Imprinting Complete Information about a Quantum Channel on its Output State

D’Ariano, Giacomo Mauro; Presti, Paoloplacido Lo

doi:10.1103/physrevlett.91.047902

Cited by 90 publications

(115 citation statements)

References 11 publications

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“…A few methods for QPT were developed, including the standard QPT [1,2], ancilla-assisted QPT [3,[7][8][9], direct characterization of quantum dynamics [10,11], and * Electronic address: xbwang@mail.tsinghua.edu.cn coherent-state QPT [12]. There are dozens of proposals and experimental realizations of QPT for systems with a few qubits.…”

Section: Introductionmentioning

confidence: 99%

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Efficient tomography of quantum-optical Gaussian processes probed with a few coherent states

Wang

et al. 2013

Phys. Rev. A

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An arbitrary quantum-optical process (channel) can be completely characterized by probing it with coherent states using the recently developed coherent-state quantum process tomography (QPT) [Lobino et al., Science 322, 563 (2008)]. In general, precise QPT is possible if an infinite set of probes is available. Thus, realistic QPT of infinite-dimensional systems is approximate due to a finite experimentally-feasible set of coherent states and its related energy-cut-off approximation. We show with explicit formulas that one can completely identify a quantum-optical Gaussian process just with a few different coherent states without approximations like the energy cut-off. For tomography of multimode processes, our method exponentially reduces the number of different test states, compared with existing methods.

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Section: Introductionmentioning

confidence: 99%

“…Such a process is fully characterized if the evolution of any input state ρ in is predictable: ρ out = ε(ρ in ). In general, QPT is very difficult to implement in high-dimensional spaces, and, more challengingly, in an infinite-dimensional space, such as a Fock space [9,12]. Recently, Ref.…”

Section: Introductionmentioning

confidence: 99%

Efficient tomography of quantum-optical Gaussian processes probed with a few coherent states

Wang

et al. 2013

Phys. Rev. A

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“…In principle, the input state of the system and ancilla can be prepared in either an entangled mixed state (entanglementassisted) or a separable mixed state. Intuitively, the input state in AAPT must be faithful enough to the map E such that by quantum state tomography on the outputs one can identify E completely and unambiguously [10]. This faithfulness condition can formalized.…”

Section: Ancilla-assisted Process Tomographymentioning

confidence: 99%

“…A further unavoidable step in indirect methods is the application of an inversion map on the final output data. Standard Quantum Process Tomography (SQPT) [1,5,6] and Ancilla-Assisted Process Tomography (AAPT) [7,8,9,10] belong to this class. On the other hand, in direct methods each experimental outcome directly provides information about properties of the underlying dynamics, without the need for state tomography.…”

Section: Introductionmentioning

confidence: 99%

Quantum-process tomography: Resource analysis of different strategies

2008

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Characterization of quantum dynamics is a fundamental problem in quantum physics and quantum information science. Several methods are known which achieve this goal, namely Standard Quantum Process Tomography (SQPT), Ancilla-Assisted Process Tomography (AAPT), and the recently proposed scheme of Direct Characterization of Quantum Dynamics (DCQD). Here, we review these schemes and analyze them with respect to some of the physical resources they require. Although a reliable figure-of-merit for process characterization is not yet available, our analysis can provide a benchmark which is necessary for choosing the scheme that is the most appropriate in a given situation, with given resources. As a result, we conclude that for quantum systems where two-body interactions are not naturally available, SQPT is the most efficient scheme. However, for quantum systems with controllable two-body interactions, the DCQD scheme is more efficient than other known QPT schemes in terms of the total number of required elementary quantum operations.

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“…Even if this operation is known to be unitary, it still needs Θ(4 n ) observables. Although many improvements and variants of QPT have been proposed [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], in general the resource consumption of this approach still grows quickly as the system becomes large.…”

Section: Introductionmentioning

confidence: 99%

Property testing of unitary operators

Wang

2011

Phys. Rev. A

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In this paper, we systematically study property testing of unitary operators. We first introduce a distance measure that reflects the average difference between unitary operators. Then we show that, with respect to this distance measure, the orthogonal group, quantum juntas (i.e. unitary operators that only nontrivially act on a few qubits of the system) and Clifford group can be all efficiently tested. In fact, their testing algorithms have query complexities independent of the system's size and have only one-sided error. Then we give an algorithm that tests any finite subset of the unitary group, and demonstrate an application of this algorithm to the permutation group. This algorithm also has one-sided error and polynomial query complexity, but it is unknown whether it can be efficiently implemented in general.

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Imprinting Complete Information about a Quantum Channel on its Output State

Cited by 90 publications

References 11 publications

Efficient tomography of quantum-optical Gaussian processes probed with a few coherent states

Efficient tomography of quantum-optical Gaussian processes probed with a few coherent states

Quantum-process tomography: Resource analysis of different strategies

Property testing of unitary operators

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