Andrzej Grudka, Antoni Wojcik
We will present a method of implementation of general projective measurement of two-photon polarization state with the use of linear optics elements only. The scheme presented succeeds with a probability of at least 1/16. For some specific measurements, (e.g. parity measurement) this probability reaches 1/4.
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A scheme for direct projection of a quantum state on Bell states is described. The method is based on constructing an average Hamiltonian with Bell eigenstates and then, projecting the state on these eigenstates. The projection is performed by adding the results of a direct and time-reversed evolution. Experimental demonstration is shown for pairs of dipolar-coupled nuclear spins.
Positive Operator Value Measures (POVMs) are the most general class of quantum measurements. We propose a setup in which all possible POVMs of a single photon polarization state (corresponding to all possible sets of two-dimensional Kraus operators) can be implemented easily using linear optics elements. This method makes it possible to experimentally realize any projective orthogonal, projective non-orthogonal or non-projective sets of any number of POVM operators. Furthermore our implementation only requires vacuum ancillas, and is deterministic rather than probabilistic. Thus it realizes ev…
We investigate the implementation of binary projective measurements with linear optics. This problem can be viewed as a single-shot discrimination of two orthogonal pure quantum states. We show that any two orthogonal states can be perfectly discriminated using only linear optics, photon counting, coherent ancillary states, and feedforward. The statement holds in the asymptotic limit of large number of these physical resources.
We investigate the possibility of implementing a given projection measurement using linear optics and arbitrarily fast feedforward based on the continuous detection of photons. In particular, we systematically derive the so-called Dolinar scheme that achieves the minimum error discrimination of binary coherent states. Moreover, we show that the Dolinar-type approach can also be applied to projection measurements in the regime of photonic-qubit signals. Our results demonstrate that for implementing a projection measurement with linear optics, in principle, unit success probability may be approa…
We derive a set of criteria to decide whether a given projection measurement can be, in principle, exactly implemented solely by means of linear optics. The derivation can be adapted to various detection methods, including photon counting and homodyne detection. These criteria enable one to obtain easily No-Go theorems for the exact distinguishability of orthogonal quantum states with linear optics including the use of auxiliary photons and conditional dynamics.
We propose a method for preparing maximal path entanglement with a definite photon number N, larger than two, using projective measurements. In contrast with the previously known schemes, our method uses only linear optics. Specifically, we exhibit a way of generating four-photon, path-entangled states of the form |4,0> + |0,4>, using only four beam splitters and two detectors. These states are of major interest as a resource for quantum interferometric sensors as well as for optical quantum lithography and quantum holography.
A projective measurement of energy (PME) on a quantum system is a quantum measurement, determined by the Hamiltonian of the system. PME protocols exist when the Hamiltonian is given in advance. Unknown Hamiltonians can be identified by quantum tomography, but the time cost to achieve a given accuracy increases exponentially with the size of the quantum system. In this letter, we improve the time cost by adapting quantum phase estimation, an algorithm designed for computational problems, to measurements on physical systems. We present a PME protocol without quantum tomography for Hamiltonians w…
We present a scheme for a universal device which can be programmed by quantum states to approximate a chosen projective measurement to a given precision. Our scheme can be viewed as an extension of the swap test to the instance where one state is supplied many times. As such, it has many potential applications given the variety of quantum information tasks which make use of the swap test. In particular, we show that our scheme is optimal for state discrimination under the one-sided error requirement, and optimally approximates any projective measurement. Furthermore, we propose a practical imp…
Optical quantum nondemolition devices can provide essential tools for quantum information processing. Here, we describe several optical interferometers that signal the presence of a single photon in a particular input state without destroying it. We discuss both entanglement-assisted and non-entanglement-assisted interferometers, with ideal and realistic detectors. We found that existing detectors with 88% quantum efficiency and single-photon resolution can yield output fidelities of up to 89%, depending on the input state. Furthermore, we construct expanded protocols to perform QND detections…
We discuss the problem of implementing generalized measurements (POVMs) with linear optics, either based upon a static linear array or including conditional dynamics. In our approach, a given POVM shall be identified as a solution to an optimization problem for a chosen cost function. We formulate a general principle: the implementation is only possible if a linear-optics circuit exists for which the quantum mechanical optimum (minimum) is still attainable after dephasing the corresponding quantum states. The general principle enables us, for instance, to derive a set of necessary conditions f…
So far, various multi-photon entangled states have been observed experimentally by using different experimental set-ups. Here, we present a scheme to realize many SLOCC-inequivalent states of three and four qubits via projective measurements on suitable entangled states. We demonstrate how these states can be observed experimentally in a single set-up and study the feasibility of the implementation with present-day technology.
Blockwise Optimization for Projective Variational Quantum Dynamics (BLOP-VQD): Algorithm and Implementation for Lattice Systems
BLOP-VQD通过块级优化降低计算成本，实现高效模拟复杂量子系统的时间演化。
One of the peculiar features in quantum mechanics is that a superposition of macroscopically distinct states can exits. In optical system, this is highlighted by a superposition of coherent states (SCS), i.e. a superposition of classical states. Recently this highly nontrivial quantum state and its variant have been demonstrated experimentally. Here we demonstrate the superposition of coherent states in quantum measurement which is also a key concept in quantum mechanics. More precisely, we propose and implement a projection measurement onto the arbitrary superposition of the SCS bases in opti…
We report the implementation of projective measurement on a single 1/2 nuclear spin of the 171Yb atom by measuring the polarization of cavity-enhanced fluorescence. To obtain cavity-enhanced fluorescence having a nuclear-spin-dependent polarization, we construct a two-mode cavity QED system, in which two cyclic transitions are independently coupled to each of the orthogonally polarized cavity modes, by manipulating the energy level of 171Yb. This system can associate the nuclear spin degrees of freedom with the polarization of photons, which will facilitate the development of hybrid quantum sy…
We report on an optical setup generating more than one bit of randomness from one entangled bit (i.e. a maximally entangled state of two-qubits). The amount of randomness is certified through the observation of Bell non-local correlations. To attain this result we implemented a high-purity entanglement source and a non-projective three-outcome measurement. Our implementation achieves a gain of 27$\%$ of randomness as compared with the standard methods using projective measurements. Additionally we estimate the amount of randomness certified in a one-sided device independent scenario, through t…
We discuss a novel implementation of the minimum error state discrimination measurement, originally introduced by Helstrom. In this implementation, instead of performing the optimal projective measurement directly on the system, it is first entangled to an ancillary system and the measurement is performed on the ancilla. We show that, by an appropriate choice of the entanglement transformation, the Helstrom bound can be attained. The advantage of this approach is twofold. First, it provides a novel implementation when the optimal projective measurement cannot be directly performed. For example…
Implementation of the Projective Quantum Eigensolver on a Quantum Computer
本研究在IBM量子硬件上测试射影量子特征求解器（PQE）结合误差缓解技术的性能，在H₂单量子比特模型和临界点四格点横场Ising模型上验证了效果，并提出误差缓解优化建议。
Research in non-orthogonal state discrimination has given rise to two conventional optimal strategies: unambiguous discrimination (UD) and minimum error (ME) discrimination. This paper explores the experimentally relevant range of measurement strategies between the two, where the rate of inconclusive results is minimized for a bounded-error rate. We first provide some constraints on the problem that apply to generalized measurements (POVMs). We then provide the theory for the optimal projective measurement (PVM) in this range. Through analytical and numerical results we investigate this family…
We consider a device which can be programmed using coherent states of light to approximate a given projective measurement on an input coherent state. We provide and discuss three practical implementations of this programmable projective measurement device with linear optics, involving only balanced beam splitters and single photon threshold detectors. The three schemes optimally approximate any projective measurement onto a program coherent state in a non-destructive fashion. We further extend these to the case where there are no assumptions on the input state. In this setting, we show that ou…
Demonstration of quantum projective simulation on a single-photon-based quantum computer
本文在单光子量子计算机Ascella上实现了结合线性光学干涉仪与投影模拟的变分强化学习算法，通过量子游走选择动作，并在测试任务中展示了量子智能体相对经典智能体的潜力。
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.
We review some applications of entanglement to improve quantum measurements and communication, with the main focus on the optical implementation of quantum information processing. The evolution of continuos variable entangled states in active optical fibers is also analyzed.
Projective measurements are sufficient for recycling nonlocality
针对顺序观察者共享纠缠态的非定域性回收问题，本文证明无需非锐测量或量子辅助系统，仅用投影测量即可实现，并给出 CHSH 情形下的最优权衡与更大顺序违背。
Efficient quantum state tomography with two complementary projective measurements
本文提出一种基于Kirkwood-Dirac拟概率的量子态层析协议，仅需两组互补投影测量，结合复数逻辑回归与投影梯度算法，在GPU上20分钟内完成15量子比特混合态重构，显著降低测量与计算成本。
We present a review and discussions on characterizations and quantifications of macroscopic quantum states as well as their implementations and applications in optical systems. We compare and criticize different measures proposed to define and quantify macroscopic quantum superpositions and extend such comparisons to several types of optical quantum states actively considered for experimental implementations within recent research topics.
Simulating quantum instruments with projective measurements and quantum post-processing
本文研究量子仪器能否仅用投影测量和测量后量子处理来模拟，将其与纠缠分类问题关联，给出一般仪器的计算高效判据和量子比特的完整刻画，并应用于噪声容忍、信息-扰动权衡及贝尔不等式违反增强等任务。
We present a feasible scheme to implement the non-deterministic quantum logic operation of Knill, Laflamme and Milburn (Nature, 409, 46-52(2001)) by using a teleportation protocol, which requires only single-photon sources, linear optical elements and photon detectors.
Conditions for implementing projective measurements through continuous monitoring
本文针对有限维量子系统，明确了连续监测实现投影测量的条件，推导了收敛速率与时间-误差关系，为优化量子测量协议提供了清晰框架。
We report on a fiber-optics implementation of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms for 8-point functions. The measured visibility of the 8-path interferometer is about 97.5%. Potential applications of our setup to quantum communication or cryptographic protocols using several qubits are discussed.
In this paper, we report on experimental implementation of a linear-optical quantum router. Our device allows single-photon polarization-encoded qubits to be routed coherently into two spatial output modes depending on the state of two identical control qubits. The polarization qubit state of the routed photon is maintained during the routing operation. The success probability of our scheme can be increased up to 25% making it the most efficient linear-optical quantum router known to this date.
Macroscopic Schrödinger-cat states of nonequilibrium electrons induced by cat-state optical driving and projective measurements on the light field
研究通过投影测量量子光场，在非平衡多电子系统中诱导并恢复宏观猫态，揭示了光场测量对物质量子态的控制作用。
We propose a scheme to implement a single-mode quantum filter, which selectively eliminates the one-photon state in a quantum state $α|0>+β|1>+γ|2>$. The vacuum state and the two photon state are transmitted without any change. This scheme requires single-photon sources, linear optical elements and photon detectors. Furthermore we demonstrate, how this filter can be used to realize a two-qubit projective measurement and to generate multi-photon polarization entangled states.
We design optimal interferometric schemes for implementation of two-qubit linear optical quantum filters diagonal in the computational basis. The filtering is realized by interference of the two photons encoding the qubits in a multiport linear optical interferometer, followed by conditioning on presence of a single photon in each output port of the filter. The filter thus operates in the coincidence basis, similarly to many linear optical unitary quantum gates. Implementation of the filter with linear optics may require an additional overhead in terms of reduced overall success probability of…
Projective squeezing for translation symmetric bosonic codes
针对平移对称玻色编码计算精度受压缩水平限制的问题，提出投影压缩方法，推导压缩水平与投影概率的解析关系，给出具体实现方案并通过数值验证其可缓解光子损耗影响。
Unsharp POVM measurements allow a variety of measurement applications which minimally disrupt the state of the quantum system. Experimental schemes are proposed for implementing unsharp measurements on the qubit levels of a trapped ion. The schemes rely on introducing weak entanglement between the state of a target ion, and that of an auxiliary ion, using standard ion trap quantum logic operations, and then realizing an unsharp measurement through projective measurement on the auxiliary atom. We analyze common sources of error and their effect on different applications of unsharp measurements.
The 'disentanglement eraser' or 'entanglement restorer' scheme allows retrieving entanglement by erasing the information about the formation of a classical (or separable) state. It suggests an analogy between the pairs of properties: entangled-separable and wave-particle, the latter as described in the 'quantum eraser'. The scheme illustrates the physical importance of information in quantum systems, and it is also useful as a building block for quantum computation. An optical setup for its simple implementation using three-photon decay in a centro-symmetrical crystal is proposed.
We present a new optical scheme enabling the implementation of highly stable and configurable non-Markovian dynamics. Here one photon qubit can circulate in a multipass bulk geometry consisting of two concatenated Sagnac interferometers to simulate the so called collisional model, where the system interacts at discrete times with a vacuum environment. We show the optical features of our apparatus and three different implementations of it, replicating a pure Markovian scenario and two non-Markovian ones, where we quantify the information backflow by tracking the evolution of the initial entangl…
We report on the first experimental realization of optimal linear-optical controlled phase gates for arbitrary phases. The realized scheme is entirely flexible in that the phase shift can be tuned to any given value. All such controlled phase gates are optimal in the sense that they operate at the maximum possible success probabilities that are achievable within the framework of any postselected linear-optical implementation. The quantum gate is implemented using bulk optical elements and polarization encoding of qubit states. We have experimentally explored the remarkable observation that the…
Discrimination of unitary operations is a fundamental quantum information processing task. Assisted with linear optical elements, we experimentally demonstrate perfect discrimination between single-bit unitary operations using two methods--sequential scheme and parallel scheme. The complexity and resource consumed in these two schemes are analyzed and compared.
We propose an experimental setup for the implementation of weak measurements in the context of the gedankenexperiment known as Hardy's Paradox. As Aharonov et al. showed, these weak values form a language with which the paradox can be resolved. Our analysis shows that this language is indeed consistent and experimentally testable. It also reveals exactly how a combination of weak values can give rise to an apparently paradoxical result.
We consider transmission of an (unknown) quantum state between two distant atoms via photons. Based on a quantum-optical realistic model, we define a noisy quantum channel which includes systematic errors as well as errors due to coupling to the environment. We present a protocol that allows one to accomplish ideal transmission by repeating the transfer operation as many times as needed.
The continuous-variable coherent (conat) channel is a useful resource for coherent communication, producing coherent teleportation and coherent superdense coding. We extend the conat channel to multiparty conditions by proposing definitions about multiparty position-quadrature conat channel and multiparty momentum-quadrature conat channel. We additionally provide two methods to implement this channel using linear optics. One method is the multiparty version of coherent communication assisted by entanglement and classical communication (CCAECC). The other is multiparty coherent superdense codin…
Positive operator valued measurements (POVMs) play an important role in efficient quantum communication and computation. While optical systems are one of the strongest candidates for long distance quantum communication and information processing, efficient methods to implement POVMs in these systems are scarce. Here we propose an all-optical scheme to implement an arbitrary POVM using linear optical components on m-dimensional Hilbert space of internal degrees of freedom. Linear optical nature of the proposed scheme makes it efficient and robust. We show how the scheme can be applied for state…
In a recent paper Bennett et al.[Phys. Rev.A 59, 1070 (1999)] have shown the existence of a basis of product states of a bipartite system with manifest non-local properties. In particular these states cannot be completely discriminated by means of bilocal measurements. In this paper we propose an optical realization of these states and we will show that they cannot be completely discriminate by means of a global measurement using only optical linear elements, conditional transformation and auxiliary photons.
Optimal quantum machines can be implemented by linear projective operations. In the present work a general qubit symmetrization theory is presented by investigating the close links to the qubit purification process and to the programmable teleportation of any generic optimal anti-unitary map. In addition, the contextual realization of the N ->M cloning map and of the teleportation of the N->(M-N) universal NOT gate is analyzed by a novel and very general angular momentum theory. An extended set of experimental realizations by state symmetrization linear optical procedures is reported. These in…
We revisit the problem of finding the Naimark extension of a probability operator-valued measure (POVM), i.e. its implementation as a projective measurement in a larger Hilbert space. In particular, we suggest an iterative method to build the projective measurement from the sole requirements of orthogonality and positivity. Our method improves existing ones, as it may be employed also to extend POVMs containing elements with rank larger than one. It is also more effective in terms of computational steps.
A scheme to encode arbitrarily long integer pairs on degenerate optical parametric oscillations multiplexed in time is proposed. The classical entanglement between the polarization directions and the phases of the oscillating pulses, regarded as two computational registers, furnishes the integer correlations within each pair. We show the major algorithmic steps, modular exponentiation and discrete Fourier transform, of Shor's quantum factoring algorithm can be executed in the registers as pulse interferences under the assistance of external logics. The factoring algorithm is thus rendered equi…
We present the experimental realization of optimal symmetric and asymmetric phase-covariant 1->2 cloning of qubit states using fiber optics. State of each qubit is encoded into a single photon which can propagate through two optical fibers. The operation of our device is based on one- and two-photon interference. We have demonstrated creation of two copies of any state of a qubit from the equator of the Bloch sphere. The measured fidelities of both copies are close to the theoretical values and they surpass the theoretical maximum obtainable with the universal cloner.
Classical optics can be used to efficiently implement certain quantum information processing tasks with a high degree of control, for example, one-dimensional quantum walks through the space of orbital angular momentum of light directed by its polarization. To explore the potential of quantum information processing with classical light, we here suggest a method to realize d-dimensional quantum walks with classical optics---an important step towards robust implementation of certain quantum algorithms. In this scheme, different degrees of freedom of light, such as frequency, orbital angular mome…
A recent experimental proposal by Ahnert and Payne [S.E. Ahnert and M.C. Payne, Phys. Rev. A 70, 042102 (2004)] outlines a method to measure the weak value predictions of Aharonov in Hardy's paradox. This proposal contains flaws such as the state preparation method and the procedure for carrying out the requisite weak measurements. We identify previously published solutions to some of the flaws.
Single-photon resolution (SPR) detectors can tell the difference between incoming wave packets of n and n+1 photons. Such devices are especially important for linear optical quantum computing with projective measurements. However, in this paper I show that it is impossible to construct a photodetector with single-photon resolution when we are restricted to single-photon sources, linear optical elements and projective measurements with standard (non-photon-number discriminating) photodetectors. These devices include SPR detectors that sometimes fail to distinguish one- and two-photon inputs, bu…
The comment by Lundeen et al. contains two criticisms of our proposal. While we agree that the state-preparation procedure could be replaced by a simpler setup as proposed by the authors of the comment, we do not agree with the authors on their second, and more important point regarding two-particle weak measurements. We believe this to be the result of a misunderstanding of our original paper.
We propose a simple implementation scheme of quantum delayed-choice experiment in linear optical system without initial entanglement resource. By choosing different detecting devices, one can selectively observe the photon's different behaviors after the photon has been passed the Mach-Zehnder interferometer. The scheme shows that the photon's wave behavior and particle behavior can be observed with a single experimental setup by postselection, that is, the photon can show the superposition behavior of wave and particle. Especially, we compare the wave-particle superposition behavior and the w…
We develop some calculation schemes to determine dynamics of a wide class of integrable quantum-optical models using their symmetry adapted reformulation in terms of polynomial Lie algebras $su_{pd}(2)$. These schemes, based on "diagonal" representations of model evolution operators (via diagonalizing Hamiltonians with the help of the $su_{pd}(2)$ defining relations), are implemented in the form adapted for numerical calculations. Their efficiency is demonstrated on the example of the second-harmonic-generation model.
Robust self-test of the maximally entangled state of two-qubits without assuming unitary observables
研究不假设酉可观测量的两量子比特最大纠缠态的稳健自测试问题，通过规避测量装置的扩张，对物理非投影算子进行正则化并得出解析稳健性界限。
We address the implementation of the positive operator-valued measure (POVM) describing the optimal M-outcomes discrimination of the polarization state of a single photon. Initially, the POVM elements are extended to projective operators by Naimark theorem, then the resulting projective measure is implemented by a Knill-Laflamme-Milburn scheme involving an optical network and photon counters. We find the analytical expression of the Naimark extension and the detection scheme that realise it for an arbitrary number of outcomes M = 2^N.
We experimentally demonstrate a single-qubit decohering quantum channel using linear optics. We implement the channel, whose special cases include both the amplitude-damping channel and the bit-flip channel, using a single, static optical setup. Following a recent theoretical result [M. Piani et al., Phys. Rev. A, 84, 032304 (2011)], we realize the channel in an optimal way, maximizing the probability of success, i.e., the probability for the photonic qubit to remain in its encoding. Using a two-photon entangled resource, we characterize the channel using ancilla-assisted process tomography an…
According to the Schrödinger equation, a closed quantum system evolves continuously in time. If it is subject to a measurement however, its state changes randomly and discontinuously, which is mathematically described by the projection postulate. But how long does it take for this discontinuous change to occur? Based on simple estimates, whose validity rests solely on the fact that all fundamental forces in nature are finite-ranged, we show that the implementation of a quantum measurement requires a minimum time. This time scales proportionally with the diameter of the quantum mechanical objec…
We show that the optical Kerr effect can be used to construct a quantum phase gate. It is well known from quantum nondemolition techniques that, as two photon field modes pass through a Kerr medium, the phase of each mode will be shifted, and the size of the phase shift will depend on the number of photons in both modes. We discuss the Hamiltonian responsible for this effect and show how this can produce an effective photon-photon interaction which corresponds to the quantum phase gate operating on two qubits each of which is represented by the elliptical polarization of one photon field. We d…
Implementation of photon partial distinguishability in a quantum optical circuit simulation
本文提出一种基于 Gram-Schmidt 正交归一化的模拟实现方法，通过扩展光子信道纳入波包自由度，在现有理想量子电路模拟器中表示光子部分可区分性。
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