5,288 research outputs found
Variational Quantum Fidelity Estimation
Computing quantum state fidelity will be important to verify and characterize states prepared on a quantum computer. In this work, we propose novel lower and upper bounds for the fidelity F(ρ,σ) based on the “truncated fidelity'” F(ρ_m,σ) which is evaluated for a state ρ_m obtained by projecting ρ onto its mm-largest eigenvalues. Our bounds can be refined, i.e., they tighten monotonically with mm. To compute our bounds, we introduce a hybrid quantum-classical algorithm, called Variational Quantum Fidelity Estimation, that involves three steps: (1) variationally diagonalize ρ, (2) compute matrix elements of σ in the eigenbasis of ρ, and (3) combine these matrix elements to compute our bounds. Our algorithm is aimed at the case where σ is arbitrary and ρ is low rank, which we call low-rank fidelity estimation, and we prove that no classical algorithm can efficiently solve this problem under reasonable assumptions. Finally, we demonstrate that our bounds can detect quantum phase transitions and are often tighter than previously known computable bounds for realistic situations
Bounds of concurrence and their relation with fidelity and frontier states
The bounds of concurrence in [F. Mintert and A. Buchleitner, Phys. Rev. Lett.
98 (2007) 140505] and [C. Zhang \textit{et. al.}, Phys. Rev. A 78 (2008)
042308] are proved by using two properties of the fidelity. In two-qubit
systems, for a given value of concurrence, the states achieving the maximal
upper bound, the minimal lower bound or the maximal difference upper-lower
bound are determined analytically
Matrices of fidelities for ensembles of quantum states and the Holevo quantity
The entropy of the Gram matrix of a joint purification of an ensemble of K
mixed states yields an upper bound for the Holevo information Chi of the
ensemble. In this work we combine geometrical and probabilistic aspects of the
ensemble in order to obtain useful bounds for Chi. This is done by constructing
various correlation matrices involving fidelities between every pair of states
from the ensemble. For K=3 quantum states we design a matrix of root fidelities
that is positive and the entropy of which is conjectured to upper bound Chi.
Slightly weaker bounds are established for arbitrary ensembles. Finally, we
investigate correlation matrices involving multi-state fidelities in relation
to the Holevo quantity.Comment: 24 pages, 3 figure
Partitioned trace distances
New quantum distance is introduced as a half-sum of several singular values
of difference between two density operators. This is, up to factor, the metric
induced by so-called Ky Fan norm. The partitioned trace distances enjoy similar
properties to the standard trace distance, including the unitary invariance,
the strong convexity and the close relations to the classical distances. The
partitioned distances cannot increase under quantum operations of certain kind
including bistochastic maps. All the basic properties are re-formulated as
majorization relations. Possible applications to quantum information processing
are briefly discussed.Comment: 8 pages, no figures. Significant changes are made. New section on
majorization is added. Theorem 4.1 is extended. The bibliography is enlarged
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