This paper defines a notion of parallel transport in a lattice of quantum particles, such that the transformation associated with each link of the lattice is determined by the quantum state of the two particles joined by that link. We focus particularly on a one-dimensional lattice--a ring--of entangled rebits, which are binary quantum objects confined to a real state space. We consider states of the ring that maximize the correlation between nearest neighbors, and show that some correlation must be sacrificed in order to have non-trivial parallel transport around the ring. An analogy is made with lattice gauge theory, in which non-trivial parallel transport around closed loops is associated with a reduction in the probability of the field configuration. We discuss the possibility of extending our result to qubits and to higher dimensional lattices.
We propose a physical scheme to generate entangled light at high temperatures through the excitation of vacuum fluctuations of the electromagnetic field using periodic modulations of a refractive index of a ring resonator. We consider the processes of dissipation and decoherence resulting from the coupling of the system with an environment at finite temperature and show that the total amount of entanglement generated does not depend on the temperature, which only affects the time necessary for the system to produce such an amount of entanglement.
We demonstrate time-bin entanglement generation in telecom wavelength using a 7 μm radius Si micro-ring resonator pumped by a continuous wave laser. The resonator structure can enhance spontaneous four wave mixing, leading to a photon pair generation rate of about 90-100 Hz with a laser pump power of as low as -3.92 dBm (0.41 mW). We succeed in observing time-bin entanglement with the visibility over 92%. Moreover, wavelength-tunability of the entangled photon pair is demonstrated by changing the operation temperature.
We present recent findings towards developing brighter entangled photon sources in critically phase matched (CPM) nonlinear crystals. Specifically, we use type-I collinear phase matching at non-degenerate wavelengths in parallel \b{eta}-Barium Borate (BBO) crystals to generate pairs of polarization entangled photons for free-space quantum key distribution (QKD). We first review the entangled source configuration and then discuss ways to further improve the source brightness by means of tailoring the pump and collection modes. We present preliminary results that may lead to brighter entangled p…
We present an optical design where polarization-entangled photon pairs are generated within two $β$-Barium Borate crystals whose optical axes are parallel. This design increases the spatial mode overlap of the emitted photon pairs enhancing single mode collection without the need for additional spatial walk-off compensators. The observed photon pair rate is at least 65000 pairs/s/mW with a quantum state fidelity of 99.53$\pm$0.22% when pumped with an elliptical spatial profile.
Bell inequalities (BIs) derived in terms of quantum probability statistics are extended to general bipartite-entangled states of arbitrary spins with parallel polarization. The original formula of Bell for the two-spin singlet is slightly modified in the parallel configuration, while, the inequality for- mulated by Clauser-Horne-Shimony-Holt remains not changed. The violation of BIs indeed resulted from the quantum non-local correlation for spin-1=2 case. However, the inequalities are always satisfied for the spin-1 entangled states regardless of parallel or antiparallel polarizations of two s…
The behavior of games repeated in parallel, when played with quantumly entangled players, has received much attention in recent years. Quantum analogues of Raz's classical parallel repetition theorem have been proved for many special classes of games. However, for general entangled games no parallel repetition theorem was known. We prove that the entangled value of a two-player game $G$ repeated $n$ times in parallel is at most $c_G n^{-1/4} \log n$ for a constant $c_G$ depending on $G$, provided that the entangled value of $G$ is less than 1. In particular, this gives the first proof that the…
We suggest the generation of photon pairs in a thermally induced nonlinear periodically-poled silica fiber by spontaneous parametric down-conversion. Photons are generated directly in eigenstates of optical angular momentum. Photons in a pair can be entangled in these states as well as in frequencies. We identify suitable spatial and polarization modes giving an efficient nonlinear interaction. By changing the pump field properties both narrow- and broad-band down-converted fields can be obtained.
We report on the observation of an unusual type of parametric down-conversion. In the regime where collinear degenerate emission is in the anomalous range of group-velocity dispersion, its spectrum is restricted in both angle and wavelength. Detuning from exact collinear-degenerate phasematching leads to a ring shape of the wavelength-angular spectrum, suggesting a new type of spatiotemporal coherence and entanglement of photon pairs. By imposing a phase varying in a specific way in both angle and wavelength, one can obtain an interesting state of an entangled photon pair, with the two photons…
Parallelization of frequency domain quantum gates: manipulation and distribution of frequency-entangled photon pairs generated by a 21 GHz silicon micro-resonator
The experimental test of Bell's inequality is mainly focused on Clauser-Horne-Shimony-Holt (CHSH) form, which provides a quantitative bound, while little attention has been pained on the violation of Wigner inequality (WI). Based on the spin coherent state quantum probability statistics we in the present paper extend the WI and its violation to arbitrary two-spin entangled states with antiparallel and parallel spin-polarizations. The local part of density operator gives rise to the WI while the violation is a direct result of non-local interference between two components of the entangled state…
We report a wavelength division multiplexed time-bin entangled photon pair source in telecom wavelength using a 10 μm radius Si ring resonator. This compact resonator has two add ports and two drop ports. By pumping one add port by a continuous laser, we demonstrate an efficient generation of two-wavelength division multiplexed time-bin entangled photon pairs in the telecom C-band, which come out of one drop port, and are then split into the signal and idler photons via a wavelength filter. The resonator structure enhances four wave mixing for pair generation. Moreover, we demonstrate the doub…
In a two-player game, two cooperating but non communicating players, Alice and Bob, receive inputs taken from a probability distribution. Each of them produces an output and they win the game if they satisfy some predicate on their inputs/outputs. The entangled value $ω^*(G)$ of a game $G$ is the maximum probability that Alice and Bob can win the game if they are allowed to share an entangled state prior to receiving their inputs. The $n$-fold parallel repetition $G^n$ of $G$ consists of $n$ instances of $G$ where the players receive all the inputs at the same time and produce all the outputs …
Algorithms to simulate the ring-exchange models using the projected entangled pair states (PEPS) are developed. We generalize the imaginary time evolution (ITE) method to optimize PEPS wave functions for the models with ring-exchange interactions. We compare the effects of different approximations to the environment. To understand the numerical instability during the optimization, we introduce the ``singularity'' of a PEPS and develop a regulation procedure that can effectively reduce the singularity of a PEPS. We benchmark our method with the toric code model, and obtain extremely accurate gr…
The capacity of optical communication channels can be increased by space division multiplexing in structured optical fibers. Radial core optical fibers allows for the propagation of twisted light--eigenmodes of orbital angular momentum, which have attracted considerable attention for high-dimensional quantum information. Here we study the generation of entangled photons that are tailor-made for coupling into ring core optical fibers. We show that the coupling of photon pairs produced by parametric down-conversion can be increased by close to a factor of three by pumping the non-linear crystal …
We show that the $n$-round parallel repetition of the Magic Square game of Mermin and Peres is rigid, in the sense that for any entangled strategy succeeding with probability $1 -\varepsilon$, the players' shared state is $O(\mathrm{poly}(n\varepsilon))$-close to $2n$ EPR pairs under a local isometry. Furthermore, we show that, under local isometry, the players' measurements in said entangled strategy must be $O(\mathrm{poly}(n\varepsilon))$ close to the "ideal" strategy when acting on the shared state.
We study the behavior of the entangled value of two-player one-round projection games under parallel repetition. We show that for any projection game $G$ of entangled value 1-eps < 1, the value of the $k$-fold repetition of G goes to zero as O((1-eps^c)^k), for some universal constant c\geq 1. Previously parallel repetition with an exponential decay in $k$ was only known for the case of XOR and unique games. To prove the theorem we extend an analytical framework recently introduced by Dinur and Steurer for the study of the classical value of projection games under parallel repetition. Our proo…
We present two parallel repetition theorems for the entangled value of multi-player, one-round free games (games where the inputs come from a product distribution). Our first theorem shows that for a $k$-player free game $G$ with entangled value $\mathrm{val}^*(G) = 1 - ε$, the $n$-fold repetition of $G$ has entangled value $\mathrm{val}^*(G^{\otimes n})$ at most $(1 - ε^{3/2})^{Ω(n/sk^4)}$, where $s$ is the answer length of any player. In contrast, the best known parallel repetition theorem for the classical value of two-player free games is $\mathrm{val}(G^{\otimes n}) \leq (1 - ε^2)^{Ω(n/s)…
Mutually unbiased bases plays a central role in quantum mechanics and quantum information processing. As an important class of mutually unbiased bases, mutually unbiased maximally entangled bases (MUMEBs) in bipartite systems have attracted much attention in recent years. In the paper, we try to construct MUMEBs in $\mathbb{C}^{2^s} \otimes \mathbb{C}^{2^s}$ by using Galois rings, which is different from the work in \cite{xu2}, where finite fields are used. As applications, we obtain several new types of MUMEBs in $\mathbb{C}^{2^s}\otimes\mathbb{C}^{2^s}$ and prove that $M(2^s,2^s)\geq 3(2^s-1…
High coherent frequency-entangled photons at telecom band are critical in quantum information protocols and quantum tele-communication. While photon pairs generated by spontaneous parametric down-conversion in nonlinear crystal or modulation instability in optical fiber exhibit random fluctuations, making the photons distinguishable among consecutive roundtrips. Here, we demonstrate a frequency-entangled photons based on parametric instability in an active fiber ring cavity, where periodic modulation of dispersion excites parametric resonance. The characteristic wave number in parametric insta…
We present a strong parallel repetition theorem for the entangled value of multi-player, one-round free games (games where the inputs come from a product distribution). Our result is the first parallel repetition theorem for entangled games involving more than two players. Furthermore, our theorem applies to games where the players are allowed to output (possibly entangled) quantum states as answers. More specifically, let $G$ be a $k$-player free game, with entangled value $\mathrm{val}^*(G) = 1 - ε$. We show that the entangled value of the $n$-fold repetition of $G$, $\mathrm{val}^*(G^{\otim…
In a two-player game, two cooperating but non communicating players, Alice and Bob, receive inputs taken from a probability distribution. Each of them produces an output and they win the game if they satisfy some predicate on their inputs/outputs. The entangled value $ω^*(G)$ of a game $G$ is the maximum probability that Alice and Bob can win the game if they are allowed to share an entangled state prior to receiving their inputs. The $n$-fold parallel repetition $G^n$ of $G$ consists of $n$ instances of $G$ where Alice and Bob receive all the inputs at the same time and must produce all the o…
Sequences of commuting quantum operators can be parallelized using entanglement. This transformation is behind some optimal quantum metrology protocols and recent results on quantum circuit complexity. We show that dephasing quantum maps in arbitrary dimension can also be parallelized. This implies that for general dephasing noise the protocol with entanglement is not more fragile than the corresponding sequential protocol and, conversely, the sequential protocol is not less effective than the entangled one. We derive this result using tensor networks. Furthermore, we only use transformations …
In this study, we present a technique based on the quantum Fourier transform (QFT) that allows the generation of disjoint sets of entangled particles, in such a way that particles of the same set are entangled with each other, while particles of different sets are completely independent. Several applications of this technique are implemented on three physical platforms, of 5 (Belem), 7 (Oslo), and 14 (Melbourne) qubits, of the international business machine (IBM Q) quantum experience program, where all these applications were specially selected due to their particular commitment to the future …
Frequency entangled photon sources are in high demand in a variety of optical quantum technologies, including quantum key distribution, cluster state quantum computation and quantum metrology. In the recent decade, chip-scale entangled photon sources have been developed using silicon platforms, offering robustness, large scalability and CMOS technology compatibility. Here, we report the generation of frequency correlated photon pairs using a 150-GHz silicon nitride ring cavity. First, the device is characterized for studying the phase matching condition during spontaneous four-wave mixing. Nex…
Entangled photon sources (EPS), the major building block for a variety of quantum communication protocols, are commonly developed by utilizing the spontaneous parametric down-conversion (SPDC) in $χ^{2}$ nonlinear bulk optical materials. While high nonlinearity and long interaction length have established the superiority of the periodically poled crystals for EPSs, the phase-matching condition of such crystals is very sensitive to the fluctuation of the crystal temperature and the laser wavelength. As a result, deploying such sources outside the laboratory, for example, satellite-based applica…
Parallel distributed quantum gates for dual-species quantum emitters
MIIT Key Laboratory of Semiconductor Microstructure and Quantum Sensing, School of Physics, Nanjing University of Science and Technology（南京理工大学物理学院）；Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University（亚当·密茨凯维奇大学物理学院自旋电子学与量子信息研究所）；Center for Quantum Computing, RIKEN（理化学研究中心量子计算中心）；Engineering Research Center of Semiconductor Device Optoelectronic Hybrid Integration in Jiangsu Province（江苏省半导体器件光电混合集成工程研究中心）；Physics Department, The University of Michigan（密歇根大学物理系）
This paper shows how to construct quantum entanglement states of n qubits based on a self-stabilizing token ring algorithm. The entangled states can be applied to the fields of the quantum network, quantum Internet, distributed quantum computing, and quantum cloud. To the best of our knowledge, this is the first attempt to construct quantum entanglement based on the self-stabilizing algorithm. By the quantum circuit implementation based on the IBM Quantum Experience platform, it is demonstrated that the construction indeed can achieve specific n qubit entangled states, which in turn can be use…
Uniformly accelerated frame mimics a thermal bath whose temperature is proportional to the proper acceleration. Using this phenomenon we give a detailed construction of an Otto cycle between two energy eigenstates of a system, consists of two entangled qubits. In the isochoric stages the thermal bath is being provided via the vacuum fluctuations of the background field for a monopole interaction by accelerating them. We find that making of Otto cycle is possible when one qubit is accelerating in the right Rindler wedge and other one is moving in the left Rindler wedge; i.e. in anti-parallel mo…
Distributed quantum metrology can enhance the sensitivity for sensing spatially distributed parameters beyond the classical limits. Here we demonstrate distributed quantum phase estimation with discrete variables to achieve Heisenberg limit phase measurements. Based on parallel entanglement in modes and particles, we demonstrate distributed quantum sensing for both individual phase shifts and an averaged phase shift, with an error reduction up to 1.4 dB and 2.7 dB below the shot-noise limit. Furthermore, we demonstrate a combined strategy with parallel mode entanglement and multiple passes of …
Quantum networks provide a prominent platform for realizing quantum information processing and quantum communication, with entanglement being a key resource in such applications. Here, we describe the dissipative transport protocol for entangled states, where entanglement stored in the first node of quantum network can be transported with high fidelity to the second node via a 1D chiral waveguide. In particular, we exploit the directional asymmetry in chirally-coupled single-mode ring resonators to transport entangled states. For the fully chiral waveguide, Bell states, multipartite $W$-states…
The mapping of quantum circuits to qubits represented by ion states in a storage ring quantum computer is examined. Serial, parallel and hybrid architectures for mapping such qubits onto a storage ring quantum computer are presented. Parallelism is an important part of the SRQC architecture in terms of multiple ions, windows and lasers. A "predecessor problem" that arises in such architectures is identified and a solution is proposed. Representative numerical sizing and timing calculations are presented. The entire methodology is very general and extends to several implementation options. Open…
Aspects of quantum mechanics on a ring are studied. Either one or two impenetrable barriers are inserted at nodal and non-nodal points to turn the ring into either one or two infinite square wells. In the process, the wave function of a particle can change its energy, as it gets entangled with the barriers and the insertion points become nodes. Two seemingly innocuous assumptions representing locality and linearity are investigated. Namely, a barrier insertion at a fixed node needs no energy, and barrier insertions can be described by linear maps. It will be shown that the two assumptions are …
The precise measurement of a magnetic field is one of the most fundamental and important tasks in quantum metrology. Although extensive studies on quantum magnetometry have been carried out over past decades, the ultimate precision that can be achieved for the estimation of all three components of a magnetic field with entangled probe states under the parallel scheme remains unknown. Here we present the ultimate lower bound for the sum of arbitrarily weighted variances in the estimation of all three components of a magnetic field under the parallel scheme and show that this lower bound can be …
The original formula of Bell inequality (BI) in terms of two-spin singlet has to be modified for the entangled-state with parallel spin polarization. Based on classical statistics of the particle-number correlation, we prove in this paper an extended BI, which is valid for two-spin entangled states with both parallel and antiparallel polarizations. The BI and its violation can be formulated in a unified formalism based on the spin coherent-state quantum probability statistics with the state-density operator, which is separated to the local and non-local parts. The local part gives rise to the …
