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An important task for quantum information processing is optimal discrimination between two non-orthogonal quantum states, which until now has only been realized optically. Here, we present and compare experimental realizations of optimal quantum measurements for distinguishing between two non-orthogonal quantum states encoded in a single ^14 N nuclear spin. Implemented measurement schemes are the minimum-error measurement (known as Helstrom measurement), unambiguous state discrimination using a standard projective measurement, and optimal unambiguous state discrimination (known as IDP measurement), which utilizes a three-dimensional Hilbert space. Measurement efficiencies are found to be above 80% for all schemes and reach a value of 90% for the IDP measurement
Quantum walks have by now been realized in a large variety of different physical settings. In some of these, particularly with trapped ions, the walk is implemented in phase space, where the corresponding position states are not orthogonal. We develo
We propose a classical to quantum information encoding system using non--orthogonal states and apply it to the problem of searching an element in a quantum list. We show that the proposed encoding scheme leads to an exponential gain in terms of quant
In this article we extend results from our previous work [Bendersky, de la Torre, Senno, Figueira and Acin, Phys. Rev. Lett. 116, 230406 (2016)] by providing a protocol to distinguish in finite time and with arbitrarily high success probability any a
Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the ground state
Several proposed techniques for distinguishing between optical coherent states are analyzed under a physically realistic model of photodetection. Quantum error probabilities are derived for the Kennedy receiver, the Dolinar receiver and the unitary r