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IEEE International Conference on Acoustics Speech and Signal Processing

Intrasystem Entanglement Generator and Unambiguos Bell States Discriminator on Chip

Fabio Antonio Bovino

Published Apr 17, 2019• 2 citations
Publisher

Abstract

Bell measurements, jointly projecting two qubits onto the so-called Bell basis, constitute a crucial step in many quantum computation and communication protocols, including dense coding, quantum repeaters, and teleportation-based quantum computation. A problem is the impossibility of deterministic unambiguous Bell measurements using passive linear optics, even when arbitrarily many auxiliary photons, photon-number-resolving detectors, and dynamical (conditionally changing) networks are available. Current proposals for going over the 50% upper bound without using experimentally challenging nonlinearities rely on using entangled photon ancilla states and a sufficiently large interferometer to combine the signal and ancilla modes. We demonstrate that the novel Multiple Rail architecture, based on the propagation of a single photon in a complex multipath optical circuit (or multiwaveguide optical circuit), provides the possibility to perform deterministic Bell measurements so to unambiguously discrimate all four Bell States.

DOI
10.1109/icassp.2019.8683820

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Bell measurements, jointly projecting two qubits onto the so-called Bell basis, constitute a crucial step in many quantum computation and communication protocols, including dense coding, quantum repeaters, and teleportation-based quantum computation. A problem is the impossibility of deterministic unambiguous Bell measurements using passive linear optics, even when arbitrarily many auxiliary photons, photon-number-resolving detectors, and dynamical (conditionally changing) networks are available. Current proposals for going over the 50% upper bound without using experimentally challenging nonlinearities rely on using entangled photon ancilla states and a sufficiently large interferometer to combine the signal and ancilla modes. We demonstrate that the novel Multiple Rail architecture, based on the propagation of a single photon in a complex multipath optical circuit (or multiwaveguide optical circuit), provides the possibility to perform deterministic Bell measurements so to unambiguously discrimate all four Bell States.
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.
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.
Quantum information processing using linear optics is challenging due to the limited set of deterministic operations achievable without using complicated resource-intensive methods. While techniques such as the use of ancillary photons can enhance the information processing capabilities of linear optical systems, they are technologically demanding. Therefore, determining the constraints posed by linear optics and optimizing linear optical operations for specific tasks under those constraints, without the use of ancillae, can facilitate their potential implementation. Here, we consider the task of unambiguously discriminating between Bell-like states using linear optics and without the use of ancillary photons. This is a basic problem relevant in diverse settings, for example, in the measurement of the output of an entangling quantum circuit or for entanglement swapping at a quantum repeater station. While it is known that exact Bell states of two qubits can be discriminated with an optimal success probability of 50%, we find, surprisingly, that for Bell-like states the optimal probability can be only 25%. We analyze a set of Bell-like states in terms of their distinguishability, entanglement as measured by concurrence, and parameters of the beam-splitter network used for unambiguous discrimination. Further, we provide the linear optical configuration comprising single-photon detectors and beam splitters with input-state-dependent parameters that achieves optimal discrimination in the Bell-like case.
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.
In quantum communication and fusion-based quantum computation, photonic Bell measurements are fundamentally limited when only passive linear optics is employed. While for qubits, some Bell states can be unambiguously identified with static beam splitters and no extra photons or entanglement, additional auxiliary photons or at least additional auxiliary degrees of freedom with a certain level of additional entanglement are needed to approach or attain a complete, deterministic Bell measurement. Here, we prove an exact resource threshold when the same two photons carry system qudits of dimension ddd and a fixed auxiliary entangled state ΦΦΦ, possibly distributed over several additional degrees of freedom, with total Schmidt rank rΦr_ΦrΦ​. We show that a single conclusive Bell-label functional can occur for rΦ⩾⌈d/2⌉r_Φ\geqslant\lceil d/2\rceilrΦ​⩾⌈d/2⌉, but deterministic discrimination of all d2d^2d2 Bell-state labels requires rΦ⩾dr_Φ\geqslant drΦ​⩾d. A maximally entangled rank-ddd auxiliary state achieves the bound by local Bell-basis sorting between each photon's system and auxiliary degrees of freedom. Thus, the auxiliary Schmidt rank is a certified resource for ancilla-photon-free, embedded photonic Bell measurements.