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.
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.
In the last decade Grice [Phys. Rev. A 84, 042331 (2011)] and Ewert and van Loock [Phys. Rev. Lett. 113, 140403 (2014)] found linear optical networks achieving near-unit efficiency unambiguous Bell state discrimination, when fed with increasingly complex ancillary states. However, except for the vacuum ancilla case [Appl. Phys. B 72, 67 (2001)], the optimality of these schemes is unknown. Here, the optimality of these networks is investigated through analytical and numerical means. We show an analytical upper bound to the success probability for interferometers that preserve the polarization of the input photons, saturated by both Grice's and Ewert--van Loock's strategies. Furthermore, such an upper bound links the complexity of their ancilla states with the scaling of their performance. We also show a computer-aided approach to the optimization of such measurement schemes for generic interferometers, by simulating an optical network supplied with various kinds of ancillary input states. We numerically confirm the optimality of known small schemes. We use both methods to investigate other ancilla states, some of them never studied before.
Linear-optical realizations of Bell state measurement (BSM) on two single-photon qubits succeed with probability
ps no higher than 0.5. However, predetection quadrature squeezing, i.e., quantum noise limited phase sensitive amplification, in the usual linear-optical BSM circuit, can yield ${p}_{s}\ensuremath{\approx}0.643$. The ability to achieve
ps>0.5 has been found to be critical in resource-efficient realizations of linear-optical quantum computing and all-photonic quantum repeaters. Yet, the aforesaid value of
ps>0.5 is not known to be the maximum achievable using squeezing, thereby leaving it open whether close-to-
100 efficient BSM might be achievable using squeezing as a resource. In this paper, we report insights on why squeezing-enhanced BSM achieves
ps>0.5. Using this, we show that the previously reported ${p}_{s}\ensuremath{\approx}0.643$ at single-mode squeezing strength
r=0.6585---for unambiguous state discrimination (USD) of all four Bell states---is an experimentally unachievable point result, which drops to ${p}_{s}\ensuremath{\approx}0.59$ with the slightest change in
r. We, however, show that squeezing-induced boosting of
ps with USD operation is still possible over a continuous range of
r, with an experimentally achievable maximum occurring at
r=0.5774, achieving ${p}_{s}\ensuremath{\approx}0.596$. Finally, deviating from USD operation, we explore a trade space between
ps, the probability with which the BSM circuit declares a ``success,'' versus the probability of error
pe, the probability of an input Bell state being erroneously identified given the circuit declares a success. Since quantum error correction could correct for some
pe>0, this tradeoff may enable better quantum repeater designs by potentially increasing the entanglement generation rates with
ps exceeding what is possible with traditionally studied USD operation of BSMs.
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.