We propose a framework to analyze linear optical circuits based on an analogy with stabilizer formalism in quantum circuits, which provides efficiently computable formulas related to state discriminations. Hence, we analyze a Bell-state discrimination scheme with linear optics and ancillary single photons. With an increasing number of ancilla photons, the success probability of Bell-state discrimination has a maximum of
512403≃0.787 at
28 ancilla photons. By contrast, the corresponding two-qubit measurement asymptotically approaches a maximally entangling measurement.
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.
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.
A linear optics-based scheme to implement various quantum information processing tasks is of paramount importance due to ease of implementation and low noise. Many information-theoretic tasks depend on the successful discrimination of Bell states. A no-go theorem has been proved in literature which tells that it is not possible to perfectly discriminate among the four Bell states by restricting measurement apparatus to linear optical elements. The success probability is only
50%. Through using extra resources such as hyper entanglement, ancillary entanglement, and even a minimum amount of non-linearity complete Bell-state discrimination can be achieved. The success probability for Bell-like state discrimination is only
25%. We find that this can be boosted up to
50% using hyperentanglement in polarization, momentum, or OAM degrees of freedom of the photons which is in contrast to the Bell-state discrimination scenario where
100% can be achieved. Furthermore, we find that by using correlation in time of the photons all four Bell states can be distinguished with
100% success probability while for the Bell-like state discrimination, it strictly lies between
25% and
50% depending on the state parameter with only three Bell-like states being distinguishable. We also observe a similar contrast when we use ancillary entangled photons. While the success probability for all four Bell-state discrimination increases as
1−2N1 where N is the number of ancillary photons for Bell-like states it depends again on the state parameters and can be less than
25% in some cases. Also adding further ancillary photons decreases the success probability. We then show that using non-linear gadgets namely SFG
100% success probability can be achieved even for Bell-like state discrimination.