Photonic quantum systems are among the most promising architectures for quantum computers. It is well known that for dual-rail photons effective non-linearities and near-deterministic non-trivial two-qubit gates can be achieved via the measurement process and by introducing ancillary photons. While in principle this opens a legitimate path to scalable linear optical quantum computing, the technical requirements are still very challenging and thus other optical encodings are being actively investigated. One of the alternatives is to use single-rail encoded photons, where entangled states can be deterministically generated. Here we prove that even for such systems universal optical quantum computing using only passive optical elements such as beam splitters and phase shifters is not possible. This no-go theorem proves that photon bunching cannot be passively suppressed even when extra ancilla modes and arbitrary number of photons are used. Our result provides useful guidance for the design of optical quantum computers.Photonic quantum systems are among the most promising architectures for quantum computers. It is well known that for dual-rail photons effective non-linearities and near-deterministic non-trivial two-qubit gates can be achieved via the measurement process and by introducing ancillary photons. While in principle this opens a legitimate path to scalable linear optical quantum computing, the technical requirements are still very challenging and thus other optical encodings are being actively investigated. One of the alternatives is to use single-rail encoded photons, where entangled states can be deterministically generated. Here we prove that even for such systems universal optical quantum computing using only passive optical elements such as beam splitters and phase shifters is not possible. This no-go theorem proves that photon bunching cannot be passively suppressed even when extra ancilla modes and arbitrary number of photons are used. Our result provides useful guidance for the design of optical quantum computers.

arXiv:1107.4646Jul 23, 20110 citations

Generating entanglement with linear optics

Stasja Stanisic, Noah Linden, Ashley Montanaro +1 more

Entanglement is the basic building block of linear optical quantum computation, and as such understanding how to generate it in detail is of great importance for optical architectures. We prove that Bell states cannot be generated using only three photons in the dual-rail encoding, and give strong numerical evidence for the optimality of the existing four photon schemes. In a setup with a single photon in each input mode, we find a fundamental limit on the possible entanglement between a single mode Alice and arbitrary Bob. We investigate and compare other setups aimed at characterizing entanglement in settings more general than dual-rail encoding. The results draw attention to the trade-off between the entanglement a state has and the probability of postselecting that state, which can give surprising constant bounds on entanglement even with increasing numbers of photons.Entanglement is the basic building block of linear optical quantum computation, and as such understanding how to generate it in detail is of great importance for optical architectures. We prove that Bell states cannot be generated using only three photons in the dual-rail encoding, and give strong numerical evidence for the optimality of the existing four photon schemes. In a setup with a single photon in each input mode, we find a fundamental limit on the possible entanglement between a single mode Alice and arbitrary Bob. We investigate and compare other setups aimed at characterizing entanglement in settings more general than dual-rail encoding. The results draw attention to the trade-off between the entanglement a state has and the probability of postselecting that state, which can give surprising constant bounds on entanglement even with increasing numbers of photons.

arXiv:1702.05209Physical Review AOct 26, 201721 citations

Creation of Entangled Photonic States Using Linear Optics

Sara Bartolucci, Patrick M. Birchall, Mercedes Gimeno-Segovia +7 more

Using only linear optical elements, the creation of dual-rail photonic entangled states is inherently probabilistic. Known entanglement generation schemes have low success probabilities, requiring large-scale multiplexing to achieve near-deterministic operation of quantum information processing protocols. In this paper, we introduce multiple techniques and methods to generate photonic entangled states with high probability, which have the potential to reduce the footprint of Linear Optical Quantum Computing (LOQC) architectures drastically. Most notably, we are showing how to improve Bell state preparation from four single photons to up to p=2/3, boost Type-I fusion to 75% with a dual-rail Bell state ancilla and improve Type-II fusion beyond the limits of Bell state discrimination.Using only linear optical elements, the creation of dual-rail photonic entangled states is inherently probabilistic. Known entanglement generation schemes have low success probabilities, requiring large-scale multiplexing to achieve near-deterministic operation of quantum information processing protocols. In this paper, we introduce multiple techniques and methods to generate photonic entangled states with high probability, which have the potential to reduce the footprint of Linear Optical Quantum Computing (LOQC) architectures drastically. Most notably, we are showing how to improve Bell state preparation from four single photons to up to p=2/3, boost Type-I fusion to 75% with a dual-rail Bell state ancilla and improve Type-II fusion beyond the limits of Bell state discrimination.

arXiv:2106.13825Jun 25, 202118 citations

Beating the One-Half Limit of Ancilla-Free Linear Optics Bell Measurements

Hussain Zaidi, Peter van Loock

We show that optically encoded two-qubit Bell states can be unambiguously discriminated with a success probability of more than 50% in both single-rail and dual-rail encodings by using active linear-optical resources that include Gaussian squeezing operations. These results are in contrast to the well-known upper bound of 50% for unambiguous discrimination of dual-rail Bell states using passive, static linear optics and arbitrarily many vacuum modes. We present experimentally feasible schemes that improve the success probability to 64.3% in dual-rail and to 62.5% in single-rail for a uniform random distribution of Bell states. Conceptually, this demonstrates that neither interactions that induce nonlinear mode transformations (such as Kerr interactions) nor auxiliary entangled photons are required to go beyond the one-half limit. We discuss the optimality of our single-rail scheme and talk about an application of our dual-rail scheme in quantum communication.We show that optically encoded two-qubit Bell states can be unambiguously discriminated with a success probability of more than 50% in both single-rail and dual-rail encodings by using active linear-optical resources that include Gaussian squeezing operations. These results are in contrast to the well-known upper bound of 50% for unambiguous discrimination of dual-rail Bell states using passive, static linear optics and arbitrarily many vacuum modes. We present experimentally feasible schemes that improve the success probability to 64.3% in dual-rail and to 62.5% in single-rail for a uniform random distribution of Bell states. Conceptually, this demonstrates that neither interactions that induce nonlinear mode transformations (such as Kerr interactions) nor auxiliary entangled photons are required to go beyond the one-half limit. We discuss the optimality of our single-rail scheme and talk about an application of our dual-rail scheme in quantum communication.

arXiv:1301.2749Physical Review LettersJun 24, 201362 citations

Deterministic entangling gates with nonlinear quantum photonic interferometers

Francesco Scala, Davide Nigro, Dario Gerace

Abstract The single-photon quantum computing paradigm currently relies on the multi-port interference in linear optical devices, which is intrinsically based on probabilistic measurements outcome, and thus non-deterministic. Devising a fully deterministic, universal, and practically achievable quantum computing platform based on single-photon encoding and integrated photonic circuits is still an open challenge. Here we propose to exploit the interplay of distributed self-Kerr nonlinearity and localized hopping in quantum photonic interferometers to implement deterministic entangling quantum gates with dual rail photonic qubits. It is shown that a universal set of single- and two-qubit gates can be designed by a suitable concatenation of few optical interferometric elements, reaching optimal fidelities arbitrarily close to 100% that are theoretically demonstrated through a bound constrained optimization algorithm. The actual realization would require the concatenation of a few tens of elementary operations, as well as on-chip optical nonlinearities that are compatible with some of the existing quantum photonic platforms, as it is finally discussed.Abstract The single-photon quantum computing paradigm currently relies on the multi-port interference in linear optical devices, which is intrinsically based on probabilistic measurements outcome, and thus non-deterministic. Devising a fully deterministic, universal, and practically achievable quantum computing platform based on single-photon encoding and integrated photonic circuits is still an open challenge. Here we propose to exploit the interplay of distributed self-Kerr nonlinearity and localized hopping in quantum photonic interferometers to implement deterministic entangling quantum gates with dual rail photonic qubits. It is shown that a universal set of single- and two-qubit gates can be designed by a suitable concatenation of few optical interferometric elements, reaching optimal fidelities arbitrarily close to 100% that are theoretically demonstrated through a bound constrained optimization algorithm. The actual realization would require the concatenation of a few tens of elementary operations, as well as on-chip optical nonlinearities that are compatible with some of the existing quantum photonic platforms, as it is finally discussed.

arXiv:2306.05072Communications PhysicsApr 5, 202410 citations

Minimal ancilla for boosting type-I photonic fusion

A. A. Melkozerov, S. S. Straupe, M. Yu. Saygin

Fusion gates enable the creation of large entangled photonic states for linear-optical quantum computing and communication protocols. However, their success probability is limited to $1/2$ without additional photonic resources. Previous schemes for boosting type-I fusion have used four ancillary single photons or a two-qubit Bell state, whose preparation is probabilistic and resource intensive. Here we propose a boosted type-I fusion gate using only two independent ancillary single photons and no entangled ancillary input. It achieves a direct success probability of $5/8$ , matching that of the previous four-single-photon proposal while using half as many ancillary photons. The circuit is predominantly passive, with a single active element that applies a phase shift or swaps two modes according to intermediate photodetection outcomes. Unlike the previous schemes, successful outputs occupy fixed modes and require no further conditional output routing. In particular, we show that the gate is more robust to heralded ancillary-photon loss than previously proposed boosted gates and reduces the average number of single photons required to generate a six-qubit ring graph state by more than $4.6\%$ compared with other type-I schemes. It therefore offers a resource-efficient primitive for scalable fusion-based photonic quantum information processing.Fusion gates enable the creation of large entangled photonic states for linear-optical quantum computing and communication protocols. However, their success probability is limited to $1/2$ without additional photonic resources. Previous schemes for boosting type-I fusion have used four ancillary single photons or a two-qubit Bell state, whose preparation is probabilistic and resource intensive. Here we propose a boosted type-I fusion gate using only two independent ancillary single photons and no entangled ancillary input. It achieves a direct success probability of $5/8$, matching that of the previous four-single-photon proposal while using half as many ancillary photons. The circuit is predominantly passive, with a single active element that applies a phase shift or swaps two modes according to intermediate photodetection outcomes. Unlike the previous schemes, successful outputs occupy fixed modes and require no further conditional output routing. In particular, we show that the gate is more robust to heralded ancillary-photon loss than previously proposed boosted gates and reduces the average number of single photons required to generate a six-qubit ring graph state by more than $4.6\%$ compared with other type-I schemes. It therefore offers a resource-efficient primitive for scalable fusion-based photonic quantum information processing.

quant-pharXiv:2610.34257Oct 27, 20260 citations

Fusion gates enable the creation of large entangled photonic states for linear-optical quantum computing and communication protocols. However, their success probability is limited to

1/2

without additional photonic resources. Previous schemes for boosting type-I fusion have used four ancillary single photons or a two-qubit Bell state, whose preparation is probabilistic and resource intensive. Here we propose a boosted type-I fusion gate using only two independent ancillary single photons and no entangled ancillary input. It achieves a direct success probability of

5/8

, matching that of the previous four-single-photon proposal while using half as many ancillary photons. The circuit is predominantly passive, with a single active element that applies a phase shift or swaps two modes according to intermediate photodetection outcomes. Unlike the previous schemes, successful outputs occupy fixed modes and require no further conditional output routing. In particular, we show that the gate is more robust to heralded ancillary-photon loss than previously proposed boosted gates and reduces the average number of single photons required to generate a six-qubit ring graph state by more than

4.6\%

compared with other type-I schemes. It therefore offers a resource-efficient primitive for scalable fusion-based photonic quantum information processing.