We experimentally demonstrate amplitude and phase modulation of a time-energy entangled two-photon wave function. The entangled photons are produced by spontaneous parametric down-conversion, spectrally dispersed in an prism compressor, modulated in amplitude and/or phase, and detected in coincidence by sum-frequency generation. First, we present a Fourier optical analysis of the optical setup yielding an analytic expression for the resulting field distribution at the exit plane of the shaping apparatus. We then introduce amplitude and/or phase shaping and present results which can only be obtained through a combination of the two. Specifically, we use a shaper-based interferometer to measure the two-photon interference of an almost bandwidth-limited two-photon wave function.
We demonstrate a new type of quantum mechanical correlation where phase modulators at distant locations, acting on the photons of an entangled pair, interfere to determine the apparent depth of modulation. When the modulators have the same phase, the modulation depth doubles; when oppositely phased, the modulators negate each other.
In this paper, we provide a simple but powerful module to generate entangled qudits. This module assisted with cross-Kerr nonlinearity is available to the entangled qudits generation with arbitrary dimension, and it could work well even when the two independent qudits lose the same number of single photons. Moreover, with the cascade uses of modules, the deterministic generation but with nonidentical forms of entangled qudits is possible.
We describe a proof-of-principal experiment demonstrating a Fourier technique for measuring the shape of biphoton wavepackets. The technique is based on the use of synchronously driven fast modulators and slow (integrating) detectors.
The observation of the so-called dispersion cancelation (Opt. Express 17, 19244, 2009) and temporal phase modulation (Phys. Rev. Lett. 103, 163601, 2009) of paired photons is generally attributed to the presence of frequency entanglement between two frequency anticorrelated photons. In this paper, it is shown that by introducing the appropriate amount of chromatic dispersion or phase modulation between non-entangled photons, it is also possible to observe these effects. Indeed, it is found that the relevant characteristic for the observation of dispersion cancelation or the cancelation of temp…
In this paper, we present the first experimental demonstration on continuous variable quantum key distribution using determinant Einstein-Podolsky-Rosen entangled states of optical field. By means of the instantaneous measurements of the quantum fluctuations of optical modes respectively distributed at sender and receiver, the random bits of secret key are obtained without the need for signal modulation. The post-selection boundaries for the presented entanglement-based scheme against both Gaussian collective and individual attacks are theoretically concluded. The final secret key rates of 84 …
Entanglement is a universal resource in quantum networks, yet entangled photon sources are typically custom-made for a specific use case. Versatility, both in terms of state modulation and tunability of the temporal properties of the photons, is the key to flexible network architectures and cryptographic primitives that go beyond quantum key distribution. Here, we report on a flexible source design that produces high-quality entanglement in continuous-wave and GHz-rate-pulsed operation modes. Utilizing off-the-shelf optical components, our approach uses a fiber-based Sagnac loop to generate po…
The dynamics of maximum entangled coherent state travels through an amplitude damping channel is investigated. For small values of the transmissivity rate the travelling state is very fragile to this noise channel, where it suffers from the phase flip error with high probability. The entanglement decays smoothly for larger values of the transmissivity rate and speedily for smaller values of this rate. As the number of modes increases, the travelling state over this noise channel loses its entanglement hastily. The odd and even states vanish at the same value of the field intensity.
In the first days of quantum mechanics Dirac pointed out an analogy between the time-dependent coefficients of an expansion of the Schrödinger equation and the classical position and momentum variables solving Hamilton's equations. Here it is shown that the analogy can be made an equivalence in that, in principle, systems of classical oscillators can be constructed whose position and momenta variables form time-dependent amplitudes which are identical to the complex quantum amplitudes of the coupled wavefunction of an N-level quantum system with real coupling matrix elements. Hence classical m…
We propose a particular encoding for bipartite entangled states derived from multipartite cluster-type entangled coherent states (CTECSs). We investigate the effects of amplitude damping on the entanglement content of this bipartite state, as well as its usefulness as a quantum channel for teleportation. We find interesting relationships among the amplitude of the coherent states constituting the CTECSs, the number of subsystems forming the logical qubits (redundancy), and the extent to which amplitude damping affects the entanglement of the channel. For instance, in the sense of sudden death …
Building partially entangled states with Grover's amplitude amplification process
讨论了如何构造$n$两态量子系统（量子比特）的部分纠缠态。具有高对称度的最佳部分纠缠态被认为是有用的，以克服散粒噪声限制的拉姆齐光谱在一定的退相干。该状态在任何两个量子比特的置换和每个量子比特的基态$|0\ket$和激发态$|1\ket$之间的反转下是不变的。我们证明了，通过在一定的基矢上进行选择性相移和Grover关于平均操作的反演，我们可以通过对两个或三个量子比特进行$({polynomial in $ n个$})\times 2^{n/2}$连续的么正变换来构造这种高对称纠缠态.我们可以利用我们的方法构造更一般的纠缠态。
We propose a method to produce pure single photons with an arbitrary designed temporal shape in a heralded, lossless and scalable way. As the indispensable resource, the method uses pairs of time-energy entangled photons. To accomplish the shaping, one photon of a pair undergoes temporal modulation according to the desired shape. Subsequent frequency-resolving detection of the photon heralds its entangled counterpart in a pure quantum state with a temporal shape non-locally affected by the modulation. We found conditions for the shape of the heralded photon to reproduce the modulation function…
The development of efficient protocols for pure and mixed states preparation is challenging task. Most of the theory of quantum information applications has been developed for fully coherent or completely incoherent light. However, in many situations of interest partially coherent light has been proved to be a more robust model of radiation. In this paper the underpinning theory of two photon amplitude functions for down-converted fields with partially coherent pump beams is investigated. By using the generalised Siegert relations and the coherent mode representation of the cross spectral dens…
We present a quantum model for electro-optic amplitude modulation, which is built upon quantum models of the main photonic components that constitute the modulator, that is, the guided-wave beamsplitter and the electro-optic phase modulator and accounts for all the different available modulator structures. General models are developed both for single and dual drive configurations and specific results are obtained for the most common configurations currently employed. Finally, the operation with two-photon input for the control of phase-modulated photons and the important topic of multicarrier …
For systems described by the two-site Bose-Hubbard Hamiltonian, we show that a sinusoidal modulation of the tunneling matrix element assists higher-order co-tunneling processes. Using this mechanism, we propose an efficient new scheme for creating a coherent superposition of states in which all particles are either on one site or all on the other site, the so-called NOON state. This scheme yields an almost perfect NOON state periodically. For larger numbers of particles, further reduction of the time to create the state is possible if more than one modulation frequency is employed. With this s…
We propose a simple scheme for implementing fast arbitrary phase gates and employ pulse modulation to improve the gate robustness against different sources of noise. Parametric driving of a cavity is introduced to induce Rabi interactions between the cavity and qutrits, and then a two-qubit arbitrary phase gate is constructed by designing proper logical states. On this basis, we implement amplitude-shaped gates to obtain enhanced resilience to control errors in gate time and frequency detuning. By virtue of specifically designed logical states, the scheme displays intrinsic resistance to the e…
Recently it has been discovered that certain two-qutrit entangled states interacting with global and/or multi-local decoherence undergo distillability sudden death (DSD). We investigate this phenomenon for qutrit-qutrit systems interacting with statistically independent zero-temperature reservoirs. We show that certain initially prepared free-entangled states become bound-entangled in a finite time due to the action of Markovian dissipative environment. Moreover, in contrast with local dephasing, simple local unitary transformations can completely avoid distillability sudden death under amplit…
We study the dynamics of strongly coupled nanophotonic systems with time-variable parameters. The approximate analytic solutions are obtained for a broad class of open quantum systems including a two-level fermion emitter strongly coupled to a multimode quantized electromagnetic field in a cavity with time-varying cavity resonances or the electron transition energy. The coupling of the fermion and photon subsystems to their dissipative reservoirs is included within the stochastic equation of evolution approach, which is equivalent to the Lindblad approximation in the master equation formalism.…
For carrying out many quantum information protocols entanglement must be established in advance between two distant parties. Practically, inevitable interaction of entangled subsystems with their environments during distribution and storage will result in degradation of entanglement. Here we investigate the decoherence of two-qubit entangled states in the local amplitude noise. We show that there exists a set of partially entangled states that are more robust than maximally entangled states in terms of the residual quantum correlation measured by concurrence, fully entangled fraction, and quan…
With a resonant amplitude-modulation field on two Rydberg atoms, we propose a Rydberg antiblockade (RAB) regime, where the Rabi oscillation between collective ground and excited states is induced. A controlled-Z gate can be yielded through a Rabi cycle. Further, several common issues of the RAB gates are solved by modifying the parameter relation. The gate fidelity and the gate robustness against the control error are enhanced with a shaped pulse. The requirement of control precision of the Rydberg-Rydberg interaction strength is relaxed. In addition, the atomic excitation is restrained and th…
We develop theory of realization of hybrid entanglement between discrete-variable (single photon) and continuous-variable states (coherent states). A highly transmissive beam splitter (HTBS) is used for interaction of the ingredients. Mechanism for generating the hybrid entangled states is based on the simultaneous displacement of the discrete-variable state on equal in absolute value but opposite in sign displacement amplitudes by coherent components, in such a way that all the information about the displacement amplitudes is lost with subsequent registration of photons in the auxiliary mode.…
The entanglement behavior of two classes of multi-qubit system, GHZ and GHZ like states passing through a generalized amplitude damping channel is discussed. Despite this channel causes degradation of the entangled properties and consequently their abilities to perform quantum teleportation, one can always improve the lower values of the entanglement and the fidelity of the teleportrd state by controlling on Bell measurements, analyzer angle and channel's strength. Using GHZ-like state within a generalized amplitude damping channel is much better than using the normal GHZ-state, where the deca…
The effect of noise on various protocols of secure quantum communication has been studied. Specifically, we have investigated the effect of amplitude damping, phase damping, squeezed generalized amplitude damping, Pauli type as well as various collective noise models on the protocols of quantum key distribution, quantum key agreement,quantum secure direct quantum communication and quantum dialogue. From each type of protocol of secure quantum communication, we have chosen two protocols for our comparative study; one based on single qubit states and the other one on entangled states. The compar…
We introduce a novel time-frequency quantum key distribution (TFQKD) scheme based on photon pairs entangled in these two conjugate degrees of freedom. The scheme uses spectral detection and phase modulation to enable measurements in the temporal basis by means of time-to-frequency conversion. This allows large-alphabet encoding to be implemented with realistic components. A general security analysis for TFQKD with binned measurements reveals a close connection with finite-dimensional QKD protocols and enables analysis of the effects of dark counts on the secure key size.
We discuss a mechanism of generating two separable beams of light with high degree of entanglement in momentum using a fast and sharp optical boundary. Three regimes of light generation are identified depending on the number of resonant interactions between the optical perturbation and the electromagnetic field. The intensity of the process is discussed in terms of the relevant physical parameters: variation of refractive index and apparent velocity of the optical boundary. Our results suggest a different class of generation entangled light robust against thermal degradation by exciting zero p…
We consider a hybrid optomechanical system which is composed of the atomic ensemble and a standard optomechanical cavity driven by the periodically modulated external laser field. We investigate the asymptotic behaviors of Heisenberg operator first moments and clearly show the approaching process between the exact numerical results and analytical solutions. Based on the specific modulation forms of external driving and effective optomechanical coupling, we discuss in detail the atom-mirror entanglement enhancement, respectively. Compared with the constant driving regime, the entanglement can b…
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…
Cross-phase modulation at the single-photon level has a wide variety of fundamental applications in quantum optics including the generation of macroscopic entangled states. Here we describe a practical method for producing a weak cross-phase modulation at the single-photon level using metastable xenon in a high finesse cavity. We estimate the achievable phase shift and give a brief update on the experimental progress towards its realization. A single-photon cross-phase modulation of approximately 20 milliradians is predicted by both a straightforward perturbation theory calculation and a numer…
Due to coherent population oscillation (CPO) effect, we theoretically examine the generation and manipulation of Laguerre-Gaussian beams in terms of phase and amplitude modulation respectively in semiconductor quantum dots (SQDs). The results indicate that both phase modulation with low absorption of probe field and amplitude modulation with high efficiency can be achieved. Thus the practical way demonstrates that the SQDs system can function as effective optically addressed spatial light modulator with which the transverse spatial properties of probe fields can be artificially modulated.
We exploit the impact of exact frequency modulation on transition time of steering nuclear spin states from theoretical point of view. 1-stage and 2-stage Frequency-Amplitude-Phase modulation (FAPM) algorithms are proposed in contrast with 1-stage and 3-stage Amplitude-Phase modulation (APM) algorithms. The sufficient conditions are further present for transiting nuclear spin states within the specified time by these four modulation algorithms. It is demonstrated that transition time performance can be significantly improved if exact frequency modulation is available. It is exemplified that th…
We study the set of two-qubit pure states with real amplitudes and their geometrical representation in the three-dimensional sphere. In this representation, we show that the maximally entangled states --those locally equivalent to the Bell States --form two disjoint circles perpendicular to each other. We also show that taking the natural Riemannian metric on the sphere, the set of states connected by local gates are equidistant to this pair of circles. Moreover, the unentangled, or so-called product states, are $π/4$ units away to the maximally entangled states. This is, the unentangled state…
A silicon quantum photonic circuit was proposed and demonstrated as an integrated quantum light source for telecom band polarization entangled Bell state generation and dynamical manipulation. Biphoton states were firstly generated in four silicon waveguides by spontaneous four wave mixing. They were transformed to polarization entangled Bell states through on-chip quantum interference and quantum superposition, and then coupled to optical fibers. The property of polarization entanglement in generated photon pairs was demonstrated by two-photon interferences under two non-orthogonal polarizati…
We consider the problem of teleporting superposed coherent state using non-maximally entangled coherent state as quantum channel and study the effect of entanglement over quality of teleportation. We show that if maximally entangled coherent state (MECS) used by Van Enk and Hirota [Phys. Rev. A 64, 022313 (2001)] and by H Prakash et al. [Phys. Rev. A 75, 044305 (2007)] is replaced by a particular non-maximally entangled coherent state (NMECS), average fidelity of quantum teleportation increases appreciably at small coherent amplitudes. Since it is very challenging to produce superposed coheren…
Noninteracting bosons were proposed to be used for a demonstration of quantum-computing supremacy in a boson-sampling setup. A similar demonstration with fermions would require that the fermions are initially prepared in an entangled state. I suggest that pairwise entanglement of fermions would be sufficient for this purpose. Namely, it is shown that computing multi-particle scattering amplitudes for fermions entangled pairwise in groups of four single-particle states is #P hard. In linear algebra, such amplitudes are expressed as exterior products of two-forms of rank two. In particular, a pe…
Conditions to generate high-purity entangled vacuum-evacuated coherent states ($|0>|α>^0 - |-α>^0 |0>$ were studied for two cascade-placed beam splitters, with one squeezed state input and two coherent state inputs whenever a single photon is detected. Controlling the amplitudes and the phases of the beams allows for various amplitudes of the vacuum-evacuated coherent states ($|α>^ 0 = |α> -e^{-|α|^2} |0> $) up to $α= 2.160$ to be manipulated with high-purity.
Hybrid quantum information devices that combine disparate physical systems interacting through photons offer the promise of combining low-loss telecommunications wavelength transmission with high fidelity visible wavelength storage and manipulation. The realization of such systems requires control over the waveform of single photons to achieve spectral and temporal matching. Here, we experimentally demonstrate the simultaneous wavelength translation and amplitude modulation of single photons generated by a quantum dot emitting near 1300 nm with an exponentially-decaying waveform (lifetime $\ap…
Single epitaxially-grown semiconductor quantum dots have great potential as single photon sources for photonic quantum technologies, though in practice devices often exhibit non-ideal behavior. Here, we demonstrate that amplitude modulation can improve the performance of quantum-dot-based sources. Starting with a bright source consisting of a single quantum dot in a fiber-coupled microdisk cavity, we use synchronized amplitude modulation to temporally filter the emitted light. We observe that the single photon purity, temporal overlap between successive emission events, and indistinguishabilit…
The authors demonstrate a form of two-photon-counting interferometry by measuring the coincidence counts between single-photon-counting detectors at an output port of a Mach-Zehnder Interferometer (MZI) following injection of broad-band time-frequency-entangled photon pairs (EPP) generated from collinear spontaneous parametric down conversion into a single input port. Spectroscopy and refractometry are performed on a sample inserted in one internal path of the MZI by scanning the other path in length, which acquires phase and amplitude information about the samples linear response. Phase modul…
Discrete-modulation continuous-variable quantum key distribution with probabilistic amplitude shaping over a linear quantum channel
Scuola Superiore Sant’Anna（圣安娜高等学院）；National Laboratory of Photonic Networks, CNIT（光子网络国家实验室，CNIT）；Palacký University（帕拉茨基大学）；Università degli Studi di Milano（米兰大学）；INFN, Sezione di Milano（意大利国家核物理研究所，米兰分部）
In this work we report on a new mechanism to generate dissipative steady state entanglement in two coupled qubits driven by strong periodic ac fields. We show that steady entanglement can be generated at one side of a multiphoton resonance between a non-entangled ground state and an entangled excited state. The degree of entanglement can be tuned as a function of the amplitude of the periodic drive. A rich dynamic behavior with creation, death and revival of entanglement can be observed for certain parameter regimes, accessible in current experimental devices.
We consider the effect of self-phase modulation and cross-phase modulation on the joint spectral amplitude of photon pairs generated by spontaneous four-wave mixing. In particular, the purity of a heralded photon from a pair is considered, in the context of schemes that aim to maximise the purity and minimise correlation in the joint spectral amplitude using birefringent phase-matching and short pump pulses. We find that non-linear phase modulation effects will be detrimental, and will limit the quantum interference visibility that can be achieved at a given generation rate. An approximate exp…
We demonstrate that the transport characteristics of deep optical lattices with one or multiple off-resonant external energy offsets can be greatly-enhanced by modulating the lattice depth in an exotic way. We derive effective stationary models for our proposed modulation schemes in the strongly interacting limit, where only one particle can occupy any given site. Afterwards we discuss the modifications necessary to recover transport when more than one particle may occupy the lattice sites. For the specific five-site lattices discussed, we numerically predict transport gains for ranging from $…
One of the main milestones in the study of opto- and electro-mechanical systems is to certify entanglement between a mechanical resonator and an optical or microwave mode of a cavity field. In this work, we show how a suitable time-periodic modulation can help to achieve large degrees of entanglement, building upon the framework introduced in [Phys. Rev. Lett. 103, 213603 (2009)]. It is demonstrated that with suitable driving, the maximum degree of entanglement can be significantly enhanced, in a way exhibiting a non-trivial dependence on the specifics of the modulation. Such time-dependent dr…
