Related papers: On Minimum Uncertainty States
Uncertainty and entanglement are both profound and key concepts in quantum theory. For three observables, the tightest uncertainty constants for both product and summation forms are revealed. In this work, we give an alternative proof for…
We consider the problem of existence of constrained minimizers for the focusing mass-subcritical Half-Wave equation with a defocusing mass-subcritical perturbation. We show the existence of a critical mass such that minimizers do exist for…
We propose a single observable to witness the nonzero quantum discord of an unknown quantum state provided that we have four copies of the state. The expectation value of this observable provides a necessary and sufficient condition for…
Two special situations where the standard uncertainty product inequality appears to be useless are modified. One such case is noted to also trivialize the recently-introduced alternatives [Phys. Rev. Lett. 113, 260401 (2014); Sci. Rep. 6,…
Bounded uncertainty relations provide the minimum value of the uncertainty assuming some additional information on the state. We derive analytically an uncertainty relation bounded by a pair of constraints, those of purity and Gaussianity.…
The necessary and suffcient condition for a set of matrices to commute is given and proven.
General wisdom tells us that if two quantum states are ``macroscopically distinguishable'' then their superposition should be hard to observe. We make this intuition precise and general by quantifying the difficulty to observe the quantum…
We establish necessary and sufficient conditions for the uniform integrability of the stochastic exponential E(M).
For a system randomly prepared in a number of quantum states, we present a lower bound for the distinguishability of the quantum states, that is, the success probability of determining the states in the form of entropy. When the states are…
In this paper we focus on providing sufficient conditions for some well-known stochastic orders in reliability but dealing with the discrete versions of them, filling a gap in the literature. In particular, we find conditions based on the…
We provide a necessary and sufficient condition for separability of Gaussian states of bipartite systems of arbitrarily many modes. The condition provides an operational criterion since it can be checked by simple computation. Moreover, it…
Experimental determination of an unknown quantum state usually requires several incompatible measurements. However, it is also possible to determine the full quantum state from a single, repeated measurement. For this purpose, the quantum…
Entropic uncertainty relations for the position and momentum within the generalized uncertainty principle are examined. Studies of this principle are motivated by the existence of a minimal observable length. Then the position and momentum…
We show how an unknown mixed quantum state's entanglement can be quantified by a suitable, local parity measurement on its two-fold copy.
Condition for distinguishability of countably infinite number of pure states by a single measurement is given. Distinguishability is to be understood as possibility of an unambiguous measurement. For finite number of states, it is known…
Three remarks concerning the form and the range of validity of the state-extended characteristic uncertainty relations (URs) are presented. A more general definition of the uncertainty matrix for pure and mixed states is suggested. Some new…
Error probability is a popular and well-studied optimization criterion in discriminating non-orthogonal quantum states. It captures the threat from an adversary who can only query the actual state once. However, when the adversary is able…
A necessary and sufficient condition is given for a subshift presentation to have a continuous $g$-function. An invariant necessary and sufficient condition is formulated for a subshift to posses a presentation that has a continuous…
Entanglement, or quantum inseparability, is a crucial resource in quantum information applications, and therefore the experimental generation of separated yet entangled systems is of paramount importance. Experimental demonstrations of…
Measurement uncertainty relations are quantitative bounds on the errors in an approximate joint measurement of two observables. They can be seen as a generalization of the error/disturbance tradeoff first discussed heuristically by…