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

International Journal of Quantum Information

EXPLORING A NEW POST-SELECTION CONDITION FOR EFFICIENT LINEAR OPTICS COMPUTATION

Ruben Coen-Cagli, Paolo Aniello, Nicola Cesario, Francesco Foncellino

Published Dec 1, 2005• 1 citation
Publisher

Abstract

Recently, it has been shown that fundamental gates for theoretically efficient quantum information processing can be realized by using single photon sources, linear optics and photon counters. One of these fundamental gates is the NS-gate, that is, the one-mode non-linear sign shift. In this work, firstly, we prove by an elementary and rigorous proof that the upper bound of success probability of NS-gates with only one helper photon and an undefined number of ancillary modes is bounded by 0.25. Secondly, we explore the upper bound of the success probability of the NS-gate with a new post-selection measurement. The idea behind this new post-selection measurement is to condition the success of NS-gate transformation to the observation of only one helper photon in whichever of the output modes.

DOI
10.1142/s021974990500147x

Related papers

Exploring a New Post-Selection Condition for Efficient Linear Optics Quantum Computation

R. Coen Cagli, Paolo Aniello, Nicola Cesario +1 more

Recently, it was shown that fundamental gates for theoretically efficient quantum information processing can be realized by using single photon sources, linear optics and quantum counters. One of these fundamental gates is the NS-gate, that is, the one-mode non-linear sign shift. In this work, firstly, we prove by a new rigorous proof that the upper bound of success probability of NS-gates with only one helper photon and an undefined number of ancillary modes is bounded by 0.25. Secondly, we explore the upper bound of success probability of NS-gate with a new post-selection measurement. The idea behind this new post-selection measurement is to condition the success of NS-gate transformation to the observation of only one helper photon in whichever of the output modes.

arXiv:quant-ph/0412207•Dec 28, 2004•0 citations

Bounds on the probability of success of postselected nonlinear sign shifts implemented with linear optics

Emanuel H. Knill

The fundamental gates of linear optics quantum computation are realized by using single photons sources, linear optics, and photon counters. Success of these gates is conditioned on the pattern of photons detected without using feedback. Here it is shown that the maximum probability of success of these gates is typically strictly less than 1. For the one-mode nonlinear sign shift, the probability of success is bounded by 1/2. For the conditional sign shift of two modes, this probability is bounded by 3/4. These bounds are still substantially larger than the highest probabilities shown to be achievable so far, which are 1/4 and 2/27, respectively.

arXiv:quant-ph/0307015•Physical Review A•Dec 18, 2003•58 citations

Upper Bounds on Success Probabilities in Linear Optics

Stefan Scheel

We shortly review the basic ideas of generating nonlinear operators with single‐photon sources, linear optical elements, and appropriate measurements of auxiliary modes. This theory allows for an algorithmic construction of useful single‐mode and multi‐mode quantum gates necessary for all‐optical quantum information processing. From this amplitude‐operator point of view all known schemes that realize the nonlinear sign shift gate can be generated, and generalizations to some multi‐mode gates are easily obtained.We will use these ideas of measurement‐induced nonlinearities to develop an abstract way of defining linear‐optics networks. That allows us to treat the problem of maximizing the success probability of generating these conditional quantum gates in a semi‐analytical way. In particular, we show that for a wide class of auxiliary states the success probability of generating a nonlinear sign shift gate does not exceed 1/4 which is the strongest bound to date. Particularly interesting is the observation that the Hilbert space dimension of the ancilla state can be kept to a minimum. We generalize the theory to show that the nonlinear sign shift on single‐mode states with up to N photons can be performed with a success probability that scales as 1/N2.

AIP conference proceedings•Jan 1, 2004•3 citations

Quantum gates using linear optics and postselection

E. Knill

Recently it was realized that linear optics and photodetectors with feedback can be used for theoretically efficient quantum information processing. The first of three steps toward efficient linear optics quantum computation is to design a simple postselected gate that implements a nonlinear phase shift on one mode. Here a computational strategy is given for finding postselected gates for bosonic qubits with helper photons. A more efficient conditional sign flip gate is obtained. What is the maximum efficiency for such gates? This question is posed and it is shown that the probability of success cannot be 1.

arXiv:quant-ph/0110144•Physical Review A•Nov 14, 2002•113 citations

Optimizing Linear Optics Quantum Gates

Jens Eisert

In this Letter, the problem of finding optimal success probabilities of linear optics quantum gates is linked to the theory of convex optimization. It is shown that by exploiting this link, upper bounds for the success probability of networks realizing single-mode gates can be derived, which hold in generality for postselected networks of arbitrary size, any number of auxiliary modes, and arbitrary photon numbers. As a corollary, the previously formulated conjecture is proven that the optimal success probability of a nonlinear sign shift without feedforward is 1/4, a gate playing the central role in the scheme of Knill-Laflamme-Milburn for quantum computation. The concept of Lagrange duality is shown to be applicable to provide rigorous proofs for such bounds, although the original problem is a difficult nonconvex problem in infinitely many objective variables. The versatility of this approach is demonstrated.

arXiv:quant-ph/0409156•Physical Review Letters•Jul 22, 2005•55 citations

Linear optical fan-out gates using fewer ancillary single photons with enhanced success probability

Wen-Qiang Liu, Hai-Rui Wei

Photonic quantum gates are fundamental building blocks for a wide range of optical quantum information processing tasks. We propose an efficient linear-optical scheme for implementing a post-selected three-qubit fan-out gate (also known as a controlled-NOT-NOT gate) using only two ancillary single photons and linear optical elements. The scheme can be generalized to an $n$-qubit fan-out gate, requiring $(n-1)$ ancillary single photons and $(3n-3)$ polarizing beam splitters (PBSs), with a success probability of $\left(\frac{1}{4}\right)^{n-1}$. Compared to the standard gate decomposition approach, which requires $(2n-2)$ ancillary single photons, $(5n-5)$ PBSs, and yields a success probability of $\left(\frac{1}{8}\right)^{n-1}$. Our scheme significantly reduces the resource overhead and improves the success probability. We further evaluate the gate performance and demonstrate improved robustness compared to gate decomposition-based methods.

quant-pharXiv:2608.15608•Physical Review Applied•Aug 18, 2026•0 citations
Recently, it has been shown that fundamental gates for theoretically efficient quantum information processing can be realized by using single photon sources, linear optics and photon counters. One of these fundamental gates is the NS-gate, that is, the one-mode non-linear sign shift. In this work, firstly, we prove by an elementary and rigorous proof that the upper bound of success probability of NS-gates with only one helper photon and an undefined number of ancillary modes is bounded by 0.25. Secondly, we explore the upper bound of the success probability of the NS-gate with a new post-selection measurement. The idea behind this new post-selection measurement is to condition the success of NS-gate transformation to the observation of only one helper photon in whichever of the output modes.
Recently, it was shown that fundamental gates for theoretically efficient quantum information processing can be realized by using single photon sources, linear optics and quantum counters. One of these fundamental gates is the NS-gate, that is, the one-mode non-linear sign shift. In this work, firstly, we prove by a new rigorous proof that the upper bound of success probability of NS-gates with only one helper photon and an undefined number of ancillary modes is bounded by 0.25. Secondly, we explore the upper bound of success probability of NS-gate with a new post-selection measurement. The idea behind this new post-selection measurement is to condition the success of NS-gate transformation to the observation of only one helper photon in whichever of the output modes.
The fundamental gates of linear optics quantum computation are realized by using single photons sources, linear optics, and photon counters. Success of these gates is conditioned on the pattern of photons detected without using feedback. Here it is shown that the maximum probability of success of these gates is typically strictly less than 1. For the one-mode nonlinear sign shift, the probability of success is bounded by 1/2. For the conditional sign shift of two modes, this probability is bounded by 3/4. These bounds are still substantially larger than the highest probabilities shown to be achievable so far, which are 1/4 and 2/27, respectively.
We shortly review the basic ideas of generating nonlinear operators with single‐photon sources, linear optical elements, and appropriate measurements of auxiliary modes. This theory allows for an algorithmic construction of useful single‐mode and multi‐mode quantum gates necessary for all‐optical quantum information processing. From this amplitude‐operator point of view all known schemes that realize the nonlinear sign shift gate can be generated, and generalizations to some multi‐mode gates are easily obtained.We will use these ideas of measurement‐induced nonlinearities to develop an abstract way of defining linear‐optics networks. That allows us to treat the problem of maximizing the success probability of generating these conditional quantum gates in a semi‐analytical way. In particular, we show that for a wide class of auxiliary states the success probability of generating a nonlinear sign shift gate does not exceed 1/4 which is the strongest bound to date. Particularly interesting is the observation that the Hilbert space dimension of the ancilla state can be kept to a minimum. We generalize the theory to show that the nonlinear sign shift on single‐mode states with up to N photons can be performed with a success probability that scales as 1/N2.
Recently it was realized that linear optics and photodetectors with feedback can be used for theoretically efficient quantum information processing. The first of three steps toward efficient linear optics quantum computation is to design a simple postselected gate that implements a nonlinear phase shift on one mode. Here a computational strategy is given for finding postselected gates for bosonic qubits with helper photons. A more efficient conditional sign flip gate is obtained. What is the maximum efficiency for such gates? This question is posed and it is shown that the probability of success cannot be 1.
In this Letter, the problem of finding optimal success probabilities of linear optics quantum gates is linked to the theory of convex optimization. It is shown that by exploiting this link, upper bounds for the success probability of networks realizing single-mode gates can be derived, which hold in generality for postselected networks of arbitrary size, any number of auxiliary modes, and arbitrary photon numbers. As a corollary, the previously formulated conjecture is proven that the optimal success probability of a nonlinear sign shift without feedforward is 1/4, a gate playing the central role in the scheme of Knill-Laflamme-Milburn for quantum computation. The concept of Lagrange duality is shown to be applicable to provide rigorous proofs for such bounds, although the original problem is a difficult nonconvex problem in infinitely many objective variables. The versatility of this approach is demonstrated.
Photonic quantum gates are fundamental building blocks for a wide range of optical quantum information processing tasks. We propose an efficient linear-optical scheme for implementing a post-selected three-qubit fan-out gate (also known as a controlled-NOT-NOT gate) using only two ancillary single photons and linear optical elements. The scheme can be generalized to an nnn-qubit fan-out gate, requiring (n−1)(n-1)(n−1) ancillary single photons and (3n−3)(3n-3)(3n−3) polarizing beam splitters (PBSs), with a success probability of (14)n−1\left(\frac{1}{4}\right)^{n-1}(41​)n−1. Compared to the standard gate decomposition approach, which requires (2n−2)(2n-2)(2n−2) ancillary single photons, (5n−5)(5n-5)(5n−5) PBSs, and yields a success probability of (18)n−1\left(\frac{1}{8}\right)^{n-1}(81​)n−1. Our scheme significantly reduces the resource overhead and improves the success probability. We further evaluate the gate performance and demonstrate improved robustness compared to gate decomposition-based methods.