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Applied Physics Letters

Direct characterization of arbitrary multi-particle states with ancilla-only measurements

Zhiyuan Wang, Zijing Z. Zhang

Published Mar 30, 2026• 0 citations
Publisher

Abstract

The measurement of unknown quantum states is crucial in quantum information science. Standard quantum state tomography can retrieve information regarding unknown quantum states. However, as the number of qubits increases, the measurement basis required for standard tomography increases exponentially. When we are only interested in partial information of the quantum state, such as coherence and entanglement, global state reconstruction is not necessary. Therefore, direct characterization schemes are required to obtain the information of interest without complete state tomography. In this Letter, we present a circuit scheme with ancilla-only measurements for the direct characterization of multi-particle states that requires only four projection probabilities, independent of the system size. Ancilla-only measurements refer to a strategy where all readouts are on ancillas, never directly on the target qubits. Target state information is indirectly extracted via target–ancilla coupling. Moreover, our scheme can automatically reset the target qubits, thereby providing an immediately available quantum register for subsequent tasks and avoiding the target quantum system initialization required for the next task. Finally, numerical simulations and experimental verification were performed on a quantum cloud platform, confirming the validity of the theoretical scheme.

DOI
10.1063/5.0302536

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The measurement of unknown quantum states is crucial in quantum information science. Standard quantum state tomography can retrieve information regarding unknown quantum states. However, as the number of qubits increases, the measurement basis required for standard tomography increases exponentially. When we are only interested in partial information of the quantum state, such as coherence and entanglement, global state reconstruction is not necessary. Therefore, direct characterization schemes are required to obtain the information of interest without complete state tomography. In this Letter, we present a circuit scheme with ancilla-only measurements for the direct characterization of multi-particle states that requires only four projection probabilities, independent of the system size. Ancilla-only measurements refer to a strategy where all readouts are on ancillas, never directly on the target qubits. Target state information is indirectly extracted via target–ancilla coupling. Moreover, our scheme can automatically reset the target qubits, thereby providing an immediately available quantum register for subsequent tasks and avoiding the target quantum system initialization required for the next task. Finally, numerical simulations and experimental verification were performed on a quantum cloud platform, confirming the validity of the theoretical scheme.
Abstract In the field of quantum information, the acquisition of information for unknown quantum states is very important. When we only need to obtain specific elements of a state density matrix, the traditional quantum state tomography will become very complicated, because it requires a global quantum state reconstruction. Direct measurement of the quantum state allows us to obtain arbitrary specific matrix elements of the quantum state without state reconstruction, so direct measurement schemes have obtained extensive attention. Recently, some direct measurement schemes based on weak values have been proposed, but extra auxiliary states in these schemes are necessary and it will increase the complexity of the practical experiment. Meanwhile, the post-selection process in the scheme will reduce the utilization of resources. In order to avoid these disadvantages, a direct measurement scheme without auxiliary states is proposed in this paper. In this scheme, we achieve the direct measurement of quantum states by using quantum circuits, then we extend it to the measurement of general multi-particle states and complete the error analysis. Finally, when we take into account the dephasing of the quantum states, we modify the circuits and the modified circuits still work for the dephasing case.
Characterizing quantum states is essential for validating quantum devices, yet conventional quantum state tomography becomes prohibitively expensive as system size grows. Direct tomography offers a distinct route by enabling selective access to individual complex density-matrix elements, with a particular advantage for sparse target states and some verification tasks. Here we introduce a direct quantum state tomography scheme combining strong-measurement estimation with a fan-out coupling architecture. It enables mutually commuting interactions between system qubits and a single meter qubit, thereby achieving constant circuit depth, independent of system size. Notably, the involutory fan-out coupling reduces to the identity under repetition, enabling straightforward noise scaling for quantum error mitigation. We experimentally validate the scheme on a superconducting quantum processor via the IBM Quantum Platform, demonstrating four-qubit state reconstruction and single-circuit GHZ-state fidelity estimation up to 20 qubits with error mitigation. Consistent results with standard tomography and improved efficiency establish our scheme as a promising approach to reconstructing full quantum states and scalable verification tasks.
Characterising multi-time quantum processes is essential for analysing temporally correlated noise and for designing effective control and mitigation strategies. A complete operational description through multi-time process tomography requires an informationally complete set of probes, which necessarily includes non-deterministic intermediate operations. On present-day quantum devices, such operations are commonly implemented using mid-circuit measurements and reset, which are technologically limited and can introduce noise and overhead in terms of ancilla requirement. In this work, we study the minimal ancillary dimension required for complete characterisation of multi-time processes. We show that sequential interactions with a single qubit ancilla can generate an informationally complete family of correlated probes for processes of arbitrary length, without requiring mid-circuit measurements or reset. Our result provides a resource-efficient route for complete multi-time process tomography and establishes that one qubit of coherent ancillary memory suffices for full reconstruction of arbitrary multi-time dynamics.
Quantum process tomography (QPT) is a crucial technique for characterizing unknown quantum channels. However, traditional QPT methods encounter scalability problems as the particle numbers increase, requiring exponentially more state preparations and measurement operators. The characteristics of sparse target channels (e.g., multiqubit phase-shift gates) can be obtained by measuring only a few specific matrix elements without requiring global QPT. Therefore, direct quantum channel characterization is vital. This paper proposes a direct protocol for both qubit and qudit systems that extracts specific process matrix elements without full reconstruction. The measurement operator requirements remain independent of system size and dimensionality. Notably, the proposed protocol uses nondestructive measurements and preserves qubits after evolution through unknown processes for potential reuse, making it uniquely promising for applications such as real-time monitoring of noise processes in quantum error correction and real-time feedback control requiring quantum state preservation. To validate the theoretical correctness of our approach, we conducted experimental demonstrations of both the unitary and non-unitary processes of single qubits using a nuclear magnetic resonance system on the SpinQ quantum cloud platform. The experimental results confirmed the correctness and effectiveness of the proposed method.
The standard method of Quantum State Tomography (QST) relies on the measurement of a set of noncommuting observables, realized in a series of independent experiments. Ancilla Assisted QST (AAQST) proposed by Nieuwenhuizen and co-workers (Phys. Rev. Lett., 92, 120402 (2004)) greatly reduces the number of independent measurements by exploiting an ancilla register in a known initial state. In suitable conditions AAQST allows mapping out density matrix of an input register in a single experiment. Here we describe methods for explicit construction of AAQST experiments in multi-qubit registers. We also report nuclear magnetic resonance studies on AAQST of (i) a two- qubit input register using a one-qubit ancilla in an isotropic liquid-state system and (ii) a three-qubit input register using a two-qubit ancilla register in a partially oriented system. The experimental results confirm the effectiveness of AAQST in such many-qubit registers.
Abstract Quantum process tomography is an effective method for measuring the quantum channel parameters in the field of quantum information. However, standard quantum process tomography (SQPT) cannot obtain arbitrarily specific process–matrix elements because it requires a global reconstruction algorithm. Direct quantum tomography can be used to obtain specific matrix elements of interest without the need for a global reconstruction algorithm. Therefore, direct process quantum tomography (DQPT) has attracted widespread attention. DQPT based on weak measurements has been recently proposed. However, additional auxiliary states and post‐selection processes are necessary in these schemes, which increases the complexity of practical experiments and reduces the utilization of measurement resources. In this study, a DQPT protocol without the assistance of pointer states is proposed, which reduces the complexity of practical experiments. Subsequently, the scheme is generalized to arbitrary qubit systems and experimentally perform the protocol on a nuclear magnetic resonance (NMR) system provided by a quantum cloud platform. Finally, considering that when the qubit resources are insufficient, a superimposed coherent state is used as the pointer state to complete the direct characterization of a quantum process. The measurement protocol is easily scalable and integrated, laying the foundation for direct tomography on a chip.