulator capable of implementing any completely positive trace-preserving map. Our realization consists of one ancillary qubit, encoded in the transverse mode of a laser beam (orbital degree of freedom), one qubit system, encoded in its polarization (spin), one spin-orbit CNOT gate and four single-qubit operations performed with prisms and polarization compone…
We address the experimental determination of entropic quantum discord for systems made of a pair of polarization qubits. We compare results from full and partial tomography and found that the two determinations are statistically compatible, with partial tomography leading to a smaller value of discord for depolarized states. Despite the fact that our states are well described, in terms of fidelity, by families of depolarized or phase-damped states, their entropic discord may be largely different from that predicted for these classes of states, such that no reliable estimation procedure beyond …
We demonstrate non-degenerate down-conversion at 810 and 1550 nm for long-distance fiber based quantum communication using polarization entangled photon pairs. Measurements of the two-photon visibility, without dark count subtraction, have shown that the quantum correlations (raw visibility 89%) allow secure quantum cryptography after 100 km of non-zero dispersion shifted fiber using commercially available single photon detectors. In addition, quantum state tomography has revealed little degradation of state negativity, decreasing from 0.99 at the source to 0.93 after 100 km, indicating minima…
We present a bright, narrowband, portable, quasi-phase-matched two-crystal source generating polarization-entangled photon pairs at 809 nm and 1555 nm at a maximum rate of 1.2 10^6 s-1 THz-1 mW-1 after coupling to single-mode fiber. The quantum channel at 1555 nm and the synchronization signal gating the single photon detector are multiplexed in the same optical fiber of length 27 km by means of wavelength division multiplexers (WDM) having 100 GHz (0.8 nm) spacing between channels. This implementation makes quantum communication applications compatible with current high-speed optical networks…
We demonstrate negative polarization created by light-hole exciton excitation in g-factor engineered GaAs quantum wells measured by time-resolved Kerr rotation and polarization-resolved photoluminescence. This negative polarization is a result of polarization transfer from a photon to an electron spin mediated by a light hole. This demonstration is an important step towards achieving quantum media conversion from a photonic qubit to an electron spin qubit required for building a quantum repeater.
A quantum memory, for storing and retrieving flying photonic quantum states, is a key interface for realizing long-distance quantum communication and large-scale quantum computation. While many experimental schemes of high storage-retrieval efficiency have been performed with weak coherent light pulses, all quantum memories for true single photons achieved so far have efficiencies far below 50%, a threshold value for practical applications. Here, we report the demonstration of a quantum memory for single-photon polarization qubits with an efficiency of >85% and a fidelity of >99 %, basing on b…
Faithfully storing an unknown quantum light state is essential to advanced quantum communication and distributed quantum computation applications. The required quantum memory must have high fidelity to improve the performance of a quantum network. Here we report the reversible transfer of photonic polarization states into collective atomic excitation in a compact solid-state device. The quantum memory is based on an atomic frequency comb (AFC) in rare-earth ion doped crystals. We obtain up to 0.998 process fidelity for the storage and retrieval process of single-photon-level coherent pulse. Th…
Classical correlation and quantum discord are computed for two-qubit $X$-states. Our approach, which is inspired by the methods of classical polarization optics, is geometric in the sense that the entire analysis is tied to the correlation ellipsoid of all normalized conditional states of the A-qubit with measurement elements applied to the B-qubit. Aspects of the computation which depend on the location of the reduced state of A inside the ellipsoid get clearly separated from those which do not. Our treatment is comprehensive\,: all known results are reproduced, often more economically, and s…
Integrated photonic technologies applied to quantum optics have recently enabled a wealth of breakthrough experiments in several quantum information areas. Path encoding was initially used to demonstrate operations on single or multiple qubits. However, a polarization encoding approach is often simpler and more effective. Two-qubits integrated logic gates as well as complex interferometric structures have been successfully demonstrated exploiting polarization encoding in femtosecond-laser-written photonic circuits. Still, integrated devices performing single-qubit rotations are missing. Here w…
In this work we present an algorithm of building an adequate model of polarizing quantum state measurement. This model takes into account chromatic aberration of the basis change transformation caused by the parasitic dispersion of the wave plates crystal and finite radiation spectral bandwidth. We show that the chromatic aberration reduces the amount of information in the measurements results. Using the information matrix approach we estimate the impact of this effect on the qubit state reconstruction fidelity for different values of sample size and spectral bandwidth. We also demonstrate tha…
