Related papers: Maximally incompatible quantum observables
Incompatibility between conjugate variables and complementary pictures comes in two kinds, exclusive of one another. The first kind is unconditional, and the second conditional on quantum's indivisibility. We employ this distinction to…
We consider the problem of a state determination for a two-level quantum system which can be in one of two nonorthogonal mixed states. It is proved that for the two independent identical systems the optimal combined measurement (which…
We generalize the notion of unextendible maximally entangled basis from bipartite systems to multipartite quantum systems. It is proved that there do not exist unextendible maximally entangled bases in three-qubit systems. Moreover,two…
Mutually unbiased bases, mutually unbiased measurements and general symmetric informationally complete measurements are three related concepts in quantum information theory. We investigate multipartite systems using these notions and…
In this article, we revisit the century-old question of the minimal set of observables needed to identify a quantum state: here, we replace the natural coincidences in their spectra by effective ones, induced by an imperfect measurement. We…
Certifying maximal quantum randomness without assumptions about system dimension remains a pivotal challenge for secure communication and foundational studies. Here, we introduce a generalized framework to directly certify maximal…
Bounds analogous to entropic uncertainty relations allow one to design practical tests to detect quantum entanglement by a collective measurement performed on several copies of the state analyzed. This approach, initially worked out for…
We consider the problem of designing an optimal quantum detector that distinguishes unambiguously between a collection of mixed quantum states. Using arguments of duality in vector space optimization, we derive necessary and sufficient…
Heisenberg's uncertainty relations for measurement quantify how well we can jointly measure two complementary observables and have attracted much experimental and theoretical attention recently. Here we provide an exact tradeoff between the…
Quantum cloning machine for arbitrary mixed states in symmetric subspace is proposed. This quantum cloning machine can be used to copy part of the output state of another quantum cloning machine and is useful in quantum computation and…
Measurement incompatibility is a distinguishing property of quantum physics and an essential resource for many quantum information processing tasks. We introduce an approach to verify the joint measurability of measurements based on…
Four common optimality criteria for measurements are formulated using relations in the set of observables, and their connections are clarified. As case studies, 1-0 observables, localization observables, and photon counting observables are…
Multipartite entanglement is the premier resource for quantum technologies. Yet, its exact quantification in the laboratory is notoriously challenging, typically requiring the full knowledge of high dimensional quantum states. Here, we…
We study the problem of universal quantum cloning -- taking several identical copies of a pure but unknown quantum state and producing further copies. While it is well known that it is impossible to perfectly reproduce the state, how well…
The cloning of quantum variables with continuous spectra is analyzed. A universal - or Gaussian - quantum cloning machine is exhibited that copies equally well the states of two conjugate variables such as position and momentum. It also…
We derive by lattice theory a universal quantum certainty relation for arbitrary $M$ observables in $N$-dimensional system, which provides a state-independent maximum lower bound on the direct-sum of the probability vectors in terms of…
Standard quantum physics prevents the existence of a joint statistics for complementary observables. Nevertheless, a joint distribution for complementary observables can be derived from their imperfect simultaneous measurement followed by a…
We present a single inequality as the necessary and sufficient condition for two unsharp observables of a two-level system to be jointly measurable in a single apparatus and construct explicitly the joint observables. A complementarity…
The breakthrough of quantum error correction brought with it the picture of quantum information as a sort of combination of two complementary types of classical information, "amplitude" and "phase". Here I show how this intuition can be…
Some quantum measurements can not be performed simultaneously, i.e. they are incompatible. Here we show that every set of incompatible measurements provides an advantage over compatible ones in a suitably chosen quantum state discrimination…