<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>M</mml:mi></mml:math>-ary-state phase-shift-keying discrimination below the homodyne limit

Becerra, F. E.; Fan, Jianping; Baumgartner, Gerald; Polyakov, Sergey V.; Goldhar, J.; Kosloski, J. T.; Migdall, Alan L.

doi:10.1103/physreva.84.062324

Cited by 70 publications

(91 citation statements)

References 12 publications

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“…However, it is one of the innermost consequences of the laws of quantum mechanics that nonorthogonal states cannot be discriminated with certainty. Optimal detection strategies were first investigated by Helstrom [20,21] and Holevo [22] and a lot of attention has since been devoted to the development of optimal and near-optimal receivers for binary coherent states [23][24][25][26][27][28][29][30][31][32] and for the discrimination of larger signal alphabets [33][34][35][36][37][38][39][40][41]. An overview over different receiver schemes is provided in Appendix B.…”

Section: Binary Coherent-state Cloningmentioning

confidence: 99%

Optimally cloned binary coherent states

et al. 2017

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Binary coherent state alphabets can be represented in a two-dimensional Hilbert space. We capitalize this formal connection between the otherwise distinct domains of qubits and continuous variable states to map binary phase-shift keyed coherent states onto the Bloch sphere and to derive their quantum-optimal clones. We analyze the Wigner function and the cumulants of the clones, and we conclude that optimal cloning of binary coherent states requires a nonlinearity above second order. We propose several practical and near-optimal cloning schemes and compare their cloning fidelity to the optimal cloner.

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Section: Binary Coherent-state Cloningmentioning

confidence: 99%

Optimally cloned binary coherent states

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“…1, in the Becerra et al experiment of ref. [39] (Our slices are referred to therein as "stages"). In their more recent experiment in ref.…”

Section: Sequential Waveform Nulling Receivermentioning

confidence: 99%

“…Bondurant proposed a receiver for the 4-ary Phase Shift Keying (QPSK) constellation that is exponentially optimal [38]. Recently, Becerra and collaborators proposed a feedforward receiver structure for M -ary PSK with arbitrary M and demonstrated that it closely approximates the Helstrom limit for 4-PSK, in a partially simulated experiment without real-time switching of the local oscillator (LO) field [39]. In work that is to appear [40], the Becerra group has implemented their receiver for 4-PSK with real-time switching of the LO and demonstrated that it beats the standard quantum limit, i.e., the performance of the ideal heterodyne receiver, even without adjusting for detection inefficiency and other realistic limitations for average input photon numbers in the range of N = 2 − 15.…”

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“…First, we use the quantum Chernoff exponent in M -ary multi-copy state discrimination [21] to obtain the maximum error probability exponent allowed of a coherent-state receiver by quantum mechanics. The Kennedy [24], Bondurant [38], and Becerra [39,40] receivers rely on a strategy of attempting to null, i.e., displace to the vacuum state, the input state by successively subtracting the fields corresponding to the possible hypotheses. We generalize this strategy to any multimode M -ary coherent-state set and propose a receiver for distinguishing between them, which we call the Sequential Waveform Nulling (SWN) receiver 1 .…”

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confidence: 99%

“…Our work here was originally motivated by the design of concrete receivers, i.e., physical realizations of POVM's, for discriminating coherent states of light -a subject with a long history that remains an active area of research [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. Coherent states of light [44] and their random mixtures are the most ubiquitous quantum states of light and their discrimination is central to optical communication [45,46] and sensing [4,47] with laser light, which is in a coherent state to an excellent approximation.…”

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

Nair

Guha²,

Tan

2014

Phys. Rev. A

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Coherent states of light, and methods for distinguishing between them, are 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 waveforms via the quantum Chernoff exponent in M -ary multi-copy state discrimination. A receiver, i.e., a concrete realization of a quantum measurement, called the Sequential Waveform Nulling (SWN) receiver, is proposed for discriminating an arbitrary coherent-state 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. We generalize the philosophy of the SWN receiver, which is itself adapted from some existing coherent-state receivers, and propose a receiver -the Sequential Testing (ST) receiver-for discriminating n copies of M pure quantum states from an arbitrary Hilbert space. The ST receiver is shown to achieve the quantum Chernoff exponent in the limit of a large number of copies, and is remarkable in requiring only local operations and classical communication (LOCC) to do so. In particular, it performs adaptive copy-by-copy binary projective measurements. Apart from being of fundamental interest, these results are relevant to communication, sensing, and imaging systems that use laser light and to photonic implementations of quantum information processing protocols in general.The task of optimally discriminating between unknown nonorthogonal quantum states by making appropriate quantum measurements [1-4] is a fundamental primitive underlying many quantum information processing tasks, including communication [1], sensing and metrology [4,5], and various cryptographic protocols [6]. The paradigmatic problem of the so-called quantum detection theory [1] is to determine the quantum measurement, specified by a mathematical object known as a positive operator-valued measure (POVM) [4,7], 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 [8], although for discriminating between more than two states, the explicit solution of these conditions has been obtained only in some specific cases [9]. Over the years, the scope of quantum detection theory has been broadened beyond the above framework to ones such as unambiguous state discrimination [10], maximum confidence discrimination [11], and to specific scenarios of interest such as multi-copy state discrimination using local operations and classical communication (LOCC) [12][13][14][15][16][17], using a quantum computer with limited entanglement [18], and in the asymptotic limit of a large number of copies ...

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