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Quantum measurement incompatibility in subspaces [article]

Roope Uola, Tristan Kraft, Sébastien Designolle, Nikolai Miklin, Armin Tavakoli, Juha-Pekka Pellonpää, Otfried Gühne, Nicolas Brunner
2020 arXiv   pre-print
We consider the question of characterising the incompatibility of sets of high-dimensional quantum measurements. We introduce the concept of measurement incompatibility in subspaces.  ...  We identify three possible forms of incompatibility in subspaces: (i) incompressible incompatibility: measurements that become compatible in every subspace, (ii) fully compressible incompatibility: measurements  ...  Note that in contrast to truncating quantum states for which the normalisation, i.e., unit-trace property, can be altered, for POVMs the normalisation is unaltered when seen as measurements in the subspace  ... 
arXiv:2010.04048v1 fatcat:mmys2bpsprflvhxz4vtwrtzs3m

Using continuous measurement to protect a universal set of quantum gates within a perturbed decoherence-free subspace

Paulo E M F Mendonça, Marcelo A Marchiolli, Reginaldo d J Napolitano
2005 Journal of Physics A: Mathematical and General  
We consider a universal set of quantum gates encoded within a perturbed decoherence-free subspace of four physical qubits.  ...  We thus advance the idea of protecting or even creating a decoherence-free subspace for processing quantum information.  ...  We also aknowledge supports from the Millennium Institute for Quantum Information -Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil.  ... 
doi:10.1088/0305-4470/38/6/l04 fatcat:rlqhaefr7zgdfppisff3su5hme

High dimensional measurement device independent quantum key distribution on two dimensional subspaces [article]

Luca Dellantonio, Anders S. Sørensen, Davide Bacco
2018 pre-print
Quantum key distribution (QKD) provides ultimate cryptographic security based on the laws of quantum mechanics.  ...  This problem can be solved with measurement device independent QKD (mdi-QKD).  ...  As discussed below, the measurement projects the qubits into a two-dimensional subspace, which can be used for QKD.  ... 
doi:10.1103/physreva.98.062301 arXiv:1809.04405v1 fatcat:4dbtcydc3ngw7abwadekx4yiwq

Unavoidable decoherence in the quantum control of an unknown state

D. Kielpinski, R.A. Briggs, H.M. Wiseman
2013 Quantum Measurements and Quantum Metrology  
A common objective for quantum control is to force a quantum system, initially in an unknown state, into a particular target subspace.  ...  We show that if the subspace is required to be a decoherence-free subspace of dimension greater than 1, then such control must be decoherent.  ...  We have shown that all quantum control strategies that force an initially unknown state into a decoherence-free subspace can be reduced to a simple strategy using projective measurement followed by conditional  ... 
doi:10.2478/qmetro-2013-0001 fatcat:kahnfk2ww5defm2n6xm7y6iwca

Zeno subspace in quantum-walk dynamics

C. M. Chandrashekar
2010 Physical Review A. Atomic, Molecular, and Optical Physics  
We investigate the discrete-time quantum walk evolution under the influence of the periodic measurements in position subspace.  ...  We show that P(0, τ)^n > P(0, t) leading to the quantum Zeno effect in the position subspace when a parameter θ in the quantum coin operations and frequency of measurements is greater than the critical  ...  ZENO EFFECT IN SUBSPACE OF DISCRETE-TIME QUANTUM WALK In this section we outline the conditions for performing the measurements and using quantum coin parameters to observe the QZE in the subspace of the  ... 
doi:10.1103/physreva.82.052108 fatcat:tks34dbrivawjc2krxuwiningq

Quantum Zeno Dynamics Through Stochastic Protocols

Matthias M. Müller, Stefano Gherardini, Filippo Caruso
2017 Annalen der Physik  
Quantum Zeno Dynamics is the phenomenon that the observation or strong driving of a quantum system can freeze its dynamics to a subspace, effectively truncating the Hilbert space of the system.  ...  It represents the quantum version of the famous flying arrow Zeno paradox.  ...  When g → ∞, we obtain an ideal confinement of the quantum system in the measurement subspace.  ... 
doi:10.1002/andp.201600206 fatcat:ukf67jqw6ffeninc2mr36zatkq

Error mitigation for variational quantum algorithms through mid-circuit measurements [article]

Ludmila Botelho, Adam Glos, Akash Kundu, Jarosław Adam Miszczak, Özlem Salehi, Zoltán Zimborás
2021 arXiv   pre-print
For specific problems, valid quantum states have a unique structure as in the case of Fock states and W-states where the Hamming weight is fixed, and the evolution takes place in a smaller subspace of  ...  For the particular subspace of one-hot states, we propose a method that works by compressing the full Hilbert space to a smaller subspace, allowing projecting to the desired subspace without using any  ...  QEM aims not to recover the ideal quantum state but the ideal measurement outcome through post-processing the measurement results.  ... 
arXiv:2108.10927v2 fatcat:f4ff4ttrtrhpbcuz2f6lz3sifa

Non-Hermitian dynamics in the quantum Zeno limit

W. Kozlowski, S. F. Caballero-Benitez, I. B. Mekhov
2016 Physical Review A  
Frequent measurements of a quantum system lead to quantum Zeno dynamics where time evolution becomes confined to a subspace defined by the projections.  ...  Measurement is one of the most counter-intuitive aspects of quantum physics.  ...  In the Quantum Zeno regime projective measurements are made frequently confining the system dynamics to a subspace of the Hilbert space, called the Zeno subspace, spanned by eigenvectors degenerate to  ... 
doi:10.1103/physreva.94.012123 fatcat:7mqfee5ixrg5hk54qlrl36tbxa

Quantum-State Reconstruction by Maximizing Likelihood and Entropy

Yong Siah Teo, Huangjun Zhu, Berthold-Georg Englert, Jaroslav Řeháček, Zdeněk Hradil
2011 Physical Review Letters  
Quantum state reconstruction on a finite number of copies of a quantum system with informationally incomplete measurements does, as a rule, not yield a unique result.  ...  the von Neumann entropy functionals are maximized in order to systematically select the most-likely estimator with the largest entropy, that is the least-bias estimator, consistent with a given set of measurement  ...  This implies that the n >0 -dimensional subspace is spanned by the basis operators that uniquely specify the POM outcomes. We will coin this subspace the measurement subspace.  ... 
doi:10.1103/physrevlett.107.020404 pmid:21797584 fatcat:jzehv4hzqral5ildhy5ubafdzu

Observation of entanglement witnesses for orbital angular momentum states

M. Agnew, J. Leach, R.W. Boyd
2012 European Physical Journal D : Atomic, Molecular and Optical Physics  
These measurements demonstrate the degree of entanglement and therefore the suitability of the resulting subspaces for quantum information applications.  ...  Entanglement witnesses provide an efficient means of determining the level of entanglement of a system using the minimum number of measurements.  ...  Quantum tomography is one approach to determine the exact density matrix of a quantum state [10] [11] [12] [13] [14] [15] [16] ; however, tomography requires a large number of measurements, particularly  ... 
doi:10.1140/epjd/e2012-30057-9 fatcat:2bi2ynxserbvplenh6xxb5eea4

Crystallizing highly-likely subspaces that contain an unknown quantum state of light

Yong Siah Teo, Dmitri Mogilevtsev, Alexander Mikhalychev, Jaroslav Řeháček, Zdeněk Hradil
2016 Scientific Reports  
We provide a straightforward and numerically feasible procedure to uniquely determine the appropriate reconstruction subspace for any given unknown quantum state of light and measurement scheme.  ...  The procedure can be understood as the maximum-likelihood reconstruction for quantum subspaces, which is an analog to, and fully compatible with that for quantum states.  ...  contains the unknown quantum state and, at the same time, maximizes the (log-)likelihood with respect to the measured data.  ... 
doi:10.1038/srep38123 pmid:27905511 pmcid:PMC5131478 fatcat:hm6ri3qwjjdlpkgshjckgptmni

Measurement-Based Teleportation along Quantum Spin Chains

J. P. Barjaktarevic, R. H. McKenzie, J. Links, G. J. Milburn
2005 Physical Review Letters  
Within each of these subspaces, it is possible to take any superposition of states, and use projective measurements to perform unit fidelity teleportation.  ...  We consider teleportation of an arbitrary spin-1/2 target quantum state along the ground state of a quantum spin chain.  ...  Further, we have shown that if any quantum state belongs to a Bell subspace, then we may perform unit fidelity teleportation with it, using only measurements in the Bell basis.  ... 
doi:10.1103/physrevlett.95.230501 pmid:16384284 fatcat:bruuxz7zlfb2rfckq5wo7gpyw4

Perturbative approach for the dynamics of the quantum Zeno subspaces

Yi-Xin Chen, Zhuowen Fang
2004 Physical Review A. Atomic, Molecular, and Optical Physics  
In these examples, as the coupling constant of the interactions increases, the measurement keeps the system remaining in its initial subspace and the quantum Zeno effect takes place.  ...  In this paper we investigate the dynamics of the quantum Zeno subspaces which are the eigenspaces of the interaction Hamiltonian, belonging to different eigenvalues.  ...  These subspaces, which the measurement process is able to distinguish, are called quantum Zeno subspaces. Quantum zeno dynamics is not absolutely developed yet.  ... 
doi:10.1103/physreva.70.062102 fatcat:r4jr2krhlfb6np47zn7muowrwy

Incoherent control of locally controllable quantum systems

Daoyi Dong, Chenbin Zhang, Herschel Rabitz, Alexander Pechen, Tzyh-Jong Tarn
2008 Journal of Chemical Physics  
The results support the suggestion that projective measurements can serve as an effective control and local controllability information can be used to design control laws for quantum systems.  ...  An incoherent control scheme for state control of locally controllable quantum systems is proposed.  ...  Sugawara [38] studied quantum dynamics driven by continuous laser fields under the measurement process and explored the possibility of measurement-assisted quantum control.  ... 
doi:10.1063/1.2992557 pmid:19045172 fatcat:nkpwzvfuavfcjpmm24iu3n3qym

Multi-dimensional entanglement transport through single-mode fibre [article]

Jun Liu, Isaac Nape, Qianke Wang, Adam Valles, Jian Wang, Andrew Forbes
2019 arXiv   pre-print
We show high fidelity hybrid entanglement preservation down 250 m of SMF across multiple 2x2 dimensions, demonstrating quantum key distribution protocols, quantum state tomographies and quantum erasers  ...  achieve this by entangling the spin-orbit degrees of freedom of a bi-photon pair, passing the polarisation (spin) photon down the SMF while accessing multi-dimensional orbital angular momentum (orbital) subspaces  ...  (b) The measured mode spectrum of the = ±1 subspace and (c) the = ±2 subspace after transmitting through 250 m of SMF. FIG. 3 . 3 Quantum state tomography of hybrid multi-dimensional states.  ... 
arXiv:1904.03114v1 fatcat:5gaz4cvhmzae5cxbgpud32txre
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