90 research outputs found
Bound on trace distance based on superfidelity
We provide a bound for the trace distance between two quantum states. The
lower bound is based on the superfidelity, which provides the upper bound on
quantum fidelity. One of the advantages of the presented bound is that it can
be estimated using a simple measurement procedure. We also compare this bound
with the one provided in terms of fidelity.Comment: 4 pages, 3 figure
Distinguishability of generic quantum states
Properties of random mixed states of order distributed uniformly with
respect to the Hilbert-Schmidt measure are investigated. We show that for large
, due to the concentration of measure, the trace distance between two random
states tends to a fixed number , which yields the
Helstrom bound on their distinguishability. To arrive at this result we apply
free random calculus and derive the symmetrized Marchenko--Pastur distribution,
which is shown to describe numerical data for the model of two coupled quantum
kicked tops. Asymptotic values for the fidelity, Bures and transmission
distances between two random states are obtained. Analogous results for quantum
relative entropy and Chernoff quantity provide other bounds on the
distinguishablity of both states in a multiple measurement setup due to the
quantum Sanov theorem.Comment: 13 pages including supplementary information, 6 figure
Diagonal unitary entangling gates and contradiagonal quantum states
Nonlocal properties of an ensemble of diagonal random unitary matrices of
order are investigated. The average Schmidt strength of such a bipartite
diagonal quantum gate is shown to scale as , in contrast to the behavior characteristic to random unitary gates. Entangling power of a
diagonal gate is related to the von Neumann entropy of an auxiliary quantum
state , where the square matrix is obtained by
reshaping the vector of diagonal elements of of length into a square
matrix of order . This fact provides a motivation to study the ensemble of
non-hermitian unimodular matrices , with all entries of the same modulus and
random phases and the ensemble of quantum states , such that all their
diagonal entries are equal to . Such a state is contradiagonal with
respect to the computational basis, in sense that among all unitary equivalent
states it maximizes the entropy copied to the environment due to the coarse
graining process. The first four moments of the squared singular values of the
unimodular ensemble are derived, based on which we conjecture a connection to a
recently studied combinatorial object called the "Borel triangle". This allows
us to find exactly the mean von Neumann entropy for random phase density
matrices and the average entanglement for the corresponding ensemble of
bipartite pure states.Comment: 14 pages, 6 figure
A model for quantum queue
We consider an extension of Discrete Time Markov Chain queueing model to the
quantum domain by use of Discrete Time Quantum Markov Chain. We introduce
methods for numerical analysis of such models. Using this tools we show that
quantum model behaves fundamentally differently from the classical one.Comment: 14 pages, 7 figure
Minimal Renyi-Ingarden-Urbanik entropy of multipartite quantum states
We study the entanglement of a pure state of a composite quantum system
consisting of several subsystems with levels each. It can be described by
the R\'enyi-Ingarden-Urbanik entropy of a decomposition of the state in a
product basis, minimized over all local unitary transformations. In the case
this quantity becomes a function of the rank of the tensor representing
the state, while in the limit the entropy becomes related to the
overlap with the closest separable state and the geometric measure of
entanglement. For any bipartite system the entropy coincides with the
standard entanglement entropy. We analyze the distribution of the minimal
entropy for random states of three and four-qubit systems. In the former case
the distributions of -tangle is studied and some of its moments are
evaluated, while in the latter case we analyze the distribution of the
hyperdeterminant. The behavior of the maximum overlap of a three-qudit system
with the closest separable state is also investigated in the asymptotic limit.Comment: 19 page
Strong Majorization Entropic Uncertainty Relations
We analyze entropic uncertainty relations in a finite dimensional Hilbert
space and derive several strong bounds for the sum of two entropies obtained in
projective measurements with respect to any two orthogonal bases. We improve
the recent bounds by Coles and Piani, which are known to be stronger than the
well known result of Maassen and Uffink. Furthermore, we find a novel bound
based on majorization techniques, which also happens to be stronger than the
recent results involving largest singular values of submatrices of the unitary
matrix connecting both bases. The first set of new bounds give better results
for unitary matrices close to the Fourier matrix, while the second one provides
a significant improvement in the opposite sectors. Some results derived admit
generalization to arbitrary mixed states, so that corresponding bounds are
increased by the von Neumann entropy of the measured state. The majorization
approach is finally extended to the case of several measurements.Comment: Revised versio
Conditional entropic uncertainty relations for Tsallis entropies
The entropic uncertainty relations are a very active field of scientific
inquiry. Their applications include quantum cryptography and studies of quantum
phenomena such as correlations and non-locality. In this work we find
entanglement-dependent entropic uncertainty relations in terms of the Tsallis
entropies for states with a fixed amount of entanglement. Our main result is
stated as Theorem~\ref{th:bound}. Taking the special case of von Neumann
entropy and utilizing the concavity of conditional von Neumann entropies, we
extend our result to mixed states. Finally we provide a lower bound on the
amount of extractable key in a quantum cryptographic scenario.Comment: 11 pages, 4 figure
Qubit flip game on a Heisenberg spin chain
We study a quantum version of a penny flip game played using control
parameters of the Hamiltonian in the Heisenberg model. Moreover, we extend this
game by introducing auxiliary spins which can be used to alter the behaviour of
the system. We show that a player aware of the complex structure of the system
used to implement the game can use this knowledge to gain higher mean payoff.Comment: 13 pages, 3 figures, 3 table
Distinguishing classically indistinguishable states and channels
We investigate an original family of quantum distinguishability problems,
where the goal is to perfectly distinguish between quantum states that
become identical under a completely decohering map. Similarly, we study
distinguishability of quantum channels that cannot be distinguished when
one is restricted to decohered input and output states. The studied problems
arise naturally in the presence of a superselection rule, allow one to quantify
the amount of information that can be encoded in phase degrees of freedom
(coherences), and are related to time-energy uncertainty relation. We present a
collection of results on both necessary and sufficient conditions for the
existence of perfectly distinguishable states (channels) that are
classically indistinguishable.Comment: 22 pages, 8 figures. Published versio
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