Related papers: Truncated moment sequences and a solution to the c…
Separability of quantum states is analyzed with the use of the Choi-Jamiolkowski isomorphism. Spectral separability criteria are derived. The presented approach is illustrated with various examples, among which a separable decomposition of…
We map the quantum entanglement problem onto the mathematically well-studied truncated moment problem. This yields a necessary and sufficient condition for separability that can be checked by a hierarchy of semi-definite programs. The…
Certifying high-dimensional quantum channels is essential for ensuring the reliability of quantum communication protocols. Existing certification schemes often rely on fully trusted internal devices, which is difficult to achieve in…
Quantum entanglement can be studied through the theory of completely positive maps in a number of ways, including by making use of the Choi-Jamilkowski isomorphism, which identifies separable states with entanglement breaking quantum…
When the algebraic variety associated with a truncated moment sequence is finite, solving the moment problem follows a well-defined procedure. However, moment problems involving infinite algebraic varieties are more complex and less…
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…
By using the Choi-Jamio{\l}kowski isomorphism, we propose two classes of coherence monotones of quantum channels based on the unified $(r,s)$-relative entropy and the sandwiched R\'{e}nyi relative entropy. Elegant properties of the…
We investigate the coherence of quantum channels and establish a resource theory for quantifying the coherence of quantum channels via Choi matrix. To this aim, we define the incoherent channels and incoherent superchannels. This theory…
The separability detecting problem of mixed states is one of the fundamental problems in quantum information theory. In the last 20 years, almost all methods are based on the sufficient or necessary conditions for entanglement. However, in…
Quantum process tomography, the task of estimating an unknown quantum channel, is a central problem in quantum information theory. A long-standing open question is to determine the optimal number of uses of an unknown channel required to…
In quantum information and computation, the generation of entanglement through unitary gates remains a significant and active area of research. However, there are states termed as absolutely separable, from which entanglement cannot be…
We investigate an original family of quantum distinguishability problems, where the goal is to perfectly distinguish between $M$ quantum states that become identical under a completely decohering map. Similarly, we study distinguishability…
In the space of quantum channels, we establish the geometry that allows us to make statistical predictions about relative volumes of entanglement breaking channels among all the Gaussian quantum channels. The underlying metric is…
We look into the task of differentiating between any two quantum channels and reconstructing them from the obtained measurement statistics with possibly limited information about the experimental set-up. We employ the communication matrix…
We investigate the coherence of quantum channels using the Choi-Jamio\l{}kowski isomorphism. The relation between the coherence and the purity of the channel respects a duality relation. It characterizes the allowed values of coherence when…
We give a sufficient condition that an operator sum representation of a separable quantum channel in terms of product operators is the unique product representation for that channel, and then provide examples of such channels for any number…
We propose a unifying approach to the separability problem using covariance matrices of locally measurable observables. From a practical point of view, our approach leads to strong entanglement criteria that allow to detect the entanglement…
In the problem of quantum channel discrimination, one distinguishes between a given number of quantum channels, which is done by sending an input state through a channel and measuring the output state. This work studies applications of…
Quantum states are represented by positive semidefinite Hermitian operators with unit trace, known as density matrices. An important subset of quantum states is that of separable states, the complement of which is the subset of…
The truncated moment problem consists of determining whether a given finitedimensional vector of real numbers y is obtained by integrating a basis of the vector space of polynomials of bounded degree with respect to a non-negative measure…