Related papers: Test of Purity by LOCC
In hypothesis testing with quantum states, given a black box containing one of the two possible states, measurement is performed to detect in favor of one of the hypotheses. In postselected hypothesis testing, a third outcome is added,…
We study how to unambiguously identify a given quantum pure state with one of the two reference pure states when no classical knowledge on the reference states is given but a certain number of copies of each reference quantum state are…
The problem of optimally estimating an unknown unitary quantum operation with the aid of entanglement is addressed. The idea is to prepare an entangled pair, apply the unknown unitary to one of the two parts and then measure the joint…
A core principle of quantum theory is that non-orthogonal quantum states cannot be perfectly distinguished with single-shot measurements. However, it is possible to exclude a subset of non-orthogonal states without error in certain…
We study the stochastic local operation and classical communication (SLOCC) equivalence for arbitrary dimensional multipartite quantum states. For multipartite pure states, we present a necessary and sufficient criterion in terms of their…
Irreversibility between preparation and discrimination processes is manifested in the indistinguishability of orthogonal product states via local operations and classical communication (LOCC). Characterizing quantum properties for sets of…
We have investigated the problem of discriminating between nonorthogonal quantum states with least probability of error. We have determined that the best strategy for some sets of states is to make no measurement at all, and simply to…
In this paper, we consider the problem of discriminating quantum states by local operations and classical communication (LOCC) when an arbitrarily small amount of error is permitted. This paradigm is known as asymptotic state…
We show how to test the bipartiteness of an intersection graph of n line segments or simple polygons in the plane, or of balls in R^d, in time O(n log n). More generally we find subquadratic algorithms for connectivity and bipartiteness…
We consider online strategies for discriminating between symmetric pure states with zero error when $n$ copies of the states are provided. Optimized online strategies involve local, possibly adaptive measurements on each copy and are…
Finding ways to test the behaviour of quantum devices is a timely enterprise, especially in the light of the rapid development of quantum technologies. Device-independent self-testing is one desirable approach, as it makes minimal…
We introduce a new entanglement measure based on optimal entanglement witness. First of all, we show that the entanglement measure satisfies some necessary properties, including zero entanglements for all separable states, convexity,…
We consider the problem of discriminating between states of a specified set with maximum confidence. For a set of linearly independent states unambiguous discrimination is possible if we allow for the possibility of an inconclusive result.…
Local operations on subsystems and classical communication between parties (LOCC) constitute the most general protocols available on spatially separated quantum systems. Every LOCC protocol implements a separable generalized measurement --…
We show that the bipartite perfect matching problem is in quasi-NC$^2$. That is, it has uniform circuits of quasi-polynomial size $n^{O(\log n)}$, and $O(log^2 n)$ depth. Previously, only an exponential upper bound was known on the size of…
In this paper, we consider the LOCC distinguishability of product states. We employ polygons to analyze orthogonal product states in any system to show that with LOCC protocols, to distinguish seven orthogonal product states, one can…
Many mathematical imaging problems are posed as non-convex optimization problems. When numerically tractable global optimization procedures are not available, one is often interested in testing ex post facto whether or not a locally…
We study the problem of transforming a set of pure bipartite states into another using deterministic LOCC (local operations and classical communication). Necessary conditions for the existence of such a transformation are obtained using…
In this paper we consider the problem of unambiguous discrimination between a set of linearly independent pure quantum states. We show that the design of the optimal measurement that minimizes the probability of an inconclusive result can…
There has been a surge of progress in recent years in developing algorithms for testing and learning quantum states that achieve optimal copy complexity. Unfortunately, they require the use of entangled measurements across many copies of…