Realizable receivers for discriminating coherent and multicopy quantum states near the quantum limit

Nair, Ranjith; Guha, Saikat; Tan, Si-Hui

doi:10.1103/physreva.89.032318

Cited by 42 publications

(39 citation statements)

References 64 publications

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“…Bondurant generalized the Dolinar receiver for QPSK states 22 and found two nearoptimal strategies that surpass the SQL for QPSK, which, in the limit of high input powers, have error probabilities with the same exponential scaling as the Helstrom limit. In recent theoretical work, Izumi et al 23 and Nair et al 24 have studied discrimination strategies implementing adaptive measurements that also have the same exponential scaling of the error probability as the Helstrom limit for QPSK in the high-input-power limit and that can be generalized to larger numbers of input states 24 . However, there is no known optimal strategy for reaching the Helstrom limit for QPSK.…”

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confidence: 98%

Photon number resolution enables quantum receiver for realistic coherent optical communications

2014

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Quantum-enhanced measurements can provide information about the properties of a physical system with sensitivities beyond what is fundamentally possible with conventional technologies. However, this advantage can be achieved only if quantum measurement technologies are robust against losses and real-world imperfections, and can operate in regimes compatible with existing systems. Here, we demonstrate a quantum receiver for coherent communication, the performance of which not only surpasses the standard quantum limit, but does so for input powers extending to high mean photon numbers. This receiver uses adaptive measurements and photon number resolution to achieve high sensitivity and robustness against imperfections, and ultimately shows the greatest advantage over the standard quantum limit ever achieved by any quantum receiver at power levels compatible with state-of-the-art optical communication systems. Our demonstration shows that quantum measurements can provide real and practical advantages over conventional technologies for optical communications.M easurements based on the quantum properties of physical systems have revolutionized our understanding of information and have enabled many tasks that are not possible by any classical means. Measurements taking advantage of quantum resources have given birth to quantum communication 1,2 and quantum metrology 3,4 , which are crucial for many quantum technologies, including quantum computing 5,6 , with potential capabilities far beyond the limits of their classical counterparts. Quantum measurements for the discrimination of non-orthogonal coherent states, which cannot be perfectly discriminated due to their inherent quantum noise 7 , can enable discrimination below the standard quantum limit (SQL) 8-10 and approach the ultimate limit allowed by quantum mechanics. These measurements have great potential for improving communication technologies and many quantum information applications.Coherent states are excellent carriers of quantum and classical information due to their intrinsic resilience to loss and their highspectral-efficiency capabilities. Optical communications based on coherent states can now reach terabit-per-second transmission rates 11,12 . However, the growing need for even higher data transmission rates for communications, cloud computing and other virtualization applications 13 has motivated extensive research into novel multilevel modulation and multiplexing communication formats 14,15 , and low-noise signal amplification 16,17 and processing 18 protocols to further improve spectral efficiency and overall information exchange fidelity. State-of-the-art optical coherent receivers for non-orthogonal coherent states employ direct coherent homodyne or heterodyne detection and are now approaching their ultimate sensitivity limit 19,20 , the SQL. However, quantum mechanics allows for a much lower error bound for non-orthogonal state discrimination-the Helstrom bound 7 . For example, the SQL is about 10 6 times higher than the error rate given by the He...

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confidence: 98%

Photon number resolution enables quantum receiver for realistic coherent optical communications

2014

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“…Adding a feedforward (FF) mechanism yields the FF-SFG receiver, whose error probability achieves the Helstrom bound [33]. The FF-SFG receiver is potentially promising for other quantum-enhanced sensing scenarios, such as phase estimation, and it enlarges the toolbox for quantum-state discrimination [34][35][36][37][38][39][40][41][42][43][44][45][46][47]. In particular, it is the first architecture-short of a quantum computer-for optimum discrimination of multimode Gaussian mixed states, a major step beyond the optimum discrimination of singlemode pure states [48][49][50][51].…”

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Optimum Mixed-State Discrimination for Noisy Entanglement-Enhanced Sensing

2017

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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. Unfortunately, an implementation of the optimum quantum receiver that would reap QI's full performance advantage has remained elusive, owing to its having to deal with a huge number of very noisy optical modes. We show how sum-frequency generation (SFG) can be fruitfully applied to optimum multimode Gaussian-mixedstate discrimination. Applied to QI, our analysis and numerical evaluations demonstrate that our SFG receiver saturates QI's quantum Chernoff bound. Moreover, augmenting our SFG receiver with a feedforward (FF) mechanism pushes its performance to the Helstrom bound in the limit of low signal brightness. The FF-SFG receiver, thus, opens the door to optimum quantum-enhanced imaging, radar detection, state and channel tomography, and communication in practical Gaussian-state situations. DOI: 10.1103/PhysRevLett.118.040801 Introduction.-Entanglement is essential for deviceindependent quantum cryptography [1], quantum computing [2], and quantum-enhanced metrology [3]. It has also been employed in frequency and phase estimation to beat their standard quantum limits on measurement precision [4][5][6][7][8][9][10]. Furthermore, entanglement has applications across diverse research areas, including dynamic biological measurement [11], delicate material probing [12], gravitational wave detection [13], and quantum lithography [14]. Entanglement, however, is fragile; it is easily destroyed by quantum decoherence arising from environmental loss and noise. Consequently, the entanglement-enabled performance advantages of most quantum-enhanced sensing schemes quickly dissipate with increasing quantum decoherence, challenging their merits for practical situations.Quantum illumination (QI) is an entanglement-enhanced paradigm for target detection that thrives on entanglementbreaking loss and noise [15][16][17][18][19][20][21][22]. Its optimum quantum receiver enjoys a 6 dB advantage in error-probability exponent over optimum classical sensing using the same transmitted photon number. Remarkably, QI's advantage occurs despite the initial entanglement being completely destroyed.To date, the only in-principle realization of QI's optimum quantum receiver requires a Schur transform on a quantum computer [23], so that its physical implementation is unlikely to occur in the near future. At present, the best known suboptimum QI receivers [20,21]-one of which, the optical parametric amplifier (OPA) receiver, has been

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“…[18] for a somewhat broader overview. Here, we mention some developments of particular relevance to this paper.…”

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A realizable receiver for discriminating arbitrary coherent states near the quantum limit

Nair

Guha

Tan

2013

2013 IEEE International Symposium on Information Theory

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Discriminating coherent states of light is an important instance of quantum state discrimination that is central to all applications of laser light. We obtain the ultimate quantum limit on the error probability exponent for discriminating among any M multimode coherent-state signals via the recently developed theory of the quantum Chernoff exponent in M -ary multi-copy state discrimination. A receiver called the Sequential Waveform Nulling (SWN) receiver is proposed for discriminating an arbitrary coherentstate ensemble using only auxiliary coherent-state fields, beam splitters, and non-number-resolving single photon detectors. An explicit error probability analysis of the SWN receiver is used to show that it achieves the quantum limit on the error probability exponent, which is shown to be a factor of four greater than the error probability exponent of an ideal heterodyne-detection receiver on the same ensemble. Apart from being of fundamental interest, these results are relevant to communication, sensing, imaging, and quantum information processing systems that use laser light.The task of optimally discriminating between multiple nonorthogonal quantum states by making appropriate quantum measurements [1]-[4] is a fundamental primitive underlying many quantum information processing tasks, including communication, sensing, and metrology. The paradigmatic problem of the Bayesian formulation of quantum detection theory [1] is to determine the quantum measurement, specified by a positive operator-valued measure (POVM) [2], that minimizes the average error probability in discriminating a given ensemble of states. The mathematical solution to the problem is known in terms of necessary and sufficient conditions that the optimal POVM must satisfy [5], [6], although for discriminating between more than two states, the explicit solution of these conditions has been obtained only in very specific cases -see, e.g., refs.[4], [7] and references therein.In view of the difficulty of obtaining the optimal quantum measurement in M -ary quantum detection, it is of great interest to obtain bounds on the optimal error probability. Such bounds are of basic importance in quantum information theory [2]. From a practical perspective, it is also important to bound the performance of concrete measurements whose physical realization is known. In this work, we develop both these approaches for the discrimination of arbitrary ensembles of coherent states of light [8]. Coherent states of light and their random mixtures are the most ubiquitous quantum states of light and their discrimination is central to optical communication [9], [10] and sensing with laser light, which is in a coherent state to an excellent approximation. For optical systems, the natural resource measure is the average number of photons in a given ensemble, i.e., the average energy. In the particular cases of coherent-state ensembles that have been studied, the optimal error probability of discriminating a given ensemble of coherent states decreases exponentially with the ...

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Realizable receivers for discriminating coherent and multicopy quantum states near the quantum limit

Cited by 42 publications

References 64 publications

Photon number resolution enables quantum receiver for realistic coherent optical communications

Photon number resolution enables quantum receiver for realistic coherent optical communications

Optimum Mixed-State Discrimination for Noisy Entanglement-Enhanced Sensing

A realizable receiver for discriminating arbitrary coherent states near the quantum limit

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