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arXiv:1509.00088 · Physical Review A

Efficiency of an enhanced linear optical Bell-state measurement scheme with realistic imperfections

Stephen C. Wein, Khabat Heshami, Christopher A. Fuchs, Hari Krovi, Zachary Dutton, Wolfgang Tittel, Christoph Simon

Published Sep 29, 2016• 29 citations

Abstract

We compare the standard 50%-efficient single beam splitter method for Bell-state measurement to a proposed 75%-efficient auxiliary-photon-enhanced scheme [W. P. Grice, Phys. Rev. A 84, 042331 (2011)] in light of realistic conditions. The two schemes are compared with consideration for high input state photon loss, auxiliary state photon loss, detector inefficiency and coupling loss, detector dark counts, and non-number-resolving detectors. We also analyze the two schemes when multiplexed arrays of non-number-resolving detectors are used. Furthermore, we explore the possibility of utilizing spontaneous parametric down-conversion as the auxiliary photon pair source required by the enhanced scheme. In these different cases, we determine the bounds on the detector parameters at which the enhanced scheme becomes superior to the standard scheme and describe the impact of the different imperfections on measurement success rate and discrimination fidelity. This is done using a combination of numeric and analytic techniques. For many of the cases discussed, the size of the Hilbert space and the number of measurement outcomes can be very large, which makes direct numerical solutions computationally costly. To alleviate this problem, all of our numerical computations are performed using pure states. This requires tracking the loss modes until measurement and treating dark counts as variations on measurement outcomes rather than modifications to the state itself. In addition, we provide approximate analytic expressions that illustrate the effect of different imperfections on the Bell-state analyzer quality.

DOI: 10.1103/physreva.94.032332

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We analyse how imperfections in single-photon detectors impact the characterization of photon-pair sources. We perform exact calculations to reveal the effects of multi-pair emissions and of noisy, non-unit efficiency, nonphoton-number resolving detections on the Cauchy–Schwarz parameter, on the second-order auto-correlation and cross-correlation functions, and on the visibilities of both Hong–Ou–Mandel and Bell-like interferences. We consider sources producing either two-mode squeezed states or states with a Poissonian photon distribution. The proposed formulas are useful in practice to determine the impacts of multi-pair emissions and dark counts in standard tests used in quantum optics.

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We propose a scheme for efficient cluster state quantum computation by using imperfect polarization-entangled photon-pair sources, linear optical elements, and inefficient non-photon-number-resolving detectors. The efficiency threshold for loss tolerance in our scheme requires the product of source and detector efficiencies should be

>1/2

, the best known figure. This figure applies to uncorrelated loss. We further find that the loss threshold is unaffected by correlated loss in the photon pair source. Our approach sheds new light on efficient linear optical quantum computation with imperfect experimental conditions.

Quantum enhancements of precision in metrology can be compromised by system imperfections. These may be mitigated by appropriate optimization of the input state to render it robust, at the expense of making the state difficult to prepare. In this paper, we identify the major sources of imperfection of an optical sensor: input state preparation inefficiency, sensor losses, and detector inefficiency. The second of these has received much attention; we show that it is the least damaging to surpassing the standard quantum limit in a optical interferometric sensor. Further, we show that photonic states that can be prepared in the laboratory using feasible resources allow a measurement strategy using photon-number-resolving detectors that not only attain the Heisenberg limit for phase estimation in the absence of losses, but also deliver close to the maximum possible precision in realistic scenarios including losses and inefficiencies. In particular, we give bounds for the tradeoff between the three sources of imperfection that will allow true quantum-enhanced optical metrology

Rotation-symmetric cat (RS-cat) codes are a bosonic-code platform for quantum information processing, combining finite-energy realizability with robustness against photon loss through their discrete rotational symmetry. For applications in long-distance quantum communication and fusion-based quantum computation (FBQC), efficient Bell state measurement (BSM) is a key primitive. In this work, we consider a BSM protocol for RS-cat codes using only a half beam splitter (HBS) and photon-number-resolving detectors (PNRDs). By exploiting the characteristic photon-number structure induced by the discrete rotational symmetry of RS-cat codes, our protocol extracts both photon-number modulo and phase information for Bell-state discrimination. We show that, under ideal loss-free conditions, the proposed BSM protocol becomes deterministic for arbitrary symmetry order

N

for sufficiently large amplitudes

α

. We further numerically evaluate the success probability under photon loss and identify the loss regime in which higher-order RS-cat codes provide an advantage. Finally, we show that post-selection can enhance the success probability.

In the last decade Grice [Phys. Rev. A 84, 042331 (2011)] and Ewert and van Loock [Phys. Rev. Lett. 113, 140403 (2014)] found linear optical networks achieving near-unit efficiency unambiguous Bell state discrimination, when fed with increasingly complex ancillary states. However, except for the vacuum ancilla case [Appl. Phys. B 72, 67 (2001)], the optimality of these schemes is unknown. Here, the optimality of these networks is investigated through analytical and numerical means. We show an analytical upper bound to the success probability for interferometers that preserve the polarization of the input photons, saturated by both Grice's and Ewert--van Loock's strategies. Furthermore, such an upper bound links the complexity of their ancilla states with the scaling of their performance. We also show a computer-aided approach to the optimization of such measurement schemes for generic interferometers, by simulating an optical network supplied with various kinds of ancillary input states. We numerically confirm the optimality of known small schemes. We use both methods to investigate other ancilla states, some of them never studied before.