Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0704.0678 · Physical Review Letters

Efficient Generation of Large Number-Path Entanglement Using Only Linear Optics and Feed-Forward

Hugo V. Cable, Jonathan P. Dowling

Published Oct 18, 2007• 112 citations
arXivHTMLPDF

Abstract

We show how an idealized measurement procedure can condense photons from two modes into one and how, by feeding forward the results of the measurement, it is possible to generate efficiently superposition states commonly called N00N states. For the basic procedure sources of number states leak onto a beam splitter, and the output ports are monitored by photodetectors. We find that detecting a fixed fraction of the input at one output port suffices to direct the remainder to the same port, with high probability, however large the initial state. When instead photons are detected at both ports, macroscopic quantum superposition states are produced. We describe a linear-optical circuit for making the components of such a state orthogonal, and another to convert the output to a N00N state. Our approach scales exponentially better than existing proposals. Important applications include quantum imaging and metrology.

DOI
10.1103/physrevlett.99.163604

Related papers

Quantum optical interferometry via the mixing of coherent and photon-subtracted squeezed vacuum states of light

Richard J. Birrittella, Christopher C. Gerry

Hofmann and Ono [Phys. Rev. A76, 031806, (2007)] showed that the mixing of coherent light and single-mode squeezed light at a beam splitter gives good approximation results in a superposition of path-entangled photon number states (so-called N00N states), which can be used for phase-shift measurements by coincident detections at the output of an interferometer. They showed that N00N states for arbitrary photon number N could be produced by this procedure. Afek et al. [Science328, 879 (2010)] have implemented the Hofmann–Ono proposal in the laboratory. In this paper, we show that, for a given coherent state amplitude and a given squeezing parameter, the mixing of coherent states and photon-subtracted squeezed vacuum states at the first beam splitter of an interferometer leads to improved phase-shift measurement sensitivity when using the photon-number detection technique on one of the output beams of the device. We also show that the phase-shift measurements will also be super-resolved to a greater degree than is possible by mixing coherent and squeezed vacuum light of the same field parameters.

Journal of the Optical Society of America B•Feb 26, 2014•46 citations

Generation of macroscopic entangled states by means of x(2) nonlinearity without photon number resolving detection

Sergey A. Podoshvedov

We generalize the scheme of conditional preparation of x (2) macroscopic entangled states [S.A. Podoshvedov, JETP 129 (2006)]. The studied system consists of a system of coupled down converters with type-I phase matching pumped simultaneously by powerful optical fields in coherent states with one auxiliary photon in the superposition state of two input modes and a projective measurement system. The projective measurement system involves two Hadamard gates introduced to generated output modes followed by photodetectors. Identification of macroscopic entangled states is produced by registration of one photon. No photon number resolving detection is required for the studied scheme.

Journal of Experimental and Theoretical Physics Letters•Jun 1, 2006•0 citations

Scheme for generating a superposition of two- and four-photon maximally entangled states: Application to four-photon quantum photolithography

Christopher C. Gerry, Adil Benmoussa

We consider the action of a beam splitter with identical degenerate parametric down converters in each of the outputs and show that with single photons injected into each of the input ports, under certain conditions, a superposition of two- and four-photon maximally entangled states may be produced. Also we describe techniques for verifying the generation of the four-photon component of the state. We then discuss the application of such states to quantum photolithography assuming the existence of substrates capable of absorbing four photons. The two-photon component makes no contribution to the background.

Physical Review A•Sep 11, 2002•3 citations

High-NOON States by Mixing Quantum and Classical Light

I. Afek, O. Ambar, Yaron R. Silberberg

All and Nothing Entanglement, where a system can be in a superposition of a number of distinct states simultaneously, is a principle at the foundation of quantum mechanics (recall Schrödinger's cat, which is both dead and alive). It can also be used in many applications—imaging, communication, patterning, and metrology—with the effect being amplified by entangling larger systems. However, the systematic generation of “large” entangled systems is challenging. Afek et al. (p. 879 ; see the Perspective by Wildfeuer ) present a technique for generating many-photon entanglement in so-called NOON states, where there are two possible paths and N photons in one path and 0 in the other—the system being a superposition of “all and nothing” states. Mixing of entangled pairs with classical light at a beam splitter formed up to five photon-entangled states. The technique should be generally applicable to generate higher-order entangled states.

Science•May 13, 2010•621 citations

High--N00N State Generation: N00N State Output of Floquet Engineering

Yusef Maleki

Here, we review some quantum architectures designed for the engineering of the N00N state, a bipartite maximally entangled state crucial in quantum metrology applications. The fundamental concept underlying these schemes is the transformation of the initial state $|N\rangle \otimes |0\rangle$ to the N00N state $\frac{1}{\sqrt{2}} (|N\rangle \otimes|0\rangle +|0\rangle \otimes|N\rangle)$, where $|N\rangle$ and $|0\rangle$ are the Fock states with $N$ and $0$ excitations. We show that this state can be generated as a superposition of modes of quantum light, a combination of light and motion, or a superposition of two spin ensembles. The approach discussed here can generate mesoscopic and macroscopic entangled states, such as entangled coherent and squeezed states, as well. We show that a large class of maximally entangled states can be achieved in such an architecture. The extension of these state engineering methods to the multi-mode setting is also discussed.

arXiv:2401.00111•Dec 30, 2023•0 citations

Deterministic generation of N00N states using quantum dots in a cavity

Michael Niklaus Leuenberger, Mikhail Erementchouk

Compared to classical light sources, quantum sources based on N00N states consisting of $N$ photons achieve an $N$-times higher phase sensitivity, giving rise to super-resolution. N00N-state creation schemes based on linear optics and projective measurements only have a success probability $p$ that decreases exponentially with $N$, e.g. $p=4.4\times 10^{-14}$ for N=20. Feed-forward improves the scaling but $N$ fluctuates nondeterministically in each attempt. Schemes based on parametric down-conversion suffer from low production efficiency and low fidelity. A recent scheme based on atoms in a cavity combines deterministic time evolution, local unitary operations, and projective measurements. Here we propose a novel scheme based on the off-resonant interaction of $N$ photons with four semiconductor quantum dots (QDs) in a cavity to create N00N states deterministically with $p=1$ and fidelity above 90% for $N\lesssim 60$, without the need of any projective measurement or local unitary operation. Using our measure we obtain maximum $N$-photon entanglement $E_N=1$ for arbitrary $N$. Our method paves the way to the miniaturization of N00N-state sources to the nanoscale regime, with the possibility to integrate them on a computer chip based on semiconductor materials.

arXiv:1206.2538•Jun 12, 2012•0 citations
We show how an idealized measurement procedure can condense photons from two modes into one and how, by feeding forward the results of the measurement, it is possible to generate efficiently superposition states commonly called N00N states. For the basic procedure sources of number states leak onto a beam splitter, and the output ports are monitored by photodetectors. We find that detecting a fixed fraction of the input at one output port suffices to direct the remainder to the same port, with high probability, however large the initial state. When instead photons are detected at both ports, macroscopic quantum superposition states are produced. We describe a linear-optical circuit for making the components of such a state orthogonal, and another to convert the output to a N00N state. Our approach scales exponentially better than existing proposals. Important applications include quantum imaging and metrology.
Hofmann and Ono [Phys. Rev. A76, 031806, (2007)] showed that the mixing of coherent light and single-mode squeezed light at a beam splitter gives good approximation results in a superposition of path-entangled photon number states (so-called N00N states), which can be used for phase-shift measurements by coincident detections at the output of an interferometer. They showed that N00N states for arbitrary photon number N could be produced by this procedure. Afek et al. [Science328, 879 (2010)] have implemented the Hofmann–Ono proposal in the laboratory. In this paper, we show that, for a given coherent state amplitude and a given squeezing parameter, the mixing of coherent states and photon-subtracted squeezed vacuum states at the first beam splitter of an interferometer leads to improved phase-shift measurement sensitivity when using the photon-number detection technique on one of the output beams of the device. We also show that the phase-shift measurements will also be super-resolved to a greater degree than is possible by mixing coherent and squeezed vacuum light of the same field parameters.
We generalize the scheme of conditional preparation of x (2) macroscopic entangled states [S.A. Podoshvedov, JETP 129 (2006)]. The studied system consists of a system of coupled down converters with type-I phase matching pumped simultaneously by powerful optical fields in coherent states with one auxiliary photon in the superposition state of two input modes and a projective measurement system. The projective measurement system involves two Hadamard gates introduced to generated output modes followed by photodetectors. Identification of macroscopic entangled states is produced by registration of one photon. No photon number resolving detection is required for the studied scheme.
We consider the action of a beam splitter with identical degenerate parametric down converters in each of the outputs and show that with single photons injected into each of the input ports, under certain conditions, a superposition of two- and four-photon maximally entangled states may be produced. Also we describe techniques for verifying the generation of the four-photon component of the state. We then discuss the application of such states to quantum photolithography assuming the existence of substrates capable of absorbing four photons. The two-photon component makes no contribution to the background.
All and Nothing Entanglement, where a system can be in a superposition of a number of distinct states simultaneously, is a principle at the foundation of quantum mechanics (recall Schrödinger's cat, which is both dead and alive). It can also be used in many applications—imaging, communication, patterning, and metrology—with the effect being amplified by entangling larger systems. However, the systematic generation of “large” entangled systems is challenging. Afek et al. (p. 879 ; see the Perspective by Wildfeuer ) present a technique for generating many-photon entanglement in so-called NOON states, where there are two possible paths and N photons in one path and 0 in the other—the system being a superposition of “all and nothing” states. Mixing of entangled pairs with classical light at a beam splitter formed up to five photon-entangled states. The technique should be generally applicable to generate higher-order entangled states.
Here, we review some quantum architectures designed for the engineering of the N00N state, a bipartite maximally entangled state crucial in quantum metrology applications. The fundamental concept underlying these schemes is the transformation of the initial state ∣N⟩⊗∣0⟩|N\rangle \otimes |0\rangle∣N⟩⊗∣0⟩ to the N00N state 12(∣N⟩⊗∣0⟩+∣0⟩⊗∣N⟩)\frac{1}{\sqrt{2}} (|N\rangle \otimes|0\rangle +|0\rangle \otimes|N\rangle)2​1​(∣N⟩⊗∣0⟩+∣0⟩⊗∣N⟩), where ∣N⟩|N\rangle∣N⟩ and ∣0⟩|0\rangle∣0⟩ are the Fock states with NNN and 000 excitations. We show that this state can be generated as a superposition of modes of quantum light, a combination of light and motion, or a superposition of two spin ensembles. The approach discussed here can generate mesoscopic and macroscopic entangled states, such as entangled coherent and squeezed states, as well. We show that a large class of maximally entangled states can be achieved in such an architecture. The extension of these state engineering methods to the multi-mode setting is also discussed.
Compared to classical light sources, quantum sources based on N00N states consisting of NNN photons achieve an NNN-times higher phase sensitivity, giving rise to super-resolution. N00N-state creation schemes based on linear optics and projective measurements only have a success probability ppp that decreases exponentially with NNN, e.g. p=4.4×10−14p=4.4\times 10^{-14}p=4.4×10−14 for N=20. Feed-forward improves the scaling but NNN fluctuates nondeterministically in each attempt. Schemes based on parametric down-conversion suffer from low production efficiency and low fidelity. A recent scheme based on atoms in a cavity combines deterministic time evolution, local unitary operations, and projective measurements. Here we propose a novel scheme based on the off-resonant interaction of NNN photons with four semiconductor quantum dots (QDs) in a cavity to create N00N states deterministically with p=1p=1p=1 and fidelity above 90% for N≲60N\lesssim 60N≲60, without the need of any projective measurement or local unitary operation. Using our measure we obtain maximum NNN-photon entanglement EN=1E_N=1EN​=1 for arbitrary NNN. Our method paves the way to the miniaturization of N00N-state sources to the nanoscale regime, with the possibility to integrate them on a computer chip based on semiconductor materials.