Werner Scherer, Michael Mehring
We discuss details of the preparation and detection of entangled electron-nuclear spin states in 15N:C60 together with a quantitative evaluation of the complete density matrix. All four Bell states of a two qubit subsystem were analyzed. In addition we find a quantum critical temperature of Tq = 7.73 K for this system at an electron spin resonance frequency of 95 GHz.
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We study broadband polarization entangled states generated within the line width of type-II Spontaneous Parametric Down Conversion (SPDC). Applying a complete quantum polarization tomography protocol at arbitrary combination of frequency and angular sideband modes we reveal a complex structure of non-degenerate non-collinear polarization entangled states generated within the SPDC line width. It is demonstrated that simultaneous compensation of longitudinal and transverse walk off leads to homogenizing the structure of polarization entanglement.
Entangled Probability Distributions for Center-of-Mass Tomography
本研究回顾质心系层析图形式体系，引入质心系层析成像的可分与纠缠概率分布概念，推导得到倒摆振子纠缠态的质心系层析图的时间演化规律，为量子态的概率分布描述提供新的理论工具。
We discuss the data-pattern tomography for reconstruction of entangled states of light. We show that for a moderate number of probe coherent states it is possible to achieve high accuracy of representation not only for single-mode states but also for two-mode entangled states. We analyze the stability of these representations to the noise and demonstrate the conservation of the purity and entanglement. Simulating the probe and signal measurements, we show that systematic error inherent for representation of realistic signal response with finite sets of responses from probe states still allows …
It is well known that one can extract all the information of an unknown quantum channel by means of quantum process tomography, such as standard quantum-process tomography and ancilla-assisted quantum process tomography (AAQPT). Furthermore, it has been shown that entanglement is not necessary for AAQPT, there exist separable states which are also useful for it. Surprisingly, in this work we find that not all entangled states are useful for AAQPT, there also exist some entangled states which are useless. The realignment operation used in entanglement detection can be related to the question wh…
Similar in spirit to the preceding work [Opt. Commun. 282 (2009) 3734] where the relation between optical Fresnel transformation and quantum tomography is revealed, we study this kind of relationship in the two-mode entangled case. We show that under the two-mode Fresnel transformation the bipartite entangled state density |eta><eta| becomes density operator F_2|eta><eta|F_2 ^{dag}=|eta>_{r,s}<eta|, which is just the Radon transform of the two-mode Wigner operator (sigma,gama) in entangled form, where F_2 is an two-mode Fresnel operator in quantum optics, and s,r are the complex-value expressi…
Ancilla Assisted Quantum Process Tomography using Bound entangled states
本文研究了束缚纠缠态在辅助量子过程全息成像中的应用，证明了某些束缚纠缠态可用于该技术，并指出局部过滤操作对全息成像无效，同时通过与韦纳和各向同性态的比较，建立了定量界限。
Entangled pure-states, Werner-states and generalized mixed-states of any structure, spanning a 2x2 Hilbert space are created by a novel high-brilliance universal source of polarization-entangled photon pairs. The violation of a Bell inequality has been tested for the first time with a pure-state, indeed a conceptually relevant ideal condition, and with Werner-states. The generalized ''maximally entangled mixed states'' (MEMS) were also synthetized for the first time and their exotic properties investigated by means of a quantum tomographic technique.
We present a novel method for quantum tomography of multi-qubit states. We apply the method to spin-multi-photon states, which we produce by periodic excitation of a semiconductor quantum-dot- confined spin every 1/4 of its coherent precession period. These timed excitations lead to the deterministic generation of strings of entangled photons in a cluster state. We show that our method can be used for characterizing the periodic process map, which produces the photonic cluster. From the measured process map, we quantify the robustness of the entanglement in the cluster. The 3-fold enhanced gen…
We report on tomographic means to study the stability of a qubit register based on a string of trapped ions. In our experiment, two ions are held in a linear Paul trap and are entangled deterministically by laser pulses that couple their electronic and motional states. We reconstruct the density matrix using single qubit rotations and subsequent measurements with near-unity detection efficiency. This way, we characterize the created Bell states, the states into which they subsequently decay, and we derive their entanglement, applying different entanglement measures.
In this work we demonstrate the use of stimulated emission tomography to characterize a hyper-entangled state generated by spontaneous parametric down-conversion in a CW-pumped source. In particular, we consider the generation of hyper-entangled states consisting of photon pairs entangled in polarisation and path. These results extend the capability of stimulated emission tomography beyond the polarisation degree of freedom, and demonstrate the use of this technique to study states in higher dimension Hilbert spaces.
An experimental demonstration of two-qutrit state tomography via one-qutrit symmetric informationally complete positive operator-valued measure (SIC-POVM) is presented. A two-qutrit state is encoded in the transversal paths of a spontaneous parametric down-converted photon pair. A spatial light modulator allows to implement the necessary 81 POVM elements to reconstruct the state. The quality of the reconstruction is evaluated by comparing independent measurements with the predicted results calculated with the reconstructed state. Entanglement in the system is calculated via negativity and gene…
We investigate how decoherence affects the entanglement established between two quantum dots in micro cavities, and propose a tomographic scheme able to measure the entangled state. The scheme we consider establishes the entanglement via the exchange and measurement of a photon. Making the realistic assumption of noise dominated by pure-dephasing processes, we find that the photon must be exchanged and measured on timescales shorter than the quantum dots' characteristic dephasing time for appreciable levels of entanglement to be achieved. The tomographic scheme is able to reconstruct the full …
Frequency non-degenerate entangled photon pairs have been employed in quantum communication, imaging, and sensing. To characterize quantum entangled state with long-wavelength (infrared, IR or even terahertz, THz) photon, one needs to either develop the single-photon detectors at the corresponding wavelengths or use novel tomography technique, which does not rely on single-photon detections, such as stimulated emission tomography (SET). We use standard quantum state tomography and SET to measure the density matrix of entangled photon pairs, with one photon at 1550 nm and the other one at 810 n…
Quantum state tomography (QST) is an essential tool for characterizing an unknown quantum state. Recently, QST has been performed for entangled qudits based on orbital angular momentum, time-energy uncertainty, and frequency bins. Here, we propose a QST for time-bin qudits, with which the number of measurement settings scales linearly with dimension $d$. Using the proposed scheme, we performed QST for a four-dimensional time-bin maximally entangled state with 16 measurement settings. We successfully reconstructed the density matrix of the entangled qudits, with which the average fidelity of th…
A scheme is discussed for measuring Nth-order coherences of two orthogonally polarized light fields in a single spatial mode at very limited experimental cost. To implement the scheme, the only measurements needed are the Nth-order intensity moments after the light beam has passed through two quarter-wave plates, one half-wave plate, and a polarizing beam splitter for specific settings of the wave plates. It is shown that this method can be applied for arbitrarily large N. A set of explicit values is given for the settings of the wave plates, constituting an optimal measurement of the Nth-orde…
We demonstrate an efficient experimental procedure based on entanglement swapping to determine the Bell nonlocality measure of Horodecki et al. [Phys. Lett. A 200, 340 (1995)] and the fully-entangled fraction of Bennett et al. [Phys. Rev. A 54, 3824 (1996)] of an arbitrary two-qubit polarization-encoded state. The nonlocality measure corresponds to the amount of the violation of the Clauser-Horne-Shimony-Holt (CHSH) optimized over all measurement settings. By using simultaneously two copies of a given state, we measure directly only six parameters. Our method requires neither full quantum stat…
Spin-entaglement has been proposed and extensively used in the case of correlated triplet pairs which are intermediate states in singlet fission process in select organic semiconductors. Here, we employ quantum process tomography of polarization entangled photon-pairs resonant with the excited state absorption of these states to investigate the nature of the inherent quantum correlations and to explore for an unambiguous proof for the existence of exciton entanglement.
Path-entangled N-photon states can be obtained through the coalescence of indistinguishable photons inside linear networks. They are key resources for quantum enhanced metrology, quantum imaging, as well as quantum computation based on quantum walks. However, the quantum tomography of path-entangled indistinguishable photons is still in its infancy as it requires multiple phase estimations increasing rapidly with N. Here, we propose and implement a method to measure the quantum tomography of path-entangled two-photon states. A two-photon state is generated through the Hong-Ou-Mandel interferen…
When basic tools of quantum information are applied to the quantum tomography data presented in Nature 439, 179 (2006), none of their devices appears to be a source of entangled photons.
The development of key devices and systems in quantum information technology, such as entangled particle sources, quantum gates and quantum cryptographic systems, requires a reliable and well-established method for characterizing how well the devices or systems work. We report our recent work on experimental characterization of pulsed entangled photonic states and photonic quantum channels, using the methods of state and process tomography. By using state tomography, we could reliably evaluate the states generated from a two-photon source under development and develop a highly entangled pulsed…
The generation of quantum entangled states of many particles is a central goal of quantum information science. Characterizing such states is a complex task that demands exponentially large resources as particles are being added. Previously, we demonstrated a resource efficient source that can generate, in principal, entanglement between any number of photons. This source recursively fuse photon pairs generated by a pulsed laser into a multiphoton entangled state. In the current work, we perform quantum state tomography on the photon pair source and quantum process tomography on the fusion oper…
In this article, we introduce a framework for entanglement characterization by time-resolved single-photon counting with measurement operators defined in the time domain. For a quantum system with unitary dynamics, we generate time-continuous measurements by shifting from the Schrodinger picture to the Heisenberg representation. In particular, we discuss this approach in reference to photonic tomography. To make the measurement scheme realistic, we impose timing uncertainty on photon counts along with the Poisson noise. Then, the framework is tested numerically on quantum tomography of qubits.…
We study the formation of an entangled state in a one-dimensional chain of three nuclear spins system which interact weakly through the Ising type of interaction and taking into account first and second neighbor interactions. We can get this entangled state using two pulses ($π/2$ and $π$ pulses), and we study the efficiency of getting this entangled state as a function of the ratio of the second neighbor interaction coupling constant to the first neighbor interaction coupling constant ($J'/J$). We found that for $J'/J\ge 0.04$, the entangled state is well defined.
Quantum Optical Coherence Tomography (Q-OCT) presents many advantages over its classical counterpart, Optical Coherence Tomography (OCT): it provides an increased axial resolution and is immune to even orders of dispersion. The core of Q-OCT is quantum interference of negatively correlated entangled photon pairs obtained in a Hong-Ou-Mandel configuration. This two-photon interference can be observed in the time domain in the form of dips or in the Fourier domain by means of a joint spectrum. The latter approach proved to be practical in the sense that it alleviated the requirement posed on lig…
Entangled sensors have been attracting a lot of attention recently because they can achieve the sensitivity beyond that of the classical sensors. To exploit entanglement as a resource, it is important to understand the effect of noise because the entangled state is fragile against noise. Here, we provide a Nuclear Magnetic Resonance (NMR) model of an entangled sensor under engineered noise: one can implement an entangled sensor under various noisy environments. In particular, we experimentally investigate the performance of the entangled sensor under the effect of time-inhomogeneous noisy envi…
Entangled measurement is a crucial tool in quantum technology. We propose a new entanglement measure of multi-mode detection, which estimates the amount of entanglement that can be created in a measurement. To illustrate the proposed measure, we perform quantum tomography of a two-mode detector that is comprised of two superconducting nanowire single photon detectors. Our method utilizes coherent states as probe states, which can be easily prepared with accuracy. Our work shows that a separable state such as a coherent state is enough to characterize a potentially entangled detector. We invest…
Heralded generation and manipulation of quantum entanglement between two macroscopic and spatially separated crystals at room temperature is theoretically studied. We show that by combining an x-ray parametric down-conversion source and x-ray interferometry with nuclear resonant scattering techniques, two macroscopic crystals hosting Mössbauer nuclei located each on an interferometer arm can be entangled for few tens of nanoseconds. The coherence time of the entanglement state can be prolonged up to values comparable to the lifetime of a single nuclear excited state, on the order of hundred na…
We present an experimentally feasible and efficient method for detecting entangled states with measurements that extend naturally to a tomographically complete set. Our detection criterion is based on measurements from subsets of a quantum 2-design, e.g., mutually unbiased bases or symmetric informationally complete states, and has several advantages over standard entanglement witnesses. First, as more detectors in the measurement are applied, there is a higher chance of witnessing a larger set of entangled states, in such a way that the measurement setting converges to a complete setup for qu…
Classical State Detection Using Quantum State Tomography
本文提出利用量子态成像技术检测混入经典态的纠缠光子，通过局部偏振测量诱导经典态，并用于提升量子网络中的经典-量子共存技术。
Quantum entanglement is a fundamental property of coherent quantum states and an essential resource for quantum computing. While two-qubit entanglement has been demonstrated for spins in silicon, creation of multipartite entanglement, a first step toward implementing quantum error correction, has remained challenging due to the difficulties in controlling a multi-qubit array, such as device disorder, magnetic and electrical noises and exacting exchange controls. Here, we show operation of a fully functional three-qubit array in silicon and generation of a three-qubit Greenberger-Horne-Zeilinge…
By choosing H nucleus in Carbon-13 labelled trichloroethylene as one qubit environment, and two C nuclei as a two-qubit system, we have simulated quantum decoherence when the system lies in an entangled state using nuclear magnetic resonance (NMR). Decoupling technique is used to trace over the environment degrees of freedom. Experimental results show agreements with the theoretical predictions. Our experiment scheme can be generalized to the case that environment is composed of multiple qubits.
Quantum teleportation faces increasingly demanding requirements for transmitting large or even entangled systems. However, knowledge of the state to be transmitted eases its reconstruction, resulting in a protocol known as remote state preparation. A number of experimental demonstrations to date have been restricted to single-qubit systems. We report the remote preparation of two-qubit "hybrid" entangled states, including a family of vector-polarization beams. Our single-photon states are encoded in the photon spin and orbital angular momentum. We reconstruct the states by spin-orbit state tom…
Quantum entangled states have shown distinguished features beyond any classical state. Many methods like quantum state tomography have been presented to verify entanglement. In this work, we aim to identify unknown entanglements with partial information of the state space by developing a nonlinear entanglement witness. The witness consists of a generalized Greenberger-Horne-Zeilinger-like paradox expressed by Pauli observables, and a nonlinear inequality expressed by density matrix elements. First, we verify unknown bipartite entanglements and study the robustness of entanglement witnesses aga…
Multi-photon entangled states are a crucial resource for many applications in quantum information science. Semiconductor quantum dots offer a promising route to generate such states by mediating photon-photon correlations via a confined electron spin, but dephasing caused by the host nuclear spin environment typically limits coherence (and hence entanglement) between photons to the spin $T_2^*$ time of a few nanoseconds. We propose a protocol for the deterministic generation of multi-photon entangled states that is inherently robust against the dominating slow nuclear spin environment fluctuat…
We present methods and results of shot-by-shot correlation of noisy measurements to extract entangled state and process tomography in a superconducting qubit architecture. We show that averaging continuous values, rather than counting discrete thresholded values, is a valid tomographic strategy and is in fact the better choice in the low signal-to-noise regime. We show that the effort to measure $N$-body correlations from individual measurements scales exponentially with $N$, but with sufficient signal-to-noise the approach remains viable for few-body correlations. We provide a new protocol to…
High fidelity quantum state tomography of electron-$^{14}$N nuclear hybrid spin register in diamond using Rabi oscillations
提出基于拉比振荡的量子态层析（RQST）方法，在金刚石NV色心的电子和核自旋单比特态上实现高保真度表征，平均保真度达0.995。
A practical source of high fidelity entangled photons is desirable for quantum information applications and exploring quantum physics. Semiconductor quantum dots have recently been shown to conveniently emit entangled light when driven electrically, however the fidelity was not optimal. Here we show that the fidelity is not limited by decoherence, but by coherent interaction with nuclei. Furthermore we predict that on 100μs timescales, strongly enhanced fidelities could be achieved. This insight could allow tailoring of quantum logic to operate using quantum dots in the fault tolerant regime.
Time-bin entangled Bell state generation and tomography on thin-film lithium niobate
本文在薄膜铌酸锂光子集成电路上实现时间仓最大纠缠贝尔态生成与片上量子态层析，亮度达242 MHz/mW、保真度91.9±1.0%，展示了该平台用于高速安全量子通信模块的潜力。
Quantum optical coherence tomography (QOCT) makes use of an entangled-photon light source to carry out dispersion-immune axial optical sectioning. We present the first experimental QOCT images of a biological sample: an onion-skin tissue coated with gold nanoparticles. 3D images are presented in the form of 2D sections of different orientations.
Efficient tomography of microwave photonic cluster states
本文提出了一种基于矩阵积算符形式的高效成像方法，用于重构最多35个微波光子量子比特的簇态密度矩阵，以检测光子源性能退化并指导高保真度纠缠光子源的发展。
Consider the task of verifying that a given quantum device, designed to produce a particular entangled state, does indeed produce that state. One natural approach would be to characterise the output state by quantum state tomography; or alternatively to perform some kind of Bell test, tailored to the state of interest. We show here that neither approach is optimal amongst local verification strategies for two qubit states. We find the optimal strategy in this case and show that quadratically fewer total measurements are needed to verify to within a given fidelity than in published results for …
We discuss methods of quantum state tomography for solid-state systems with a large nuclear spin $I=3/2$ in nanometer-scale semiconductors devices based on a quantum well. Due to quadrupolar interactions, the Zeeman levels of these nuclear-spin devices become nonequidistant, forming a controllable four-level quantum system (known as quartit or ququart). The occupation of these levels can be selectively and coherently manipulated by multiphoton transitions using the techniques of nuclear magnetic resonance (NMR) [Yusa et al., Nature (London) 434, 101 (2005)]. These methods are based on an uncon…
Quantum state tomography (QST) is a universal tool for the design and optimization of entangled-photon sources. It typically requires single-photon detectors and coincidence measurements. Recently, it was suggested that the information provided by the QST of photon pairs generated by spontaneous parametric down-conversion could be obtained by exploiting the stimulated version of this process, namely difference frequency generation. In this protocol, so-called "stimulated-emission tomography" (SET), a seed field is injected along with the pump pulse, and the resulting stimulated emission is mea…
A novel method for preparation of a single photon in temporally-delocalized entangled modes is proposed and analyzed. We show that two single-photon pulses propagating in a driven nonabsorbing medium with different group velocities are temporally split under parametric interaction into well-separated pulses. In consequence, the single-photon "time-bin-entangled" states are generated with a programmable entanglement easily controlled by driving field intensity. The experimental study of nonclassical features and nonlocality of generated states by means of balanced homodyne tomography is discuss…
We demonstrate a different scheme to perform optical sectioning of a sample based on the concept of induced coherence [Zou et al., Phys. Rev. Lett. 67, 318 (1991)]. This can be viewed as a different type of optical coherence tomography scheme where the varying reflectivity of the sample along the direction of propagation of an optical beam translates into changes of the degree of first-order coherence between two beams. As a practical advantage the scheme allows probing the sample with one wavelength and measuring photons with another wavelength. In a bio-imaging scenario, this would result in…
Entanglement is not only fundamental for understanding multipartite quantum systems but also generally useful for quantum information applications. Despite much effort devoted so far, little is known about minimal resources for detecting entanglement and also comparisons to tomography which reveals the full characterization. Here, we show that all entangled states can in general be detected in an experimental scheme that estimates the fidelity of two pure quantum states. An experimental proposal is presented with a single Hong-Ou-Mandel interferometry in which only two detectors are applied re…
Single-qubit measurements are typically insufficient for inferring arbitrary quantum states of a multi-qubit system. We show that if the system can be fully controlled by driving a single qubit, then utilizing a local random pulse is almost always sufficient for complete quantum-state tomography. Experimental demonstrations of this principle are presented using a nitrogen-vacancy (NV) center in diamond coupled to a nuclear spin, which is not directly accessible. We report the reconstruction of a highly entangled state between the electron and nuclear spin with fidelity above 95%, by randomly d…
We have implemented a universal quantum logic gate between qubits stored in the spin state of a pair of trapped calcium 40 ions. An initial product state was driven to a maximally entangled state deterministically, with 83% fidelity. We present a general approach to quantum state tomography which achieves good robustness to experimental noise and drift, and use it to measure the spin state of the ions. We find the entanglement of formation is 0.54.
In this work, we experimentally created and characterized a class of qubit-ququart PPT (positive under partial transpose) entangled states using three nuclear spins on an nuclear magnetic resonance (NMR) quantum information processor. Entanglement detection and characterization for systems with a Hilbert space dimension $\ge 2 \otimes 3$ is nontrivial since there are states in such systems which are both PPT as well as entangled. The experimental detection scheme that we devised for the detection of qubit-ququart PPT entanglement was based on the measurement of three Pauli operators with high …
We report on the preparation of entangled two mode squeezed states of yet unseen quality. Based on a measurement of the covariance matrix we found a violation of the Reid and Drummond EPR-criterion at a value of only 0.36\pm0.03 compared to the threshold of 1. Furthermore, quantum state tomography was used to extract a single photon Fock state solely based on homodyne detection, demonstrating the strong quantum features of this pair of laser-beams. The probability for a single photon in this ensemble measurement exceeded 2/3.
Phase Dependent Quantum Optical Coherence Tomography
本文提出相位依赖的量子光学相干层析成像，通过在Hong-Ou-Mandel干涉仪中对纠缠光子对施加相移来消除多层样品交叉反射伪影，提升量子传感与生物医学成像的精度和可靠性。
Entangled quantum states are an important element of quantum information techniques. We determine the requirements for states of quadrupolar nuclei with spins >1/2 to be entangled. It was shown that entanglement is achieved at low temperature by applying a magnetic field to a quadrupolar nuclei possess quadrupole moments, which interacts with the electricfield gradient produced by the charge distribution in their surroundings.
We present a method for measuring quantum states encoded in the temporal modes of photons. The basis for the multilevel quantum states is defined by the use of modes propagating in a dispersive medium, which is a fiber in this case. The propagation and time-resolved single photon detection allow us to define a positive-operator valued measure (POVM). The POVM depends on the amount of dispersion and the characteristics of a detector. This framework is numerically tested by performing quantum state tomography on a large number of states for a set of realistic experimental settings. Finally, the …
We use Nuclear Magnetic Resonance (NMR) to experimentally generate a bound entangled (more precisely: pseudo bound entangled) state, i.e. a quantum state which is non-distillable but nevertheless entangled. Our quantum system consists of three qubits. We characterize the produced state via state tomography to show that the created state has a positive partial transposition with respect to any bipartite splitting, and we use a witness operator to prove its entanglement.
Direct Observation of Entangled Electronic-Nuclear Wave Packets
本研究通过相位锁定超快脉冲产生并探测纠缠电子-核波包，结合动量分辨协方差与相位依赖产率测量，直接可视化电子与核自由度的纠缠及波函数演化。
The spin state of two magnetically inequivalent protons in contiguous atoms of a molecule becomes entangeled by the indirect spin-spin interaction (j-coupling). The degree of entanglement oscillates at the beat frequency resulting from the splitting of a degeneracy. This beating is manifest in NMR spectroscopy as an envelope of the transverse magnetization and should be visible in the free induction decay signal. The period (approximately 1 sec) is long enough for interference between the linear dynamics and collapse of the wave-function induced by a Stern-Gerlach inhomogeneity to significantl…
Undergraduate setup for measuring the Bell inequalities and performing Quantum State Tomography
本文提出一种低成本、多功能的纠缠光子实验装置，用于本科教学中测量CHSH贝尔不等式和双光子态层析成像，实验实现高保真纠缠态并显著违反贝尔不等式，提升量子概念可及性。
Selective Wigner phase space tomography and its application for studying quantum chaos
本文提出选择性Wigner相空间层析（SWPST），利用Wigner矩阵的稀疏性高效重构量子态，并通过NMR实验在量子混沌kicked top模型中提取量子-经典对应特征。
Quantum measurement is essential to both the foundations and practical applications of quantum information science. Among many possible models of quantum measurement, feedback measurements that dynamically update their physical structure are highly interesting due to their flexibility which enables a wide range of measurements that might otherwise be hard to implement. Here we investigate by detector tomography a measurement consisting of a displacement operation combined with photon detection followed by a real time feedback operation. We design the measurement in order to discriminate the su…
We experimentally demonstrate that loop state-preparation-and-measurement (SPAM) tomography is capable of detecting correlated errors in a two-qubit system. We prepare photon pairs in a state that approximates a Werner state, which may or may not be entangled. By performing measurements with multiple different detector settings we are able to detect correlated errors between two single-qubit measurements performed in different locations. No assumptions are made concerning either the state preparations or the measurements, other than that the dimensions of the states and the positive-operator-v…
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