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arXiv:1211.2491 · Physical Review A

Quantum dissonance is rejected in an overlap measurement scheme

Chang‐shui Yu, Jun Zhang, Heng Fan

Published Nov 13, 2012• 9 citations
arXivHTMLPDF

Abstract

The overlap measurement scheme accomplishes the evaluation of the overlap of two input quantum states by only measuring an introduced auxiliary qubit, irrespective of the complexity of the two input states. We find a counterintuitive phenomenon that no quantum dissonance can be found in the process of overlap measurement scheme, even though the auxiliary qubit might be entangled, classically correlated, or even uncorrelated with the two input states based on different types of input states. In principle, this provides an opposite but supplementary example to the remarkable algorithm of the deterministic quantum computation with one qubit in which no entanglement is present but quantum dissonance is necessary. Finally, we consider a simple overlap measurement model to demonstrate the continuous change (including potential sudden death of quantum discord) of the input states from entangled to product states by only adjusting some initial parameters.

DOI
10.1103/physreva.86.052317

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The overlap measurement scheme accomplishes the evaluation of the overlap of two input quantum states by only measuring an introduced auxiliary qubit, irrespective of the complexity of the two input states. We find a counterintuitive phenomenon that no quantum dissonance can be found in the process of overlap measurement scheme, even though the auxiliary qubit might be entangled, classically correlated, or even uncorrelated with the two input states based on different types of input states. In principle, this provides an opposite but supplementary example to the remarkable algorithm of the deterministic quantum computation with one qubit in which no entanglement is present but quantum dissonance is necessary. Finally, we consider a simple overlap measurement model to demonstrate the continuous change (including potential sudden death of quantum discord) of the input states from entangled to product states by only adjusting some initial parameters.
We study the procedure for sequential unambiguous state discrimination. A qubit is prepared in one of two possible states and measured by two observers Bob and Charlie sequentially. A necessary condition for the state to be unambiguously discriminated by Charlie is the absence of entanglement between the principal qubit, prepared by Alice, and Bob's auxiliary system. In general, the procedure for both Bob and Charlie to recognize between two nonorthogonal states conclusively relies on the availability of quantum discord which is precisely the quantum dissonance when the entanglement is absent. In Bob's measurement, the left discord is positively correlated with the information extracted by Bob, and the right discord enhances the information left to Charlie. When their product achieves its maximum the probability for both Bob and Charlie to identify the state achieves its optimal value.
The processes for decreasing probabilistically and increasing deterministically the overlap between two quantum states must be assisted by an auxiliary quantum system. The probabilistic scheme is implemented through a unitary-reduction process, while the deterministic one is accomplished only with a joint unitary transformation. In both schemes a unitary operation is responsible for coupling the two involved systems thus introducing correlation between them. In this work we study the quantum correlations required to achieve the probabilistic scheme with optimal probability, and we characterize the quantum correlation involved in the deterministic procedure. We find a that both schemes can be accomplished with quantum discord and without entanglement. In addition, we propose a physical implementation of the probabilistic scheme with twin photons generated in the process of spontaneous parametric down-conversion. The states are encoded in the polarization of a single photon and the auxiliary system becomes its propagation path; the second photon is used for heralded detection.
A fundamental problem in quantum information is to explore what kind of quantum correlations is responsible for successful completion of a quantum information procedure. Here we study the roles of entanglement, discord, and dissonance needed for optimal quantum state discrimination when the latter is assisted with an auxiliary system. In such process, we present a more general joint unitary transformation than the existing results. The quantum entanglement between a principal qubit and an ancilla is found to be completely unnecessary, as it can be set to zero in the arbitrary case by adjusting the parameters in the general unitary without affecting the success probability. This result also shows that it is quantum dissonance that plays as a key role in assisted optimal state discrimination and not quantum entanglement. A necessary criterion for the necessity of quantum dissonance based on the linear entropy is also presented. PACS numbers: 03.65.Ta, 03.67.Mn, 42.50.Dv.
A fundamental problem in quantum information is to explore the roles of different quantum correlations in a quantum information procedure. Recent work [Phys. Rev. Lett., 107 (2011) 080401] shows that the protocol for assisted optimal state discrimination (AOSD) may be implemented successfully without entanglement, but with another correlation, quantum dissonance. However, both the original work and the extension to discrimination of ddd states [Phys. Rev. A, 85 (2012) 022328] have only proved that entanglement can be absent in the case with equal a \emph{priori} probabilities. By improving the protocol in [Sci. Rep., 3 (2013) 2134], we investigate this topic in a simple case to discriminate three nonorthogonal states of a qutrit, with positive real overlaps. In our procedure, the entanglement between the qutrit and an auxiliary qubit is found to be completely unnecessary. This result shows that the quantum dissonance may play as a key role in optimal state discrimination assisted by a qubit for more general cases.
Quantum channel identification, a standard problem in quantum metrology, is the task of estimating parameter(s) of a quantum channel. We investigate dissonance (quantum discord in the absence of entanglement) as an aid to quantum channel identification and find evidence for dissonance as a resource for quantum information processing. We consider the specific case of dissonant Bell-diagonal probes of the qubit depolarizing channel, using quantum Fisher information as a measure of statistical information extracted by the probe. In this setting dissonant quantum probes yield more statistical information about the depolarizing probability than do corresponding probes without dissonance and greater dissonance yields greater information. This effect only operates consistently when we control for classical correlation between the probe and its ancilla and the joint and marginal purities of the ancilla and probe.
It is shown that the dissonance, a quantum correlation which is equal to quantum discord for separable state, is required for assisted optimal state discrimination. We find that only one side discord is required in the optimal process of assisted state discrimination, while another side discord and entanglement is not necessary. We confirm that the quantum discord, which is asymmetric depending on local measurements, is a resource for assisted state discrimination. With the absence of entanglement, we give the necessary and sufficient condition for vanishing one side discord in assisted state discrimination for a class of ddd nonorthogonal states. As a by-product, we find that the positive-partial-transposition condition is the necessary and sufficient condition for the separability of a class of $2\ifmmode\times\else\texttimes\fi{}d$ states.