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Recently, a new and powerful separability criterion was introduced in [O. Rudolph, quant-ph/0202121] and [Chen {\it et al.}, quant-ph/0205017]. Composing the main idea behind the above criterion and the necessary and sufficient condition in…
A group of symmetric operators are introduced to carry out the separability criterion for bipartite and multipartite quantum states. Every symmetric operator, represented by a symmetric matrix with only two nonzero elements, and their…
We introduce a generalization of the set of completely positive matrices that we call "pairwise completely positive" (PCP) matrices. These are pairs of matrices that share a joint decomposition so that one of them is necessarily positive…
We construct a probabilistic quantum cloning machine by a general unitary-reduction operation. With a postselection of the measurement results, the machine yields faithful copies of the input states. It is shown that the states secretly…
Usual separability criteria applicable to distinguishable particles are not applicable to identical particles. Here we show that Partial transposition and symmetrization (or anti symmetrization) of density matrix of bipartite boson systems…
In contrast to the wide-spread opinion that any separable quantum state satisfies every classical probabilistic constraint, we present a simple example where a separable quantum state does not satisfy the original Bell inequality although…
We address perfect discrimination of two separable states. When available states are restricted to separable states, we can theoretically consider a larger class of measurements than the class of measurements allowed in quantum theory. The…
We consider the problem of deciding if a given three-party entangled pure state can be converted, with a non-zero success probability, into a given two-party pure state through local quantum operations and classical communication. We show…
We present two sets of computable entanglement measures for multipartite systems where each subsystem can have different degrees of freedom (so-called qudits). One set, called 'separability' measure, reveals which of the subsystems are…
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…
Many-body quantum systems can be characterised using the notions of \emph{k}-separability and entanglement depth. A quantum state is \emph{k}-separable if it can be expressed as a mixture of \emph{k} entangled subsystems, and its…
We study the separability of symmetric bipartite quantum states and show that a single correlation measurement is sufficient to detect the entanglement of any bipartite symmetric state with a non-positive partial transpose. We also discuss…
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 show that the quantum measurement known as the pretty good measurement can be used to identify an unknown quantum state picked from any set of $n$ mixed states that have pairwise fidelities upper-bounded by a constant below 1, given…
We study the separability of permutationally symmetric quantum states. We show that for bipartite symmetric systems most of the relevant entanglement criteria coincide. However, we provide a method to generate examples of bound entangled…
In this paper, we consider the problem of unambiguous discrimination between a set of mixed quantum states. We first divide the density matrix of each mixed state into two parts by the fact that it comes from ensemble of pure quantum…
It is a central fact in quantum mechanics that non-orthogonal states cannot be distinguished perfectly. This property ensures the security of quantum key distribution. It is therefore an important task in quantum communication to design and…
Consider a fixed universe of $N=2^n$ elements and the uniform distribution over elements of some subset of size $K$. Given samples from this distribution, the task of complement sampling is to provide a sample from the complementary subset.…
To detect frauds from some internal participants or external attackers, some verifiable threshold quantum secret sharing schemes have been proposed. In this paper, we present a new verifiable threshold structure based on a single qubit…
We present a quantum algorithm to transform the cardinality of a set of charged particles flowing along a quantum wire into a binary number. The setup performing this task (for at most N particles) involves log_2 N quantum bits serving as…