Extracting remaining information from an inconclusive result in optimal unambiguous state discrimination

Zhang, Gang; Yu, Lian; Zhang, Wenhai; Cao, Zhuo‐Liang

doi:10.1007/s11128-014-0817-8

Cited by 3 publications

(4 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…tection theory [7,[12][13][14][15][16][17], but in practice it became viable only recently with the development of experimental techniques for preparation, manipulation, and measurement of high-dimensional quantum systems. In addition to its fundamental interest, recent studies show that this concatenation provides significant improvements in probabilistic realizations of protocols like teleportation [18], entanglement swapping [19], and dense coding [20]; it will also have impact on high-dimensional quantum cryptography [20].…”

Section: Alicementioning

confidence: 99%

Enhanced discrimination of high-dimensional quantum states by concatenated optimal measurement strategies

Solís-Prosser,

Jiménez,

Delgado

et al. 2021

Preprint

View full text Add to dashboard Cite

The impossibility of deterministic and error-free discrimination among nonorthogonal quantum states lies at the core of quantum theory and constitutes a primitive for secure quantum communication. Demanding determinism leads to errors, while demanding certainty leads to some inconclusiveness. One of the most fundamental strategies developed for this task is the optimal unambiguous measurement. It encompasses conclusive results, which allow for error-free state retrodictions with the maximum success probability, and inconclusive results, which are discarded for not allowing perfect identifications. Interestingly, in high-dimensional Hilbert spaces the inconclusive results may contain valuable information about the input states. Here, we theoretically describe and experimentally demonstrate the discrimination of nonorthogonal states from both conclusive and inconclusive results in the optimal unambiguous strategy, by concatenating a minimum-error measurement at its inconclusive space. Our implementation comprises 4-and 9-dimensional spatially encoded photonic states. By accessing the inconclusive space to retrieve the information that is wasted in the conventional protocol, we achieve significant increases of up to a factor of 2.07 and 3.73, respectively, in the overall probabilities of correct retrodictions. The concept of concatenated optimal measurements demonstrated here can be extended to other strategies and will enable one to explore the full potential of high-dimensional nonorthogonal states for quantum communication with larger alphabets.

show abstract

Section: Alicementioning

confidence: 99%

Enhanced discrimination of high-dimensional quantum states by concatenated optimal measurement strategies

Solís-Prosser,

Jiménez,

Delgado

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Using Eqs. (18), (20), (25), and (26), we plot in Fig. 4 the success probability and the mutual information as functions of ξ.…”

Section: Bob's Decodingmentioning

confidence: 99%

“…The field of quantum-state discrimination has rapidly evolved in the last years, becoming a fundamental tool in quantum information theory. Many new optimized measurement strategies have been proposed [22][23][24][25][26] and applied in protocols like, for instance, quantum teleportation [27] and entanglement swapping [28].…”

Section: Introductionmentioning

confidence: 99%

Optimal probabilistic dense coding schemes

Kögler

Neves

2017

Quantum Inf Process

View full text Add to dashboard Cite

Dense coding with non-maximally entangled states has been investigated in many different scenarios. We revisit this problem for protocols adopting the standard encoding scheme. In this case, the set of possible classical messages cannot be perfectly distinguished due to the non-orthogonality of the quantum states carrying them. So far, the decoding process has been approached in two ways: (i) The message is always inferred, but with an associated (minimum) error; (ii) the message is inferred without error, but only sometimes; in case of failure, nothing else is done. Here, we generalize on these approaches and propose novel optimal probabilistic decoding schemes. The first uses quantum-state separation to increase the distinguishability of the messages with an optimal success probability. This scheme is shown to include (i) and (ii) as special cases and continuously interpolate between them, which enables the decoder to trade-off between the level of confidence desired to identify the received messages and the success probability for doing so. The second scheme, called multistage decoding, applies only for qudits (d-level quantum systems with d > 2) and consists of further attempts in the state identification process in case of failure in the first one. We show that this scheme is advantageous over (ii) as it increases the mutual information between the sender and receiver.

show abstract

“…The concatenation of a strategy at the inconclusive space will enable state retrodictions from both conclusive and inconclusive results in optimal UD; such protocol will be referred here as concatenated UD (CUD), and both UD and CUD protocols are illustrated in figure 1 as a quantum communication problem. The possibility of concatenating optimized measurements has been the subject of intense investigation in quantum detection theory [7,[12][13][14][15][16][17], but in practice it became viable only recently with the development of experimental techniques for preparation, manipulation, and measurement of high-dimensional quantum systems. In addition to its fundamental interest, recent studies show that this concatenation provides significant improvements in probabilistic realizations of protocols like teleportation [18], entanglement swapping [19], and dense coding [20]; it will also have impact on high-dimensional quantum cryptography [20].…”

Section: Introductionmentioning

confidence: 99%

Enhanced discrimination of high-dimensional quantum states by concatenated optimal measurement strategies

Solís-Prosser

Jiménez

Delgado

et al. 2021

Quantum Sci. Technol.

View full text Add to dashboard Cite

The impossibility of deterministic and error-free discrimination among nonorthogonal quantum states lies at the core of quantum theory and constitutes a primitive for secure quantum communication. Demanding determinism leads to errors, while demanding certainty leads to some inconclusiveness. One of the most fundamental strategies developed for this task is the optimal unambiguous measurement. It encompasses conclusive results, which allow for error-free state retrodictions with the maximum success probability, and inconclusive results, which are discarded for not allowing perfect identiﬁcations. Interestingly, in high-dimensional Hilbert spaces the inconclusive results may contain valuable information about the input states. Here, we theoretically describe and experimentally demonstrate the discrimination of nonorthogonal states from both conclusive and inconclusive results in the optimal unambiguous strategy, by concatenating a minimum-error measurement at its inconclusive space. Our implementation comprises 4- and 9-dimensional spatially encoded photonic states. By accessing the inconclusive space to retrieve the information that is wasted in the conventional protocol, we achieve signiﬁcant increases of up to a factor of 2.07 and 3.73, respectively, in the overall probabilities of correct retrodictions. The concept of concatenated optimal measurements demonstrated here can be extended to other strategies and will enable one to explore the full potential of high-dimensional nonorthogonal states for quantum communication with larger alphabets.

show abstract

Extracting remaining information from an inconclusive result in optimal unambiguous state discrimination

Cited by 3 publications

References 36 publications

Enhanced discrimination of high-dimensional quantum states by concatenated optimal measurement strategies

Enhanced discrimination of high-dimensional quantum states by concatenated optimal measurement strategies

Optimal probabilistic dense coding schemes

Enhanced discrimination of high-dimensional quantum states by concatenated optimal measurement strategies

Contact Info

Product

Resources

About