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We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…
We consider N quantum systems initially prepared in pure states and address the problem of unambiguously comparing them. One may ask whether or not all $N$ systems are in the same state. Alternatively, one may ask whether or not the states…
This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical…
Quantum Gaussian states can be considered as the majority of the practical quantum states used in quantum communications and more generally in quantum information. Here we consider their properties in relation with the geometrically uniform…
We developed new concentration inequalities for a quantum state on an $N$-qudit system or measurement outcomes on it that apply to an adversarial setup, where an adversary prepares the quantum state. Our one-sided concentration inequalities…
The well-known Schmidt decomposition, or equivalently, the complex singular value decomposition, states that a pure quantum state of a bipartite system can always be brought into a "diagonal" form using local unitary transformations. In…
Multipartite quantum states that cannot be uniquely determined by their reduced states of all proper subsets of the parties exhibit some inherit `high-order' correlation. This paper elaborates this issue by giving necessary and sufficient…
Efficient methods to access the entanglement of a quantum many-body state, where the complexity generally scales exponentially with the system size $N$, have long a concern. Here we propose the Schmidt tensor network state (Schmidt TNS)…
Quantum states are the key mathematical objects in quantum theory. It is therefore surprising that physicists have been unable to agree on what a quantum state truly represents. One possibility is that a pure quantum state corresponds…
Simultaneous existence of correlation in complementary bases is a fundamental feature of quantum correlation, and we show that this characteristic is present in any non-product bipartite state. We propose a measure via mutually unbiased…
Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…
There exists a physically well motivated method for approximating manifolds by certain topological spaces with a finite or a countable set of points. These spaces, which are partially ordered sets (posets) have the power to effectively…
We introduce a definition for a 'hidden measurement system', i.e., a physical entity for which there exist: (i) 'a set of non-contextual states of the entity under study' and (ii) 'a set of states of the measurement context', and which are…
We analyze a general bipartite-like representation of arbitrary pure states of $N$ indistinguishable particles, valid for both bosons and fermions, based on $M$- and $(N-M)$-particle states. It leads to exact $(M,N-M)$ Schmidt-like…
We show that probabilities of results of all possible measurements performing on a quantum system depend on the system's state only through its density matrix. Therefore all experimentally available information about the state contains in…
Understanding dissipative and decohering processes is fundamental to the study of quantum systems. An accurate and generic method for investigating these processes is to simulate both the system and environment, which, however, is…
The representation of numbers by tensor product states of composite quantum systems is examined. Consideration is limited to k-ary representations of length L and arithmetic modulo k^{L}. An abstract representation on an L fold tensor…
The general quantum superposition states containing the irreducible representation of the $n$-dimensional groups associated to the rotational symmetry of the $n$-sided regular polygon i.e. the cyclic group ($C_n$ ) and the rotational and…
What is the quantum state of the universe? Although there have been several interesting suggestions, the question remains open. In this paper, I consider a natural choice for the universal quantum state arising from the Past Hypothesis, a…
The estimation of the density matrix of a $k$-level quantum system is studied when the parametrization is given by the real and imaginary part of the entries and they are estimated by independent measurements. It is established that the…