Experimental Minimum-Error Quantum-State Discrimination in High Dimensions

Solís-Prosser, M. A.; Fernandes, Mário Foganholi; Jiménez, Omar; Delgado, A.; Neves, Leonardo

doi:10.1103/physrevlett.118.100501

Cited by 55 publications

(50 citation statements)

References 64 publications

(100 reference statements)

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“…Experimental demonstration of high-dimensional quantum communication advantage.-We present an experimental demonstration of the advantages of single-system quantum communication in the considered CCPs for d = 6, ..., 10. In our experiment, d-dimensional quantum systems are encoded into the linear transverse momentum of single photons transmitted by programmable diffractive apertures, which nowadays is a standard technique used for high-dimensional quantum information processing [44][45][46][47][48][49][50][51][52][53][54].…”

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confidence: 99%

High-Dimensional Quantum Communication Complexity beyond Strategies Based on Bell’s Theorem

et al. 2018

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Quantum resources can improve communication complexity problems (CCPs) beyond their classical constraints. One quantum approach is to share entanglement and create correlations violating a Bell inequality, which can then assist classical communication. A second approach is to resort solely to the preparation, transmission and measurement of a single quantum system; in other words quantum communication. Here, we show the advantages of the latter over the former in high-dimensional Hilbert space. We focus on a family of CCPs, based on facet Bell inequalities, study the advantage of high-dimensional quantum communication, and realise such quantum communication strategies using up to ten-dimensional systems. The experiment demonstrates, for growing dimension, an increasing advantage over quantum strategies based on Bell inequality violation. For sufficiently high dimensions, quantum communication also surpasses the limitations of the post-quantum Bell correlations obeying only locality in the macroscopic limit. Surprisingly, we find that the advantages are tied to the use of measurements that are not rank-one projective. We provide an experimental semi-device-independent falsification of such measurements in Hilbert space dimension six.Introduction.-Communication complexity problems (CCPs) are tasks in which distant parties hold local data, the collection of which is needed for a computation of their interest. To make the computation possible, the parties communicate with each other. However, the amount of communication is limited and therefore not all data can be sent. The CCP consist in parties adopting an efficient communication strategy which allows them to perform the desired computation with a probability as high as possible. Efficient use of quantitatively limited communication is a broadly relevant matter [1], which provides fundamental insights on physical limitations [2,3].The ability to process information depends on the choice of the physical system into which the information is encoded [4]. Consequently, quantum entities without a classical counterpart can be regarded as tools for quantum information processing. The most famous example is entanglement. In a quantum CCP, parties may share an entangled state on which they perform local measurements, generating strongly correlated data which violates a Bell inequality. That data can then be used to assist a classical communication strategy [5]. In fact, Bell inequalities have been systematically linked to CCPs [6-8], and their violation enables better-than-classical communication efficiencies [7][8][9][10][11][12][13][14][15].Nevertheless, quantum theory presents also a second approach to CCPs: substituting classical communication with quantum communication. The justification for such a substitution relies on the Holevo theorem [16] which implies that no more information can be extracted from quantum d-level system than from a classical d-level system. Hence, in a quantum communication strategy, information is encoded in a quantum state of a specified Hilbe...

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confidence: 99%

High-Dimensional Quantum Communication Complexity beyond Strategies Based on Bell’s Theorem

et al. 2018

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“…The constructed states with higher dimensions offer an increase in the channel capacity for quantum communication, and provide a higher error rate tolerance and enhanced security in quantum key distribution. 41 High-dimensional entanglement offers great potential for applications in quantum information, particularly in quantum communications.…”

Section: Resultsmentioning

confidence: 99%

Two and three-uniform states from irredundant orthogonal arrays

et al. 2019

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A pure quantum state of N subsystems, each with d levels, is said to be k-uniform if all of its reductions to k qudits are maximally mixed. Only the uniform states obtained from orthogonal arrays (OAs) are considered throughout this work. The Hamming distances of OAs are specially applied to the theory of quantum information. By using difference schemes and orthogonal partitions, we construct a series of infinite classes of irredundant orthogonal arrays (IrOAs), then answer the open questions of whether there exist 3-uniform states of N qubits and 2-uniform states of N qutrits, and whether 3-uniform states of qudits (d > 2) for high values of N can be explicitly constructed. In fact, we obtain 3-uniform states for an arbitrary number of N ≥ 8 qubits and 2uniform states of N qutrits for every N ≥ 4. Additionally, we provide explicit constructions of the 3-uniform states of N ≥ 8 qutrits, N = 6 and N ≥ 8 ququarts and ququints, N ≥ 6 qudits having d levels for any prime power d > 6, and N = 8 and N ≥ 12 qudits having d levels for non-prime-power d ≥ 6. Moreover, we describe an explicit construction scheme for the 2-uniform states of qudits having d ≥ 4 levels. The proofs of existence of the 2-uniform states of N ≥ 6 qubits are simplified by using a class of OAs. Two special 3uniform states are obtained from IrOA(32, 10, 2, 3) and IrOA(32, 11, 2, 3) using the interaction column property of OAs.

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“…The application of this new feature is of broad relevance for several new architectures aiming for highdimensional quantum information processing [4][5][6][7][8][9][10][11][12][13][14][15][16], and the understanding of macroscopic quantumness [3]. We demonstrate the practicability of our technique by using it to certify the generation of an irreducible 1024-dimensional photonic quantum state encoded into the linear transverse momentum of single-photons transmitted by programable diffractive apertures, which have been used for several high-dimensional quantum information processing tasks [5,35,[45][46][47].…”

Section: B)mentioning

confidence: 99%

Certifying an Irreducible 1024-Dimensional Photonic State Using Refined Dimension Witnesses

et al. 2018

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We report on a new class of dimension witnesses, based on quantum random access codes, which are a function of the recorded statistics and that have different bounds for all possible decompositions of a high-dimensional physical system. Thus, it certifies the dimension of the system and has the new distinct feature of identifying whether the high-dimensional system is decomposable in terms of lower dimensional subsystems. To demonstrate the practicability of this technique, we used it to experimentally certify the generation of an irreducible 1024-dimensional photonic quantum state. Therefore, certifying that the state is not multipartite or encoded using noncoupled different degrees of freedom of a single photon. Our protocol should find applications in a broad class of modern quantum information experiments addressing the generation of high-dimensional quantum systems, where quantum tomography may become intractable.

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Experimental Minimum-Error Quantum-State Discrimination in High Dimensions

Cited by 55 publications

References 64 publications

High-Dimensional Quantum Communication Complexity beyond Strategies Based on Bell’s Theorem

High-Dimensional Quantum Communication Complexity beyond Strategies Based on Bell’s Theorem

Two and three-uniform states from irredundant orthogonal arrays

Certifying an Irreducible 1024-Dimensional Photonic State Using Refined Dimension Witnesses

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