Optimal entanglement-assisted discrimination of quantum measurements (original) (raw)
Related papers
Optimal two-copy discrimination of quantum measurements
Physical Review A, 2009
We investigate optimal discrimination between two projective quantum measurements on a single qubit. We consider scenario where the measurement that should be identified can be performed twice and we show that adaptive discrimination strategy, entangled probe states, and feed-forward all help to increase the probability of correct identification of the measurement. We also experimentally demonstrate the studied discrimination strategies and test their performance. The employed experimental setup involves projective measurements on polarization states of single photons and preparation of required probe two-photon polarization states by the process of spontaneous parametric down-conversion and passive linear optics.
Optimal single-shot strategies for discrimination of quantum measurements
Physical Review A, 2014
We study discrimination of m quantum measurements in the scenario when the unknown measurement with n outcomes can be used only once. We show that ancilla-assisted discrimination procedures provide a nontrivial advantage over simple (ancilla-free) schemes for perfect distinguishability and we prove that inevitably m ≤ n. We derive necessary and sufficient conditions of perfect distinguishability of general binary measurements. We show that the optimization of the discrimination of projective qubit measurements and their mixtures with white noise is equivalent to the discrimination of specific quantum states. In particular, the optimal protocol for discrimination of projective qubit measurements with fixed failure rate (exploiting maximally entangled test state) is described. While minimum error discrimination of two projective qubit measurements can be realized without any need of entanglement, we show that discrimination of three projective qubit measurements requires a bipartite probe state. Moreover, when the measurements are not projective, the non-maximally entangled test states can outperform the maximally entangled ones.
Perfect discrimination of quantum measurements using entangled systems
New Journal of Physics, 2021
Distinguishing physical processes is one of the fundamental problems in quantum physics. Although distinguishability of quantum preparations and quantum channels have been studied considerably, distinguishability of quantum measurements remains largely unexplored. We investigate the problem of single-shot discrimination of quantum measurements using two strategies, one based on single quantum systems and the other one based on entangled quantum systems. First, we formally define both scenarios. We then construct sets of measurements (including non-projective) in arbitrary finite dimensions that are perfectly distinguishable within the second scenario using quantum entanglement, while not in the one based on single quantum systems. Furthermore, we show that any advantage in measurement discrimination tasks over single systems is a demonstration of Einstein–Podolsky–Rosen ‘quantum steering’. Alongside, we prove that all pure two-qubit entangled states provide an advantage in a measure...
The problem of non-orthogonal state discrimination underlies crucial quantum information tasks, such as cryptography and computing protocols. Therefore, it is decisive to find optimal scenarios for discrimination among quantum states. We experimentally investigate the strategy for the optimal discrimination of two non-orthogonal states considering a fixed rate of inconclusive outcomes (FRIO). The main advantage of the FRIO strategy is to interpolate between unambiguous and minimum error discrimination by solely adjusting the rate of inconclusive outcomes. We present a versatile experimental scheme that performs the optimal FRIO measurement for any pair of generated non-orthogonal states with arbitrary a priori probabilities and for any fixed rate of inconclusive outcomes. Considering different values of the free parameters in the FRIO protocol, we implement it upon qubit states encoded in the polarization mode of single photons generated in the spontaneous parametric down-conversion...
Minimum-error discrimination of entangled quantum states
Physical Review A, 2010
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 projecting onto entangled states, we use a result of Walgate et al. 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 non-orthogonal states. Our experimental results show a definite advantage over schemes not using feed-forward.
Experimental detection of entanglement with optimal-witness families
Physical review letters, 2014
We report an experiment in which one determines, with least tomographic effort, whether an unknown two-photon polarization state is entangled or separable. The method measures whole families of optimal entanglement witnesses. We introduce adaptive measurement schemes that greatly speed up the entanglement detection. The experiments are performed on states of different ranks, and we find good agreement with results from computer simulations.
Physical Review A, 2011
We present an experimental implementation of optimum measurements for quantum state discrimination. Optimum maximum-confidence discrimination and optimum unambiguous discrimination of two mixed single-photon polarization states were performed. For the latter the states of rank two in a four-dimensional Hilbert space are prepared using both path and polarization encoding. Linear optics and single photons from a true single-photon source based on a semiconductor quantum dot are utilized.
Method for universal detection of two-photon polarization entanglement
Physical Review A, 2015
Detecting and quantifying quantum entanglement of a given unknown state poses problems that are fundamentally important for quantum information processing. Surprisingly, no direct (i.e., without quantum tomography) universal experimental implementation of a necessary and sufficient test of entanglement has been designed even for a general two-qubit state. Here we propose an experimental method for detecting a collective universal witness, which is a necessary and sufficient test of two-photon polarization entanglement. It allows us to detect entanglement for any two-qubit mixed state, and to establish tight upper and lower bounds on its amount. A novel element of this method is the sequential character of its main components, which allows us to obtain relatively complicated information about quantum correlations with the help of simple linear-optical elements. As such, this proposal is the first to realize a universal two-qubit entanglement test within the present state of the art of quantum optics. PACS numbers: 03.67.Mn, 42.50.Dv
Proposal of Universal Detection of Two-photon Polarization Entanglement
arXiv (Cornell University), 2014
Detecting and quantifying quantum entanglement of a given unknown state poses problems that are fundamentally important for quantum information processing. Surprisingly, no direct (i.e., without quantum tomography) universal experimental implementation of a necessary and sufficient test of entanglement has been designed even for a general two-qubit state. Here we propose an experimental method for detecting a collective universal witness, which is a necessary and sufficient test of two-photon polarization entanglement. It allows us to detect entanglement for any two-qubit mixed state and to establish tight upper and lower bounds on its amount. A different element of this method is the sequential character of its main components, which allows us to obtain relatively complicated information about quantum correlations with the help of simple linear-optical elements. As such, this proposal realizes a universal two-qubit entanglement test within the present state of the art of quantum optics. We show the optimality of our setup with respect to the minimal number of measured quantities.
Strategies for optimal single-shot discrimination of quantum measurements
Physical Review A, 2018
In this work we study the problem of single-shot discrimination of von Neumann measurements, which we associate with measure-and-prepare channels. There are two possible approaches to this problem. The first one is simple and does not utilize entanglement. We focus only on the discrimination of classical probability distributions, which are outputs of the channels. We find necessary and sufficient criterion for perfect discrimination in this case. A more advanced approach requires the usage of entanglement. We quantify the distance between two measurements in terms of the diamond norm (called sometimes the completely bounded trace norm). We provide an exact expression for the optimal probability of correct distinction and relate it to the discrimination of unitary channels. We also state a necessary and sufficient condition for perfect discrimination and a semidefinite program which checks this condition. Our main result, however, is a cone program which calculates the distance between the measurements and hence provides an upper bound on the probability of their correct distinction. As a by-product, the program finds a strategy (input state) which achieves this bound. Finally, we provide a full description for the cases of Fourier matrices and mirror isometries.