Quantum channel discrimination plays a crucial role in quantum information theory. Of particular interest is the case in which the channels can be discriminated perfectly. In this work, we focus on the perfect quantum channel discrimination task in a parallel scheme. We develop an SDP formulation combined with a bisection procedure to compute a quantum state for perfect discrimination in time linear in the number of copies. In addition, we obtain the minimal number of copies of quantum channels to achieve perfect discrimination. Thanks to that, we settle in the affirmative Conjecture 1 of Duan, Guo, Li and Li [arXiv:1605.02294, IEEE ISIT 2016], which characterizes the number of parallel uses needed to discriminate perfectly a distinguished family of operator subspaces. All our results are obtained using the notion and basic properties of the numerical range. In particular, the key fact that we prove and use is that the minimal angle of the numerical range of a tensor product of matrix subspaces equals the sum of the minimal angles of the numerical ranges of the individual subspaces.
Recently, a protocol for quantum state discrimination (QSD) in a multiparty scenario has been introduced [Phys. Rev. Lett. 111, 100501 (2013)]. In this protocol, Alice generates a quantum system in one of two predefined nonorthogonal qubit states, and the goal is to send the generated state information to different parties without classical communication exchanged between them during the protocol's session. The interesting feature is that, by resorting to sequential generalized measurements onto this single system, there is a nonvanishing probability that all observers identify the state prepared by Alice. Here, we present the experimental implementation of this protocol based on polarization single-photon states. Our scheme works over an optical network, and since QSD lies in the core of many protocols, it represents a step towards experimental multiparty quantum information processing.
Strategies to optimally discriminate between quantum states are critical in quantum technologies. We present an experimental demonstration of minimum-error discrimination between entangled states, encoded in the polarization of pairs of photons. Although the optimal measurement involves projection onto entangled states, we use a result of J. Walgate et al. [Phys. Rev. Lett. 85, 4972 (2000)] to design an optical implementation employing only local polarization measurements and feed-forward, which performs at the Helstrom bound. Our scheme can achieve perfect discrimination of orthogonal states and minimum-error discrimination of nonorthogonal states. Our experimental results show a definite advantage over schemes not using feed-forward.
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.