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Physical Review A

Toward real maximally path-entangled N -photon-state sources

Milena D’Angelo, Augusto Garuccio, Vincenzo Tamma

Published Jun 17, 2008• 17 citations
Publisher

Abstract

Path-entangled $N$-photon systems described by NOON states are the main ingredient of many quantum information and quantum imaging protocols. Our analysis aims to lead the way toward the implementation of both NOON-state sources and their applications. To this end, we study the functionality of ``real'' NOON-state sources by quantifying the effect real experimental apparatuses have on the actual generation of the desired NOON state. In particular, since the conditional generation of NOON states strongly relies on photon counters, we evaluate the dependence of both the reliability and the signal-to-noise ratio of ``real'' NOON-state sources on detection losses. We find a surprising result: NOON-state sources relying on nondetection are much more reliable than NOON-state sources relying on single-photon detection. Also the comparison of the resources required to implement these two protocols comes out to be in favor of NOON-state sources based on nondetection. A scheme to improve the performances of ``real'' NOON-state sources based on single-photon detection is also proposed and analyzed.

DOI
10.1103/physreva.77.063826

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Path-entangled NNN-photon systems described by NOON states are the main ingredient of many quantum information and quantum imaging protocols. Our analysis aims to lead the way toward the implementation of both NOON-state sources and their applications. To this end, we study the functionality of real'' NOON-state sources by quantifying the effect real experimental apparatuses have on the actual generation of the desired NOON state. In particular, since the conditional generation of NOON states strongly relies on photon counters, we evaluate the dependence of both the reliability and the signal-to-noise ratio of real'' NOON-state sources on detection losses. We find a surprising result: NOON-state sources relying on nondetection are much more reliable than NOON-state sources relying on single-photon detection. Also the comparison of the resources required to implement these two protocols comes out to be in favor of NOON-state sources based on nondetection. A scheme to improve the performances of ``real'' NOON-state sources based on single-photon detection is also proposed and analyzed.
Path-entangled N-photon systems described by NOON states are the main ingredient of many quantum information and quantum imaging protocols. Our analysis aims to lead the way toward the implementation of both NOON-state sources and their applications. To this end, we study the functionality of "real" NOON-state sources by quantifying the effect real experimental apparatuses have on the actual generation of the desired NOON state. In particular, since the conditional generation of NOON states strongly relies on photon counters, we evaluate the dependence of both the reliability and the signal-to-noise ratio of "real" NOON-state sources on detection losses. We find a surprising result: NOON-state sources relying on nondetection are much more reliable than NOON-state sources relying on single-photon detection. Also the comparison of the resources required to implement these two protocols comes out to be in favor of NOON-state sources based on nondetection. A scheme to improve the performances of "real" NOON-state sources based on single-photon detection is also proposed and analyzed.
The so called NOON states are the main ingredient of many quantum optic schemes. The reliability of NOON-state production protocols thus plays an important role in view of practical applications. In realistic situations, the reliability of NOON-state sources strongly depends on the non-unitary photodetection efficiency of the single photon detectors involved in the protocol. We discuss and compare the reliability of NOON-state schemes based on both single-photon detection and non detection. Our result may be of great interest for practical implementation of NOON-state schemes.
Maximal multi-photon entangled states, known as NOON states, play an essential role in quantum metrology. With the number of photons growing, NOON states are becoming increasingly powerful and advantageous for obtaining supersensitive and super-resolved measurements. In this paper, we propose a universal scheme for generating three- and four-photon path-entangled NOON states on a reconfigurable photonic chip via photons subtracted from pairs and detected by heralding counters. Our method is postselection free, enabling phase supersensitive measurements and sensing at the Heisenberg limit. Our NOON-state generator allows for integration of quantum light sources as well as practical and portable precision phase-related measurements.
In this paper, we propose two protocols for generating super-resolving single-photon (SRSP) number-path-entangled states from general maximally number-path-entangled NOON states. It is our purpose to show that, contrary to popular belief, a field in a single-photon state can carry multifold phase information. We also show that both protocols generate the desired state with different probabilities depending on the type of detectors being used. Such SRSP number-path-entangled states preserve high resolving power but lack the requirement of a multiphoton absorbing resist, which may serve as a proof-of-principle prototype for quantum lithography in the future.
We introduce schemes for linear-optical quantum state generation. A quantum state generator is a device that prepares a desired quantum state using product inputs from photon sources, linear-optical networks, and postselection using photon counters. We show that this device can be concisely described in terms of polynomial equations and unitary constraints. We illustrate the power of this language by applying the Gr\"obner-basis technique along with the notion of vacuum extensions to solve the problem of how to construct a quantum state generator analytically for any desired state, and use methods of convex optimization to identify bounds to success probabilities. In particular, we disprove a conjecture concerning the preparation of the maximally path-entangled $\ensuremath{\mid}n,0⟩+\ensuremath{\mid}0,n⟩$ (NOON) state by providing a counterexample using these methods, and we derive a new upper bound on the resources required for NOON-state generation.
Entangled states of photons form the foundation of quantum communication, computation, and metrology. Yet their generation remains fundamentally constrained: in the absence of intrinsic photon-photon interactions, the generation of such states is inherently probabilistic rather than deterministic. The prevalent technique of post-selection verifies the creation of an entangled state by detecting and thus destroying it. Heralding offers a solution in which measuring ancillary photons in auxiliary modes signals the state generation without the need to measure it. Here, we introduce and experimentally demonstrate a scheme to generate a three-mode two-photon NOON state, where the detection of a single photon in one heralding mode signifies the presence of the state in three target modes. We validate the generated state by estimating a fidelity of 0.823 +/- 0.018 with respect to an ideal three-mode NOON state and certifying genuine multipartite entanglement. By virtue of the high success probability and small resource overhead of our scheme, our work provides a theoretical and experimental stepping stone for entangled multi-mode state generation, which is realizable with current technology. These multi-mode entangled states represent a key direction for linear optical quantum information that is complementary to multi-qubit state encoding.