Related papers: Self-Testing Positive Operator-Valued Measurements…
In this paper we consider the problem of constructing measurements optimized to distinguish between a collection of possibly non-orthogonal quantum states. We consider a collection of pure states and seek a positive operator-valued measure…
In the signal-processing literature, a frame is a mechanism for performing analysis and reconstruction in a Hilbert space. By contrast, in quantum theory, a positive operator-valued measure (POVM) decomposes a Hilbert-space vector for the…
According to quantum theory, the outcomes obtained by measuring an entangled state necessarily exhibit some randomness if they violate a Bell inequality. In particular, a maximal violation of the CHSH inequality guarantees that 1.23 bits of…
Based on a sequential communication game, semi-device independent certification of an unsharp instrument has recently been demonstrated [\href{https://iopscience.iop.org/article/10.1088/1367-2630/ab3773}{New J. Phys. 21 083034 (2019),…
The objective of this work is to develop a recursive, discrete time quantum filtering equation for a system that interacts with a probe, on which measurements are performed according to the Positive Operator Valued Measures (POVMs)…
We address the problem of constructing positive operator-valued measures (POVMs) in finite dimension $n$ consisting of $n^2$ operators of rank one which have an inner product close to uniform. This is motivated by the related question of…
The space of positive operator-valued measures on the Borel sets of a compact (or even locally compact) Hausdorff space with values in the algebra of linear operators acting on a d-dimensional Hilbert space is studied from the perspectives…
Quantum technologies offer significant advancements in information processing and communication, notably in the domain of random number generation (RNG). The use of Bell inequalities enables users to certify the randomness of outputs…
Standard quantum measurements are projective. However, the full scope of quantum measurements is represented by positive operator-valued measures (POVMs) and many of these break the limitations of projective measurements as resources in…
Localizable measurements are joint quantum measurements that can be implemented using only non-adaptive local operations and shared entanglement. We provide a protocol-independent characterization of localizable projection-valued measures…
Randomness is fundamental for secure communication and information processing. While continuous-variable optical systems offer an attractive platform for this task, certifying genuine quantum randomness in such setups remains challenging.…
Symmetric informationally complete positive operator-valued measurement (SIC-POVM) is one important class of quantum measurement which is crucial for various quantum information processing tasks. SIC-POVMs have the advantage of providing an…
The unpredictability of quantum physics gives rise to intrinsic randomness. In an adversarial scenario, any additional degrees of freedom must be attributed to an eavesdropper with correlations to the measurement set-up. The true randomness…
In this paper we shall introduce the mathematical framework for the description of measurements of quantum processes. Using this framework the process estimation problems can be treated in the similar way as the state estimation problems,…
The intrinsic random nature of quantum physics offers novel tools for the generation of random numbers, a central challenge for a plethora of fields. Bell non-local correlations obtained by measurements on entangled states allow for the…
There are two general requirements to harness the computational power of quantum mechanics: the ability to manipulate the evolution of an isolated system and the ability to faithfully extract information from it. Quantum error correction…
In this work we investigate the probability of violation of local realism under random measurements in parallel with the strength of these violations as described by resistance to white noise admixture. We address multisetting Bell…
We present a scheme for quantum random-number generation from an untrusted measurement device and a trusted source and demonstrate it experimentally. No assumptions about noise or imperfections in the measurement are required, and the…
It is well-known that observing nonlocal correlations allows us to draw conclusions about the quantum systems under consideration. In some cases this yields a characterisation which is essentially complete, a phenomenon known as…
The CHSH mod 3 Bell inequality is a natural testbed for higher-dimensional quantum nonlocality, yet its maximal quantum violation and self-testing properties have remained unresolved. We determine its exact maximal quantum value and show…