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Chinese Control Conference (CCC)

Information via parallel and antiparallel quantum states

Hongting Song

Published Jul 1, 2017• 0 citations
Publisher

Abstract

We investigate the properties of two particular sets of separable two-qubit states with maximally mixed marginals, named parallel states and antiparallel states respectively. Although these two sets of states are prepared by the same type of quantum operations acting on classically correlated states with equal classical correlations, they share different properties. By comparing two fundamental figures of merit based on quantum correlations and quantum Fisher information for accessing information quality, the superiority of parallel states over antiparallel ones is investigated. This is different from the previous results that antiparallel state turns out to be more effective in the tasks such as sending unknown direction information. The amount of the information that can be extracted from the local measurements is also presented, which turns out to be the same for these two states. This work reveals new aspects of information encoding and extraction problem.

DOI
10.23919/chicc.2017.8028918

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We investigate the properties of two particular sets of separable two-qubit states with maximally mixed marginals, named parallel states and antiparallel states respectively. Although these two sets of states are prepared by the same type of quantum operations acting on classically correlated states with equal classical correlations, they share different properties. By comparing two fundamental figures of merit based on quantum correlations and quantum Fisher information for accessing information quality, the superiority of parallel states over antiparallel ones is investigated. This is different from the previous results that antiparallel state turns out to be more effective in the tasks such as sending unknown direction information. The amount of the information that can be extracted from the local measurements is also presented, which turns out to be the same for these two states. This work reveals new aspects of information encoding and extraction problem.
We investigate the correlation properties of separable two-qubit states with maximally mixed marginals. These states are divided to two sets with the same geometric quantum correlation. However, a closer scrutiny of these states reveals a profound difference between their quantum correlations as measured by more probing measures. Although these two sets of states are prepared by the same type of quantum operations acting on classically correlated states with equal classical correlations, the amount of final quantum correlation is different. We investigate this difference and trace it back to the hidden classical correlation which exists in their preparation process. We also compare these states with regard to their usefulness for entanglement distribution and their robustness against noise.
Entanglement has been studied extensively for unveiling the mysteries of non-classical correlations between quantum systems. In the bipartite case, there are well known measures for quantifying entanglement such as concurrence, relative entropy of entanglement (REE) and negativity, which cannot be increased via local operations. It was found that for sets of non-maximally entangled states of two qubits, comparing these entanglement measures may lead to different entanglement orderings of the states. On the other hand, although it is not an entanglement measure and not monotonic under local operations, due to its ability of detecting multipartite entanglement, quantum Fisher information (QFI) has recently received an intense attraction generally with entanglement in the focus. In this work, we revisit the state ordering problem of general two qubit states. Generating a thousand random quantum states and performing an optimization based on local general rotations of each qubit, we calculate the maximal QFI for each state. We analyze the maximized QFI in comparison with concurrence, REE and negativity and obtain new state orderings. We show that there are pairs of states having equal maximized QFI but different values for concurrence, REE and negativity and vice versa.
We built a new set of suitable measures of correlations for bipartite quantum states based upon a recently introduced theoretical framework [Bussandri et al. in Quantum Inf. Proc. 18:57, 2019]. We applied these measures to examine the behavior of correlations in two-qubit states with maximally mixed marginals independently interacting with non-dissipative decohering environments in different dynamical scenarios of physical relevance. In order to get further insight about the physical meaning of the behavior of these correlation measures we compared our results with those obtained by means of well-known correlation measures such as quantum mutual information and quantum discord. On one hand, we found that the behaviors of total and classical correlations, as assessed by means of the measures introduced in this work, are qualitatively in agreement with the behavior displayed by quantum mutual information and the measure of classical correlations typically used to calculate quantum discord. We also found that the optimization of all the measures of classical correlations depends upon a single parameter and the optimal value of this parameter turns out to be the same in all cases. On the other hand, regarding the measures of quantum correlations used in our studies, we found that in general their behavior does not follow the standard quantum discord D . As the quantification by means of standard quantum discord and the measures of quantum correlations introduced in this work depends upon the assumption that total correlations are additive, our results indicate that this property needs a deeper and systematic study in order to gain a further understanding regarding the possibility to obtain reliable quantifiers of quantum correlations within this additive scheme.
Fisher information appears in quantum theory in two mathematically distinct settings: as a classical probability functional in variational reconstructions of Schrodinger dynamics and as the quantum Fisher metric of parameterized density operators. Here we examine how far these roles can be connected without identifying the two objects. Starting from a Hamilton-Jacobi ensemble action, we recover the Fisher term that generates the quantum potential and isolate its contribution to the kinetic-energy expectation. We then analyze the quantum Fisher information matrix (QFIM) of bipartite states. For any pure two-qubit state, the optimized magnitude of the off-diagonal QFIM element for normalized local generators equals the concurrence, while a collective phase generator yields FQ = 4 C^2. Extending the optimized pure-state quantity by a convex roof gives an exact identity with Wootters concurrence for arbitrary mixed two-qubit states. This differs from evaluating the QFIM directly on a mixed density operator: for Werner states the raw optimized cross-QFIM is 2 p^2/(1 + p) and remains nonzero inside the separable region. The gap between the raw and convex-roof quantities therefore isolates, for this family, correlation geometry not captured by entanglement. Finally, in a two-path interferometer with a which-way marker, the optimal phase Fisher information available from local output statistics is I_phi^opt = V^2. These results place probability-gradient energy, bipartite correlation geometry, entanglement, and decoherence-induced loss of local phase sensitivity in a common mathematical setting while preserving the distinctions between classical Fisher information, QFIM geometry, Bell nonlocality, and global phase quantization.
Antiparallel spins are superior in orienteering to parallel spins. This intriguing phenomenon is tied to entanglement associated with quantum measurements rather than quantum states. Using photonic systems, we experimentally realize the optimal orienteering protocols based on parallel spins and antiparallel spins, respectively. The optimal entangling measurements for decoding the direction information from parallel spins and antiparallel spins are realized using photonic quantum walks, which is a useful idea that is of wide interest in quantum information processing and foundational studies. Our experiments clearly demonstrate the advantage of antiparallel spins over parallel spins in orienteering. In addition, entangling measurements can extract more information than local measurements even if no entanglement is present in the quantum states.