Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1407.3448 · Physical Review A

Experimental construction of generic three-qubit states and their reconstruction from two-party reduced states on an NMR quantum information processor

Shruti Dogra, Kavita Dorai, Arvind

Published Feb 17, 2015• 40 citations
arXivHTMLPDF

Abstract

We experimentally explore the state space of three qubits on a nuclear magnetic resonance (NMR) quantum-information processor. We construct a scheme to experimentally realize a canonical form for general three-qubit states up to single-qubit unitaries. This form involves a nontrivial combination of Greenberger-Horne-Zeilinger (GHZ) and $W$-type maximally entangled states of three qubits. The general circuit that we have constructed for the generic state reduces to those for GHZ and $W$ states as special cases. The experimental construction of a generic state is carried out for a nontrivial set of parameters and the good fidelity of preparation is confirmed by complete state tomography. The GHZ and $W$ states are constructed as special cases of the general experimental scheme. Further, we experimentally demonstrate a curious fact about three-qubit states, where for almost all pure states, the two-qubit reduced states can be used to reconstruct the full three-qubit state. For the case of a generic state and for the $W$ state, we demonstrate this method of reconstruction by comparing it to the directly tomographed three-qubit state.

DOI
10.1103/physreva.91.022312

Related papers

Experimental construction of a W superposition state and its equivalence to the Greenberger-Horne-Zeilinger state under local filtration

Debmalya Das, Shruti Dogra, Kavita Dorai +1 more

We experimentally construct a three-qubit entangled $W$ superposition $(W\overline{W})$ state on an NMR quantum information processor. We give a measurement-based filtration protocol for the invertible local operation (ILO) that converts the $W\overline{W}$ state to the Greenberger-Horne-Zeilinger (GHZ) state, using a register of three ancilla qubits. Further we implement an experimental protocol to reconstruct full information about the three-party $W\overline{W}$ state using only two-party reduced density matrices. An intriguing fact unearthed recently is that the $W\overline{W}$ state, which is equivalent to the GHZ state under an ILO, is in fact reconstructible from its two-party reduced density matrices, unlike the GHZ state. We hence demonstrate that, although the $W\overline{W}$ state is interconvertible with the GHZ state, it stores entanglement very differently.

arXiv:1504.04856•Physical Review A•Aug 5, 2015•28 citations

Experimental classification of entanglement in arbitrary three-qubit pure states on an NMR quantum information processor

Amandeep Singh, Harpreet Singh, Kavita Dorai +1 more

We undertake experimental detection of the entanglement present in arbitrary three-qubit pure quantum states on an NMR quantum information processor. Measurements of only four observables suffice to experimentally differentiate between the six classes of states which are inequivalent under stochastic local operation and classical communication. The experimental realization is achieved by mapping the desired observables onto Pauli $z$ operators of a single qubit, which is directly amenable to measurement. The detection scheme is applied to known entangled states as well as to states randomly generated using a generic scheme that can construct all possible three-qubit states. The results are substantiated via direct full quantum state tomography as well as via negativity calculations and the comparison suggests that the protocol is indeed successful in detecting tripartite entanglement without requiring any a priori information about the states.

arXiv:1804.09320•Physical Review A•Sep 4, 2018•24 citations

NMR Greenberger–Horne–Zeilinger states

Raymond Laflamme, E. Knill, Wojciech Hubert Zurek +2 more

We describe the creation of a Greenberger–Horne–Zeilinger (GHZ) state of the form (|00} + |111})/✓2 (three maximally entangled quantum bits) using Nuclear Magnetic Resonance (NMR). We have successfully carried out the experiment using the proton and carbon spins of trichloroethylene, and confirmed the result using state tomography. We have thus extended the space of entangled quantum states explored systematically to three quantum bits, an essential step for quantum computation.

arXiv:quant-ph/9709025•Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Aug 15, 1998•139 citations

Experimental demonstration of selective quantum process tomography on an NMR quantum information processor

Akshay Vijay Gaikwad, Diksha Rehal, Amandeep Singh +2 more

We present the NMR implementation of a scheme for selective and efficient quantum process tomography without ancilla. We generalize this scheme such that it can be implemented efficiently using only a set of measurements involving product operators. The method allows us to estimate any element of the quantum process matrix to a desired precision, provided a set of quantum states can be prepared efficiently. Our modified technique requires fewer experimental resources as compared to the standard implementation of selective and efficient quantum process tomography, as it exploits the special nature of NMR measurements to allow us to compute specific elements of the process matrix by a restrictive set of subsystem measurements. To demonstrate the efficacy of our scheme, we experimentally tomograph the processes corresponding to ``no operation,'' a controlled-NOT (CNOT), and a controlled-Hadamard gate on a two-qubit NMR quantum information processor, with high fidelities.

arXiv:1707.06739•Physical Review A•Feb 7, 2018•36 citations

Three-qubit W state tomography via full and marginal state reconstructions on ibm_osaka

Humera Talath, Govindaraja B.P., Divyamani B.G. +3 more

Abstract We present a three-qubit quantum state tomography scheme requiring a set of 17 measurements, significantly reducing the experimental overhead compared to the conventional 63 Pauli measurements. Using IBM's 127-qubit open-access quantum processor \texttt{ibm\textunderscore{osaka}}, we prepare the three-qubit W state and employ our tomography scheme to reconstruct it. Additionally, we implement a two-qubit tomography protocol, involving a set of 7 measurements, on \texttt{ibm\textunderscore{osaka}} to reconstruct {\em two} of the two-qubit marginals of the W state. This serves as a {\em proof-of-principle} demonstration of the well-known theoretical result that any two of the two-qubit reduced density matrices can uniquely determine most of the whole three-qubit pure states. We show that the fidelity of the W-state reconstructed from its two-qubit subsystems is consistently larger than that obtained from the full three-qubit tomography, highlighting the practical advantage of the subsystem-based tomography approach.

arXiv:2507.02849•Quantum Information Processing•Oct 22, 2025•0 citations

Microscopic analogs of the Greenberger-Horne-Zeilinger experiment on an NMR quantum computer

Ushio Sakaguchi, Hiroshi Ozawa, Chikara Amano +1 more

A scheme is proposed to implement microscopic analogs of the Greenberger-Horne-Zeilinger experiment, as described by Lloyd, on a nuclear magnetic resonance (NMR) quantum computer. This scheme includes how to prepare the effective pure spin state |0000〉 (a state with all the spins pointing along the direction of the magnetic field) from a state at thermal equilibrium, how to transform it into states of the form, e.g., $(|000〉\ensuremath{-}|111〉)|0〉$ (which comprises the first three spins in an entangled state and the fourth register-spin), and how to measure the eigenvalue of the operator product like ${\ensuremath{\sigma}}_{x}^{1}{\ensuremath{\sigma}}_{y}^{2}{\ensuremath{\sigma}}_{y}^{3}$ for such three-spin entangled states, where ${\ensuremath{\sigma}}^{i}$ is the Pauli matrix for the $i\mathrm{th}$ spin, and store the result on the fourth spin. Also proposed is a general method to implement the controlled-not gate, an essential gate for any quantum algorithm, on n-qubit NMR quantum computers with $n>~4.$

Physical Review A•Sep 1, 1999•52 citations
We experimentally explore the state space of three qubits on a nuclear magnetic resonance (NMR) quantum-information processor. We construct a scheme to experimentally realize a canonical form for general three-qubit states up to single-qubit unitaries. This form involves a nontrivial combination of Greenberger-Horne-Zeilinger (GHZ) and WWW-type maximally entangled states of three qubits. The general circuit that we have constructed for the generic state reduces to those for GHZ and WWW states as special cases. The experimental construction of a generic state is carried out for a nontrivial set of parameters and the good fidelity of preparation is confirmed by complete state tomography. The GHZ and WWW states are constructed as special cases of the general experimental scheme. Further, we experimentally demonstrate a curious fact about three-qubit states, where for almost all pure states, the two-qubit reduced states can be used to reconstruct the full three-qubit state. For the case of a generic state and for the WWW state, we demonstrate this method of reconstruction by comparing it to the directly tomographed three-qubit state.
We experimentally construct a three-qubit entangled WWW superposition (WW‾)(W\overline{W})(WW) state on an NMR quantum information processor. We give a measurement-based filtration protocol for the invertible local operation (ILO) that converts the WW‾W\overline{W}WW state to the Greenberger-Horne-Zeilinger (GHZ) state, using a register of three ancilla qubits. Further we implement an experimental protocol to reconstruct full information about the three-party WW‾W\overline{W}WW state using only two-party reduced density matrices. An intriguing fact unearthed recently is that the WW‾W\overline{W}WW state, which is equivalent to the GHZ state under an ILO, is in fact reconstructible from its two-party reduced density matrices, unlike the GHZ state. We hence demonstrate that, although the WW‾W\overline{W}WW state is interconvertible with the GHZ state, it stores entanglement very differently.
We undertake experimental detection of the entanglement present in arbitrary three-qubit pure quantum states on an NMR quantum information processor. Measurements of only four observables suffice to experimentally differentiate between the six classes of states which are inequivalent under stochastic local operation and classical communication. The experimental realization is achieved by mapping the desired observables onto Pauli zzz operators of a single qubit, which is directly amenable to measurement. The detection scheme is applied to known entangled states as well as to states randomly generated using a generic scheme that can construct all possible three-qubit states. The results are substantiated via direct full quantum state tomography as well as via negativity calculations and the comparison suggests that the protocol is indeed successful in detecting tripartite entanglement without requiring any a priori information about the states.
We present the NMR implementation of a scheme for selective and efficient quantum process tomography without ancilla. We generalize this scheme such that it can be implemented efficiently using only a set of measurements involving product operators. The method allows us to estimate any element of the quantum process matrix to a desired precision, provided a set of quantum states can be prepared efficiently. Our modified technique requires fewer experimental resources as compared to the standard implementation of selective and efficient quantum process tomography, as it exploits the special nature of NMR measurements to allow us to compute specific elements of the process matrix by a restrictive set of subsystem measurements. To demonstrate the efficacy of our scheme, we experimentally tomograph the processes corresponding to ``no operation,'' a controlled-NOT (CNOT), and a controlled-Hadamard gate on a two-qubit NMR quantum information processor, with high fidelities.
Abstract We present a three-qubit quantum state tomography scheme requiring a set of 17 measurements, significantly reducing the experimental overhead compared to the conventional 63 Pauli measurements. Using IBM's 127-qubit open-access quantum processor \texttt{ibm\textunderscore{osaka}}, we prepare the three-qubit W state and employ our tomography scheme to reconstruct it. Additionally, we implement a two-qubit tomography protocol, involving a set of 7 measurements, on \texttt{ibm\textunderscore{osaka}} to reconstruct {\em two} of the two-qubit marginals of the W state. This serves as a {\em proof-of-principle} demonstration of the well-known theoretical result that any two of the two-qubit reduced density matrices can uniquely determine most of the whole three-qubit pure states. We show that the fidelity of the W-state reconstructed from its two-qubit subsystems is consistently larger than that obtained from the full three-qubit tomography, highlighting the practical advantage of the subsystem-based tomography approach.
A scheme is proposed to implement microscopic analogs of the Greenberger-Horne-Zeilinger experiment, as described by Lloyd, on a nuclear magnetic resonance (NMR) quantum computer. This scheme includes how to prepare the effective pure spin state |0000〉 (a state with all the spins pointing along the direction of the magnetic field) from a state at thermal equilibrium, how to transform it into states of the form, e.g., $(|000〉\ensuremath{-}|111〉)|0〉$ (which comprises the first three spins in an entangled state and the fourth register-spin), and how to measure the eigenvalue of the operator product like ${\ensuremath{\sigma}}_{x}^{1}{\ensuremath{\sigma}}_{y}^{2}{\ensuremath{\sigma}}_{y}^{3}$ for such three-spin entangled states, where ${\ensuremath{\sigma}}^{i}$ is the Pauli matrix for the ithi\mathrm{th}ith spin, and store the result on the fourth spin. Also proposed is a general method to implement the controlled-not gate, an essential gate for any quantum algorithm, on n-qubit NMR quantum computers with n> 4.n>~4.n> 4.