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arXiv:1210.0182 · Applied Physics Letters

Quantum-memory-assisted entropic uncertainty relation with a single nitrogen-vacancy center in diamond

Z. Xu, S. Q. Zhu, Wanli Yang

Published Dec 10, 2012• 24 citations
arXivHTMLPDF

Abstract

The limitation of simultaneous measurements of noncommuting observables can be eliminated when the measured particle is maximally entangled with a quantum memory. We present a proposal for testing this quantum-memory-assisted entropic uncertainty relation in a single nitrogen-vacancy (N-V) center in diamond only by local electronic measurements. As an application, this entropic uncertainty relation is used to witness entanglement between the electron and nuclear spins of the N-V center, which is close to reach the currently available technology.

DOI
10.1063/1.4771988

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The limitation of simultaneous measurements of noncommuting observables can be eliminated when the measured particle is maximally entangled with a quantum memory. We present a proposal for testing this quantum-memory-assisted entropic uncertainty relation in a single nitrogen-vacancy (N-V) center in diamond only by local electronic measurements. As an application, this entropic uncertainty relation is used to witness entanglement between the electron and nuclear spins of the N-V center, which is close to reach the currently available technology.
One unique feature of quantum mechanics is the Heisenberg uncertainty principle, which states that the outcomes of two incompatible measurements cannot simultaneously achieve arbitrary precision. In an information-theoretic context of quantum information, the uncertainty principle can be formulated as entropic uncertainty relations with two measurements for a quantum bit (qubit) in two-dimensional system. New entropic uncertainty relations are studied for a higher-dimensional quantum state with multiple measurements, and the uncertainty bounds can be tighter than that expected from two measurements settings and cannot result from qubits system with or without a quantum memory. Here we report the first room-temperature experimental testing of the entropic uncertainty relations with three measurements in a natural three-dimensional solid-state system: the nitrogen-vacancy center in pure diamond. The experimental results confirm the entropic uncertainty relations for multiple measurements. Our result represents a more precise demonstrating of the fundamental uncertainty principle of quantum mechanics.
One unique feature of quantum mechanics is the Heisenberg uncertainty principle, which states that the outcomes of two incompatible measurements cannot simultaneously achieve arbitrary precision. In an information-theoretic context of quantum information, the uncertainty principle can be formulated as entropic uncertainty relations with two measurements for a quantum bit (qubit) in two-dimensional system. New entropic uncertainty relations are studied for a higher-dimensional quantum state with multiple measurements, the uncertainty bounds can be tighter than that expected from two measurements settings and cannot result from qubits system with or without a quantum memory. Here we report the first room-temperature experimental testing of the entropic uncertainty relations with three measurements in a natural three-dimensional solid-state system: the nitrogen-vacancy center in pure diamond. The experimental results confirm the entropic uncertainty relations for multiple measurements. Our result represents a more precise demonstrating of the fundamental uncertainty principle of quantum mechanics.
In this paper, we investigate the dynamics of quantum memory-assisted entropic uncertainty, uncertainty-induced nonlocality and log-negativity entanglement of two nitrogen-vacancy centers (NVC). In particular, we are interested in analyzing two nitrogen-vacancy centered qubits coupled with two coherent nanocavities. We consider two different configurations of NVC qubits: when the qubits are prepared initially in separable and maximally entangled states. We demonstrate that coherent nanocavities can be successfully used to generate nonlocality and entanglement in the two NVC qubits while suppressing the associated entropic uncertainty. When the system is considered initially in separable two-NVC qubits, we show that the coupled coherent nanocavities successfully generate nonlocality and entanglement while avoiding the associated entropic uncertainty. The parameter’s adjustment determines the degree of entanglement, non-locality generation, and preservation. In comparison, we find entanglement more vulnerable to the decoherence and entropic uncertainty action between the two NVC qubits and nanocavities than the uncertainty-induced nonlocality. Furthermore, the NVC-qubits coupled with two coherent nanocavities promote entanglement’s sudden birth and death phenomena. This study contributes to the quantum mechanical protocols requiring the robust practical generation of entanglement and nonlocality as well as the related information preservation for the increased efficiency of quantum devices.
This work investigates the applicability of the nitrogen-vacancy (NV) defect center in diamond for quantum computation and metrology purposes. The NV center is a molecule like defect in the diamond lattice which is optically active and possesses an electron spin in its ground state. The spin can be used as a quantum bit and as a field sensor. The NV center has three major properties enabling individual control of single defects. Its optical properties depend on the spin state, the spin can be polarized optically and the spin state has an exceptionally long lifetime. Single NV centers can be controlled by optical and microwave radiation. Generally, the research on individually controllable quantum systems is not only motivated by quantum computation and communication. With the ongoing miniaturization nowadays electronic and electro-optic devices will soon reach the limit of single quantum building blocks. While in these applications the full complexity of single quantum systems might not be needed, small sensors based on single atoms or molecules might very well take advantage of the susceptibility of quantum coherences to environmental conditions. Major challenges for all approaches towards single quantum system control are the individual addressing, the measurement of the quantum state and the protection of quantum coherence from environmental noise. Today, there is a variety of systems (including the NV center) that allow control on the single quantum level. These are for example single photons, single ions and atoms in traps, single spins in semiconductors or single molecules in solid state systems. Rather mesoscopic examples are superconducting devices, nanomechanical oscillators or surface plasmon polaritons. Regarding the NV center it has been shown that the magnetic moment of its electron spin allows individual sensing and coupling to other surrounding electron and nuclear spins. Especially single nuclear spins were shown to be exceptional quantum memories. In this work small quantum registers of up to 5 spins have been used to test major requirements for a feasible quantum processor. Therefore, mainly artificially created high purity diamond samples with controlled spin and impurity concentration were used. The NV centers were either grown in or created via ion implantation techniques in a controlled fashion. As a first requirement for quantum computation entanglement among up to three spins has been generated and was verified by quantum state tomography. This proves the access of the full Hilbert space. Especially, entanglement among nuclear spins was very long-living. In further experiments this processor was used for first quantum algorithms like super-dense coding and the Deutsch algorithm. In addition, this work demonstrates new methods to initialize nuclear spin qubits into a desired quantum state. This is particularly important as improper initialization inhibits quantum computation. One of these methods is related to dynamic nuclear spin polarization and the other to measurement based state preparation. Nuclear spins in the diamond lattice originate mainly from the C-13 isotope. By artificially altering its content the influence on the NV center spin was investigated. The coherence times of the NV center were increasing inversely with the nuclear spin density. Even increasing nuclear spin density to offer more nuclear spin qubits to an operational quantum register was possible. As an alternative route of scaling up the quantum register pairs of closely spaced NV centers were investigated. For the first time two qubit gates among two NV centers mediated by magnetic dipolar coupling have been realized. Furthermore the sensing ability was demonstrated by measuring the relative distance of the two centers (10 nm) with sub-nm precision. Eventually, this work contains new insight into the electronically excited state of the NV center which allowed a more advanced control of the electron and nuclear spins. A comparably high magnetic field was used to decouple electron and nuclear spins. Finally, this allowed quantum nondemolition measurements on single nuclear spins which manifests in the observation of quantum jumps. The new insight was used to drastically improve the performance of quantum state readout. Summarizing, it was shown that single NV centers and proximal nuclear spins form versatile small quantum registers which can be interconnected with neighboring such NV quantum registers. Although the number of qubits used in this work is still small the experimental results propose a way of how to proceed when building a quantum computer. Regarding quantum metrology, however, the use of such a small register which can sense fields and store and process the results would already outperform a single NV electron spin by orders of magnitude.
Electron spin echoes were performed on nitrogen-vacancy $(\mathrm{N}\ensuremath{-}V)$ centers in diamond using optical polarization and detection and 35 GHz microwave control. The experiments demonstrate an approach to quantum information in the solid state. A phase memory time of $3.6 \ensuremath{\mu}\mathrm{s}$ was measured, and coupling of the electronic spin to the 14N{}^{14}\mathrm{N}14N nuclear spin was observed. Because of the favorable properties of the $\mathrm{N}\ensuremath{-}V$ center, interesting extensions of these single-qubit operations can be proposed.
The measurement outcomes of two incompatible observables on a particle can be precisely predicted when it is maximally entangled with a quantum memory. In this work, we explore the behavior of the quantum-memory-assisted entropic uncertainty relation under the influence of local unital and nonunital noisy channels. For a class of Bell-diagonal states, we demonstrate that while the unital noises only increase the amount of uncertainty, the amplitude-damping nonunital noises may reduce the amount of uncertainty in the long-time limit. The mechanism behind this phenomenon is also explored by using two dissimilar methods.