Implementation of State Transfer Hamiltonians in Spin Chains with Magnetic Resonance Techniques

Cappellaro, Paola

doi:10.1007/978-3-642-39937-4_6

Cited by 9 publications

(13 citation statements)

References 189 publications

(316 reference statements)

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“…For such techniques, in particular in nuclear magnetic resonance (NMR), if the system one is probing consists of many spins, then the large dimension of the Hilbert space together with constraints on the measurements are such that full tomography is not possible. Still, one can obtain much useful information about the state by measuring the degree of coherence relative to the quantization axis [47]. If the system is quantized along theẑ axis, then coherence of order q of the state ρ is defined as the norm of the sum of the off-diagonal terms ρ m 1 m 2 |m 1 m 2 | with m 2 − m 1 = q, where |m is the eigenstate with eigenvalue m of Jẑ, the magnetic moment in theẑ direction [47].…”

Section: Introductionmentioning

confidence: 99%

“…If the system is quantized along theẑ axis, then coherence of order q of the state ρ is defined as the norm of the sum of the off-diagonal terms ρ m 1 m 2 |m 1 m 2 | with m 2 − m 1 = q, where |m is the eigenstate with eigenvalue m of Jẑ, the magnetic moment in theẑ direction [47]. 1 Measuring the quantum coherence of different orders is relatively straightforward and has been useful in many NMR experiments, in particular, in the context of quantum information processing, as well as in simulations of many-body dynamics (see, e.g., [47][48][49]). …”

Section: Introductionmentioning

confidence: 99%

“…III A 5 for a short review). In particular, the qth quantum coherence component in the language of [47] is the same as the mode-q component in the language of [8,9]. Furthermore, the Frobenius norm of the qth quantum coherence component, which can be measured in NMR experiments, provides lower and upper bounds on a measure of coherence studied in [8,9], which quantifies the asymmetry of a state in mode q [see Eq.…”

Section: Introductionmentioning

confidence: 99%

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How to quantify coherence: Distinguishing speakable and unspeakable notions

2016

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Quantum coherence is a critical resource for many operational tasks. Understanding how to quantify and manipulate it also promises to have applications for a diverse set of problems in theoretical physics. For certain applications, however, one requires coherence between the eigenspaces of specific physical observables, such as energy, angular momentum, or photon number, and it makes a difference which eigenspaces appear in the superposition. For others, there is a preferred set of subspaces relative to which coherence is deemed a resource, but it is irrelevant which of the subspaces appear in the superposition. We term these two types of coherence unspeakable and speakable, respectively. We argue that a useful approach to quantifying and characterizing unspeakable coherence is provided by the resource theory of asymmetry when the symmetry group is a group of translations, and we translate a number of prior results on asymmetry into the language of coherence. We also highlight some of the applications of this approach, for instance, in the context of quantum metrology, quantum speed limits, quantum thermodynamics, and nuclear magnetic resonance (NMR). The question of how best to treat speakable coherence as a resource is also considered. We review a popular approach in terms of operations that preserve the set of incoherent states, propose an alternative approach in terms of operations that are covariant under dephasing, and we outline the challenge of providing a physical justification for either approach. Finally, we note some mathematical connections that hold among the different approaches to quantifying coherence.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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How to quantify coherence: Distinguishing speakable and unspeakable notions

2016

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“…For larger spin chains N > 30, the differences of the two protocols will begin decreasing again until they become negligible due to the rapid decrease of fidelity with N . The present results have been presented in a generic framework so as to provide a benchmark case and guide for the implementation of quantum-statetransfer schemes in various experimental platforms (see [19,20] for a comprehensive summary of related experiments). Although the present analysis has been in terms of relative errors in the diagonal and off-diagonal terms of the Hamiltonian, if necessary, our performance plots can be converted to plots in terms of absolute errors, by rescaling accordingly the depicted standard deviations σ ε and σ J .…”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

Evaluation of the performance of two state-transfer Hamiltonians in the presence of static disorder

Pavlis

Nikolopoulos

Lambropoulos

2016

Quantum Inf Process

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We analyse the performance of two quantum-state-transfer Hamiltonians in the presence of diagonal and off-diagonal disorder, and in terms of different measures. The first Hamiltonian pertains to a fully-engineered chain and the second to a chain with modified boundary couplings. The task is to find which Hamiltonian is the most robust to given levels of disorder and irrespective of the input state. In this respect, it is shown that the performance of the two protocols are approximately equivalent.

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“…Pulsed control techniques in Nuclear Magnetic Resonance (NMR) have reached a high degree of maturity [53] and provide a platform to observe quantum dynamics and state transfer in spin chains [54,55]. The natural dipolar interactions between the nuclear spins can be tuned [56,57] and an effective "double-quantum" Hamiltonian (3) obtained.…”

Section: A Nmr-based Implementationmentioning

confidence: 99%

Optimal quench for distance-independent entanglement and maximal block entropy

2014

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We optimize a quantum walk of multiple fermions following a quench in a spin chain to generate near ideal resources for quantum networking. We first prove an useful theorem mapping the correlations evolved from specific quenches to the apparently unrelated problem of quantum state transfer between distinct spins. This mapping is then exploited to optimize the dynamics and produce large amounts of entanglement distributed in very special ways. Two applications are considered: the simultaneous generation of many Bell states between pairs of distant spins (maximal block entropy), or high entanglement between the ends of an arbitrarily long chain (distance-independent entanglement). Thanks to the generality of the result, we study its implementation in different experimental setups using present technology: NMR, ion traps and ultracold atoms in optical lattices.

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Implementation of State Transfer Hamiltonians in Spin Chains with Magnetic Resonance Techniques

Cited by 9 publications

References 189 publications

How to quantify coherence: Distinguishing speakable and unspeakable notions

How to quantify coherence: Distinguishing speakable and unspeakable notions

Evaluation of the performance of two state-transfer Hamiltonians in the presence of static disorder

Optimal quench for distance-independent entanglement and maximal block entropy

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