Related papers: Optimal discrimination between real and complex qu…
Optimal and finite positive operator valued measurements on a finite number $N$ of identically prepared systems have been presented recently. With physical realization in mind we propose here optimal and minimal generalized quantum…
We investigate the performance of discrimination strategy in the comparison task of known quantum states. In the discrimination strategy, one infers whether or not two quantum systems are in the same state on the basis of the outcomes of…
A fundamental problem in statistics and learning theory is to test properties of distributions. We show that quantum computers can solve such problems with significant speed-ups. In particular, we give fast quantum algorithms for testing…
The state of a quantum system, consisting of two distinct subsystems, is called separable if it can be prepared by two distant experimenters who receive instructions from a common source, via classical communication channels. A necessary…
Equational reasoning is central to quantum circuit optimisation and verification: one replaces subcircuits by provably equivalent ones using a fixed set of rewrite rules viewed as equations. A finite rule set is most informative when it…
In the minimal scenario of quantum correlations, two parties can choose from two observables with two possible outcomes each. Probabilities are specified by four marginals and four correlations. The resulting four-dimensional convex body of…
We present an analytical method to estimate pure quantum states using a minimum of three measurement bases in any finite-dimensional Hilbert space. This is optimal as two bases are insufficient to construct an informationally complete…
The operational axiomatization of quantum theory can be regarded as a set of six epistemological rules for falsifying propositions of the theory. In particular, the Purification postulate-the only one that is not shared with classical…
We take quantum theory and replace $\mathbb{C}$ by $\mathbb{C}[\varepsilon]$ where $\varepsilon^2=0$, i.e. we extend quantum theory to the ring of dual complex numbers. The aim is to develop a common language in which to treat continuous…
We argue, through some philosophical considerations, on (i)dependent or (ii) an independent existence of physical reality underlying quantum states. According these simple considerations, we conclude that is impossible to have a clear…
We study quantum algorithms for verifying properties of the output probability distribution of a classical or quantum circuit, given access to the source code that generates the distribution. We consider the basic task of uniformity…
Most measurements are designed to tell you which of several alternatives have occurred, but it is also possible to make measurements that eliminate possibilities and tell you an alternative that did not occur. Measurements of this type have…
Quantum entanglement is the core resource in quantum information processing and quantum computing. It is an significant challenge to effectively characterize the entanglement of quantum states. Recently, elegant separability criterion is…
From a quantum information perspective, verifying quantum coherence in a quantum experiment typically requires adjusting measurement settings or changing inputs. A paradigmatic example is that of a double-slit experiment, where observing…
In this paper, we discuss the problem of determining whether a quantum system is in a pure state, or in a mixed state. We apply two strategies to settle this problem: the unambiguous discrimination and the maximum confidence discrimination.…
Contrary to an oft-made claim, there can be observational distinctions (say for the expansion of the universe or the cosmological constant) between "single-history" quantum theories and "many-worlds" quantum theories. The distinctions occur…
The task of testing whether quantum theory applies to all physical systems and all scales requires considering situations where a quantum probe interacts with another system that need not obey quantum theory in full. Important examples…
The universe is not locally realistic. Abandoning causality often appears more palatable than giving up on realism. This paper proposes two novel experimental setups to test realism's failure using the conservation of electric charge. The…
Quantum computing is seeking to realize hardware-optimized algorithms for application-related computational tasks. NP (nondeterministic-polynomial-time) is a complexity class containing many important but intractable problems like the…
We consider two different optimized measurement strategies for the discrimination of nonorthogonal quantum states. The first is conclusive discrimination with a minimum probability of inferring an erroneous result, and the second is…