A fundamental problem in Quantum Information Processing is the discrimination amongst a set of quantum states of a system. In this paper, we address this problem on an open quantum system described by a graph, whose evolution is defined by a Quantum Stochastic Walk. In particular, the structure of the graph mimics those of neural networks, with the quantum states to discriminate encoded on input nodes and with the discrimination obtained on the output nodes. We optimize the parameters of the network to obtain the highest probability of correct discrimination. Numerical simulations show that after a transient time the probability of correct decision approaches the theoretical optimal quantum limit. These results are confirmed analytically for small graphs. Finally, we analyze the robustness and reconfigurability of the network for different set of quantum states, and show that this architecture can pave the way to experimental realizations of our protocol as well as novel quantum generalizations of deep learning.
We demonstrate a sub-shot-noise-limit discrimination of on-off keyed coherent signals by an optimal displacement quantum receiver in which a superconducting transition edge sensor is installed. Use of a transition edge sensor and a fiber beam splitter realizes high total detection efficiency and high interference visibility of the receiver and the observed average error surpasses the shot-noise-limit in a wider range of the signal power. Our technique opens up a new technology for the sub-shot-noise-limit detection of coherent signals in optical communication channels.
We determine a fundamental upper bound on the performance of any adaptive protocol for discrimination or estimation of a channel which has an unknown parameter encoded in the state of its environment. Since our approach relies on the principle of data processing, the bound applies to a variety of discrimination measures, including quantum relative entropy, hypothesis testing relative entropy, Rényi relative entropy, fidelity, and quantum Fisher information. We apply the upper bound to thermal (amplifier) channels with a known transmissivity (gain) but unknown excess noise. In these cases, we f…
The so-called quasi-Bell entangled coherent states in a thermal environment are studied. In the analysis, we assume thermal noise affects only one of the two modes of each state. First the matrix representation of the density operators of the quasi-Bell entangled coherent states in a thermal environment is derived. Secondly we investigate the entanglement property of one of the quasi-Bell entangled coherent states with thermal noise. At that time a lower bound of the entanglement of formation for the state is computed. Thirdly the minimax discrimination problem for two cases of the binary set …
Inspired by the notion that environmental noise is in principle observable, whilst fundamental noise due to spontaneous localisation would not be, we study the estimation of the diffusion parameter induced by wave function collapse models under continuous monitoring of the environment. We take into account finite measurement efficiencies and, in order to quantify the advantage granted by monitoring, we analyse the quantum Fisher information associated with such a diffusion parameter, identify optimal measurements in limiting cases, and assess the performance of such measurements in more realis…
Measurements approaching the ultimate quantum limits of sensitivity are central in quantum information processing, quantum metrology, and communication. Quantum measurements to discriminate multiple states at the single-photon level are essential for optimizing information transfer in low-power optical communications and quantum communications, and can enhance the capabilities of many quantum information protocols. Here, we theoretically investigate and experimentally demonstrate the discrimination of multiple coherent states of light with sensitivities surpassing the quantum noise limit (QNL)…
We propose an innovative strategy to discriminate between two coherent states affected by either uniform or gaussian phase noise. The strategy is based on a homodyne-like detection scheme with photon-number-resolving detectors in the regime of low-intensity local oscillator. The experimental implementation of the detection scheme involves two hybrid photodetectors, whose outputs are used in post processing to calculate the shot-by-shot photon-number difference. The performance of this strategy is quantified in terms of the error probability in discriminating the noisy coherent signals as a fun…
We propose a scheme by using the feed-forward control (FFC) to realize a better effect of discrimination of two nonorthogonal states after passing a noise channel based on the minimum- error (ME) discrimination. We show that the application of our scheme can highly improve the effect of discrimination compared with the ME discrimination without the FFC for any pair of nonorthogonal states and any degree of amplitude damping (AD). Especially, the effect of our optimal discrimination can reach that of the two initial nonorthogonal pure states in the presence of the noise channel in a determinist…
We present theory and experiment for the task of discriminating two nonorthogonal states, given multiple copies. We implement several local measurement schemes, on both pure states and states mixed by depolarizing noise. We find that schemes which are optimal (or have optimal scaling) without noise perform worse with noise than simply repeating the optimal single-copy measurement. Applying optimal control theory, we derive the globally optimal local measurement strategy, which outperforms all other local schemes, and experimentally implement it for various levels of noise.
Near-term quantum computers are noisy, and therefore must run algorithms with a low circuit depth and qubit count. Here we investigate how noise affects a quantum neural network (QNN) for state discrimination, applicable on near-term quantum devices as it fulfils the above criteria. We find that when simulating gradient calculation on a noisy device, a large number of parameters is disadvantageous. By introducing a new smaller circuit ansatz we overcome this limitation, and find that the QNN performs well at noise levels of current quantum hardware. We also show that networks trained at higher…
Noise-robust discrimination of incoherent point sources with spatial-mode demultiplexing
School of Sciences and Zhejiang Key Laboratory of Quantum State Control and Optical Field Manipulation, Hangzhou Dianzi University（杭州电子科技大学理学院与浙江省量子态调控与光场操纵重点实验室）
Multiple-copy state discrimination is a fundamental task in quantum information processing. If there are two, pure, non-orthogonal states then both local and collective schemes are known to reach the Helstrom bound, the maximum probability of successful discrimination allowed by quantum theory. For mixed states, it is known that only collective schemes can perform optimally, so it might be expected that these schemes are more resilient to preparation noise. We calculate the probability of success for two schemes, one local and one collective, in the regime of imperfect preparation fidelity. We…
The accurate and reliable characterization of quantum dynamical processes underlies efforts to validate quantum technologies, where discrimination between competing models of observed behaviors inform efforts to fabricate and operate qubit devices. We present a novel protocol for quantum channel discrimination that leverages advances in direct characterization of quantum dynamics (DCQD) codes. We demonstrate that DCQD codes enable selective process tomography to improve discrimination between entangling and correlated quantum dynamics. Numerical simulations show selective process tomography re…
We address extended systems interacting with classical fluctuating environments and analyze the use of quantum probes to discriminate local noise, described by independent fluctuating fields, from common noise, corresponding to the interaction with a common one. In particular, we consider a bipartite system made of two non interacting harmonic oscillators and assess discrimination strategies based on homodyne detection, comparing their performances with the ultimate bounds on the error probabilities of quantum-limited measurements. We analyze in details the use of Gaussian probes, with emphasi…
The growing field of nano nuclear magnetic resonance (nano-NMR) seeks to estimate spectra or discriminate between spectra of minuscule amounts of complex molecules. While this field holds great promise, nano-NMR experiments suffer from detrimental inherent noise. This strong noise masks to the weak signal and results in a very low signal-to-noise ratio. Moreover, the noise model is usually complex and unknown, which renders the data processing of the measurement results very complicated. Hence, spectra discrimination is hard to achieve and in particular, it is difficult to reach the optimal di…
We present a charge integration photon detector (CIPD) that enables the efficient measurement of photon number states at the telecom-fiber wavelengths with a quantum efficiency of 80% and a resolution less than 0.5 electrons at 1 Hz sampling. The CIPD consists of an InGaAs PIN photodiode and a GaAs JFET in a charge integration amplifier, which is cooled to 4.2 K to reduce thermal noise and leakage current. The charge integration amplifier exhibits a low noise level of 470 nV/Hz1/2. The dark count is as low as 500 electrons/hour.
We experimentally demonstrate a quantum receiver based on Kennedy scheme for discrimination between two phase-modulated weak coherent states. The receiver is assembled entirely from the standard fiber-optic elements and operates at the conventional telecom wavelength 1.55 microns. The local oscillator and the signal are transmitted through different optical fibers, and the displaced signal is measured with a high-efficiency superconducting nanowire single-photon detector. We show the discrimination error rate two times below the shot-noise limit.
"Quantum conversation" is a way in which two parties can communicate classical information with each other using entanglement as a shared resource. We present this scheme using a multipartite entangled state after describing its generation through appropriate circuit diagrams. We make use of a discrimination scheme which allows one to perform a measurement on the system without destroying its entanglement. We later prove that this scheme is secure in a noiseless and a lossless quantum channel.
We address binary phase-shift-keyed communication channels based on Gaussian states and prove that squeezing improves state discrimination at fixed energy of the channel, also in the presence of phase diffusion. We then assess performances of homodyne detection against the ultimate quantum limits to discrimination, and show that homodyning achieves optimality in large noise regime. Finally, we consider noise in the preparation of the seed signal (before phase encoding) and show that also in this case squeezing may improve state discrimination in realistic conditions.
Quantum discrimination and estimation are pivotal for many quantum technologies, and their performance depends on the optimal choice of probe state and measurement. Here we show that their performance can be further improved by suitably tailoring the pulses that make up the interferometer. Developing an optimal control framework and applying it to the discrimination and estimation of a magnetic field in the presence of noise, we find an increase in the overall achievable state distinguishability. Moreover, the maximum distinguishability can be stabilized for times that are more than an order o…
We study discrimination of m quantum measurements in the scenario when the unknown measurement with n outcomes can be used only once. We show that ancilla-assisted discrimination procedures provide a nontrivial advantage over simple (ancilla-free) schemes for perfect distinguishability and we prove that inevitably m <= n. We derive necessary and sufficient conditions of perfect distinguishability of general binary measurements. We show that the optimization of the discrimination of projective qubit measurements and their mixtures with white noise is equivalent to the discrimination of specific…
Many quantum mechanical experiments can be viewed as multi-round interactive protocols between known quantum circuits and an unknown quantum process. Fully quantum "coherent" access to the unknown process is known to provide an advantage in many discrimination tasks compared to when only incoherent access is permitted, but it is unclear if this advantage persists when the process is noisy. Here, we show that a quantum advantage can be maintained when distinguishing between two noisy single qubit rotation channels. Numerical and analytical calculations reveal a distinct transition between optim…
Boosting State Discrimination in Quantum Brownian Motion Channel via Memory-Induced Coherence Preservation
Federal University of Piauí（皮奥伊联邦大学）；Federal University of Paraná（巴拉那联邦大学）；Universidade Federal do ABC（ABC联邦大学）；Southern University of Science and Technology（南方科技大学）；University of Coimbra（科英布拉大学）
With the purpose to introduce a useful tool for researches concerning foundations of quantum mechanics and applications to quantum technologies, here we study three quantumness quantifiers for bipartite optical systems: one based on sub-shot-noise correlations, one related to antibunching and one springing from entanglement determination. The specific cases of parametric down conversion seeded by thermal, coherent and squeezed states are discussed in detail.
Some quantum measurements can not be performed simultaneously, i.e. they are incompatible. Here we show that every set of incompatible measurements provides an advantage over compatible ones in a suitably chosen quantum state discrimination task. This is proven by showing that the Robustness of Incompatibility, a quantifier of how much noise a set of measurements tolerates before becoming compatible, has an operational interpretation as the advantage in an optimally chosen discrimination task. We also show that if we take a resource-theory perspective of measurement incompatibility, then the g…
The discrimination of two nonorthogonal states is a fundamental element for secure and efficient communication. Quantum measurements of nonorthogonal coherent states can enhance information transfer beyond the limits of conventional technologies. We demonstrate a strategy for binary state discrimination based on optimized single-shot measurements with photon number resolving (PNR) detection with finite number resolution. This strategy enables a high degree of robustness to noise and imperfections while being scalable to high rates and in principle allows for surpassing the quantum noise limit …
In this work, we consider optimal state discrimination for a quantum system that interacts with an environment, i.e., states evolve under a quantum channel. We show the conditions on a quantum channel and an ensemble of states such that a measurement for optimal state discrimination is preserved. In particular, we show that when an ensemble of states with equal {\it a priori} probabilities is given, an optimal measurement can be preserved over any quantum channel by applying local operations and classical communication, that is, by manipulating the quantum states before and after the channel a…
Understanding the fundamental sensitivity limit of an optical sensor requires a full quantum mechanical description of the sensing task. In this work, we calculate the fundamental (quantum) limit for discriminating between pure laser light and thermal noise in a photon-starved regime. The Helstrom bound for discrimination error probability for single mode measurement is computed along with error probability bounds for direct detection, coherent homodyne detection and the Kennedy receiver. A generalized Kennedy (GK) receiver is shown to closely approach the Helstrom limit. We present an experim…
We introduce a way of quantifying how informative a quantum measurement is, starting from a resource-theoretic perspective. This quantifier, which we call the robustness of measurement, describes how much `noise' must be added to a measurement before it becomes completely uninformative. We show that this geometric quantifier has operational significance in terms of the advantage the measurement provides over guessing at random in an suitably chosen state discrimination game. We further show that it is the single-shot generalisation of the accessible information of a certain quantum-to-classica…
Dynamics of many-qubit systems, that may correspond to computational processing with quantum systems, can be efficiently and generally approximated by a sequence of two- and single-qubit gates. In practical applications, however, a quantum gate prepared as a unitary transformation may appear as a noisy channel and consequently may inhibit quantum advantages. In this work, we apply the scheme of channel discrimination to detect if a quantum gate that is actually realized is unitary or noisy. We show that a two-qubit unitary transformation and its noisy counterpart can be optimally discriminated…
Finding quantitative aspects of quantum phenomena which cannot be explained by any classical model has foundational importance for understanding the boundary between classical and quantum theory. It also has practical significance for identifying information processing tasks for which those phenomena provide a quantum advantage. Using the framework of generalized noncontextuality as our notion of classicality, we find one such nonclassical feature within the phenomenology of quantum minimum error state discrimination. Namely, we identify quantitative limits on the success probability for minim…
Photonic chip based time-bin entanglement has attracted significant attention because of its potential for quantum communication and computation. Useful time-bin entanglement systems must be able to generate, manipulate and analyze entangled photons on a photonic chip for stable, scalable and reconfigurable operation. Here we report the first time-bin entanglement photonic chip that integrates time-bin generation, wavelength demultiplexing and entanglement analysis. A two-photon interference fringe with an 88.4% visibility is measured (without subtracting any noise), indicating the high perfor…
Quantum metrology utilizes nonclassical resources, such as entanglement or squeezed light, to realize sensors whose performance exceeds that afforded by classical-state systems. Environmental loss and noise, however, easily destroy nonclassical resources, and thus nullify the performance advantages of most quantum-enhanced sensors. Quantum illumination (QI) is different. It is a robust entanglement-enhanced sensing scheme whose 6 dB performance advantage over a coherent-state sensor of the same average transmitted photon number survives the initial entanglement's eradication by loss and noise.…
We analyze the capability of discriminating the statistical nature of a thermal bath by exploiting the interaction with an additional environment. We first shows that, at difference with the standard scenario where the additional environment is not present, the modified evolution induced by the mere presence of the extra bath allows to improve the discrimination task. We then also consider the possibility of continuously monitoring the additional environment and we discuss in detail how to obtain improved performances in the discrimination by considering different kinds of interaction, i.e. di…
Entanglement is the quintessential quantum mechanical phenomenon understood to lie at the heart of future quantum technologies and the subject of fundamental scientific investigations. Mixture, resulting from noise, is often an unwanted result of interaction with an environment, but is also of fundamental interest, and is proposed to play a role in some biological processes. Here we report an integrated waveguide device that can generate and completely characterize pure two-photon states with any amount of entanglement and arbitrary single-photon states with any amount of mixture. The device c…
We demonstrate an optical receiver that achieves the quantum Chernoff bound for discriminating coherent states from thermal states in the multi-copy scenario. In contrast, we find that repeated use of the receiver approaching the Helstrom bound for single-copy measurement is sub-optimal in this multi-copy case. Furthermore, for a large class of multi-copy discrimination tasks between a pure and a mixed state, we prove that any Helstrom-bound achieving single-copy receiver is suboptimal by a factor of at least two in error-probability exponent compared to the multi-copy quantum Chernoff bound. …
The quantum discrimination of two non-coherent states draws much attention recently. In this letter, we first consider the quantum discrimination of two noiseless displaced number states. Then we derive the Fock representation of noisy displaced number states and address the problem of discriminating between two noisy displaced number states. We further prove that the optimal quantum discrimination of two noisy displaced number states can be achieved by the Kennedy receiver with threshold detection. Simulation results verify the theoretical derivations and show that the error probability of on…
The task of state discrimination for a set of mutually orthogonal pure states is trivial if one has access to the corresponding sharp (projection-valued) measurement, but what if we are restricted to an unsharp measurement? Given that any realistic measurement device will be subject to some noise, such a problem is worth considering. In this paper we consider minimum error state discrimination for mutually orthogonal states with a noisy measurement. We show that by considering repetitions of commutative Lüders measurements on the same system we are able to increase the probability of successfu…
We examine the results of the paper "Precision metrology using weak measurements", [Zhang, Datta, and Walmsley, arXiv:1310.5302] from a quantum state discrimination point of view. The Heisenberg scaling of the photon number for the precision of the interaction parameter between coherent light and a spin one-half particle (or pseudo-spin) has a simple interpretation in terms of the interaction rotating the quantum state to an orthogonal one. In order to achieve this scaling, the information must be extracted from the spin rather than from the coherent state of light, limiting the applications o…
The characterisation of Quantum Channel Discrimination (QCD) offers critical insight for future quantum technologies in quantum metrology, sensing and communications. The task of multi-channel discrimination creates a scenario in which the discrimination of multiple quantum channels can be equated to the idea of pattern recognition, highly relevant to the tasks of quantum reading, illumination and more. Whilst the optimal quantum strategy for many scenarios is an entangled idler-assisted protocol, the extension to a multi-hypothesis setting invites the exploration of discrimination strategies …
Devices that achieve nonreciprocal microwave transmission are ubiquitous in radar and radio-frequency communication systems, and commonly rely on magnetically biased ferrite materials. Such devices are also indispensable in the readout chains of superconducting quantum circuits as they protect sensitive quantum systems from the noise emitted by readout electronics. Since ferrite-based nonreciprocal devices are bulky, lossy, and require large magnetic fields, there has been significant interest in magnetic-field-free on-chip alternatives, such as those recently implemented using Josephson junct…
Exploring quantum phenomena beyond predictions of any classical model has fundamental importance to understand the boundary of classical and quantum descriptions of nature. As a typical property that a quantum system behaves distinctively from a classical counterpart, contextuality has been studied extensively and verified experimentally in systems composed of at least three levels (qutrit). Here we extend the scope of experimental test of contextuality to a minimal quantum system of only two states (qubit) by implementing the minimum error state discrimination on a single $^{171}$Yb$^+$ ion. …
We present a measurement protocol for discriminating between two different quantum states of a qubit with high fidelity. The protocol, called null value, is comprised of a projective measurement performed on the system with a small probability (also known as partial-collapse), followed by a tuned postselection. We report on an optical experimental implementation of the scheme. We show that our protocol leads to an amplified signal-to-noise ratio (as compared with a straightforward strong measurement) when discerning between the two quantum states.
