The Quantum Entanglement of Binary and Bipolar Sequences
M. G. Parker, V. Rijmen
备注：
34 pages. Presented in part at SETA01, Bergen, Norway, May 13-17, 2001. v2: Minor (but annoying) equation typos fixed
发表信息：
Sequences and Their Applications, SETA'01, Discrete Mathematics and Theoretical Computer Science Series, Springer, 2001, Ed.: T.Helleseth, P.V.Kumar and K.Yang
Classification of different forms of quantum entanglement is an active area of research, central to development of effective quantum computers, and similar to classification of error-correction codes, where code duality is broadened to equivalence under all 'local' unitary transforms. We explore links between entanglement, coding theory, and sequence design, by examining multi-spectra of quantum states under local unitary action, and show that optimal error-correcting codes and sequences represent states with high multiparticle entanglement.
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Characterization of quantum devices received from unknown providers is a significant primary task for any quantum information processing protocol. Self-testing protocols are designed for this purpose of certifying quantum components from the observed statistics under a set of minimal assumptions. Here we propose a self-testing protocol for certifying binary Pauli measurements employing the violation of a Leggett-Garg inequality. The scenario based on temporal correlations does not require entanglement, a costly and fragile resource. Moreover, unlike previously proposed self-testing protocols i…
It is well known that entanglement can benefit quantum information processing tasks. Quantum illumination, when first proposed, is surprising as entanglement's benefit survives entanglement-breaking noise. Since then, many efforts have been devoted to study quantum sensing in noisy scenarios. The applicability of such schemes, however, is limited to a binary quantum hypothesis testing scenario. In terms of target detection, such schemes interrogate a single polarization-azimuth-elevation-range-Doppler resolution bin at a time, limiting the impact to radar detection. We resolve this binary-hypo…
Entanglement is an important phenomenon that enables quantum information processing algorithms and quantum communications protocols. Although entangled quantum states are often described in radix-2, higher-radix qudits can become entangled as well. In this work, we both introduce partial entanglement, a concept that does not exist for radix-2 quantum systems, and differentiate between partial and maximal entanglement within non-binary quantum information processing systems. We also develop and present higher-radix maximal entanglement generator circuits that are analogous to the well-known Bel…
We study the entanglement entropy and spectrum between components in binary Bose-Einstein condensates in $d$ spatial dimensions. We employ effective field theory to show that the entanglement spectrum exhibits an anomalous square-root dispersion relation in the presence of an intercomponent tunneling (a Rabi coupling) and a gapped dispersion relation in its absence. These spectral features are associated with the emergence of long-range interactions in terms of the superfluid velocity and the particle density in the entanglement Hamiltonian. Our results demonstrate that unusual long-range inte…
Entanglement and coherence in pure and doped Posner molecules
University of KwaZulu-Natal（夸祖鲁-纳塔尔大学）；National Institute for Theoretical and Computational Sciences, South Africa（南非国家理论与计算科学研究所）；The Guy Foundation, Dorset, UK（盖伊基金会）；The Department of Electrical and Computer Engineering, University of California Los Angeles, CA, 90095, USA（加州大学洛杉矶分校电气与计算机工程系）；School of Data Science and Computational Thinking and Department of Physics, Stellenbosch University, South Africa（斯泰伦博斯大学数据科学与计算思维学院及物理系）
In this paper, a multi-party quantum private comparison (MQPC) scheme is suggested based on entanglement swapping of Bell entangled states within d-level quantum system, which can accomplish the equality comparison of secret binary sequences from n users via one execution of scheme. Detailed security analysis shows that both the outside attack and the participant attack are ineffective. The suggested scheme needn't establish a private key among n users beforehand through the quantum key distribution (QKD) method to encrypt the secret binary sequences. Compared with previous MQPC scheme based o…
Quantum hypothesis testing has been greatly advanced for the binary discrimination of two states, or two channels. In this setting, we already know that quantum entanglement can be used to enhance the discrimination of two bosonic channels. Here, we remove the restriction of binary hypotheses and show that entangled photons can remarkably boost the discrimination of multiple bosonic channels. More precisely, we formulate a general problem of channel-position finding where the goal is to determine the position of a target channel among many background channels. We prove that, using entangled ph…
We establish a conceptual framework for the identification and the characterization of induced interactions in binary mixtures and reveal their intricate relation to entanglement between the components or species of the mixture. Exploiting an expansion in terms of the strength of the entanglement among the two species, enables us to deduce an effective single-species description. In this way, we naturally incorporate the mutual feedback of the species and obtain induced interactions for both species which are effectively present among the particles of same type. Importantly, our approach incor…
We provide a generalization for the polygamy constraint of multiparty entanglement in arbitrary dimensional quantum systems. By using the $β$th-power of entanglement of assistance for $0\leq β\leq1$ and the Hamming weight of the binary vector related with the distribution of subsystems, we establish a class of weighted polygamy inequalities of multiparty entanglement in arbitrary dimensional quantum systems. We further show that our class of weighted polygamy inequalities can even be improved to be tighter inequalities with some conditions on the assisted entanglement of bipartite subsystems.
Known quantum error correction schemes are typically able to take advantage of only a limited class of classical error-correcting codes. Entanglement-assisted quantum error correction is a partial solution which made it possible to exploit any classical linear codes over the binary or quaternary finite field. However, the known entanglement-assisted scheme requires noiseless qubits that help correct quantum errors on noisy qubits, which can be too severe an assumption. We prove that a more relaxed and realistic assumption is sufficient by presenting encoding and decoding operations assisted by…
A binary mixtures of Bose-Einstein condensate structures exhibit an incredible richness in terms of holding different kinds of phases. Depending on the ratio of the inter- and intra-atomic interactions, the transition from mixed to separated phase, which is also known as the miscibility-immiscibility transition, has been reported in different setups and by different groups. Here, we describe such type of quantum phase transition in an effective Hamiltonian approach, by applying Holstein-Primakoff transformation in the limit of large number of particles. We demonstrate that non-trivial geometri…
The three-tangle is a measure of three-way entanglement in a system of three qubits. For a pure state, it can be understood as the residual entanglement not accounted for by pairwise entanglements between individual qubits. Here we define and evaluate the analogous quantity for three rebits (that is, binary systems in the real-amplitude variant of quantum theory). We find that the resulting formula is the same as in the complex case, except that an overall absolute value sign is missing. As a result, the rebit three-tangle can be negative, expressing the possibility of non-monogamous entanglem…
In this paper we applied the no-signaling in time (NSIT) formalism discussed by Kofler and Brukner to investigate temporal entanglement between binary human behavioral unconscious choices at t1 with binary random outcomes at t2. NSIT consists of a set of inequalities and represents mathematical conditions for macro-realism which require only two measurements in time. The analyses of three independent experiments show a strong violation of NSIT in two out of three of them, supporting the hypothesis of a quantum-like temporal entanglement between human choices at t1 with binary random outcomes a…
Unlocking Exponential and Unbounded Robust Gains in Shannon Capacity of Classical Multiple Access Channels with Causal CSIT via Quantum Entanglement Assistance
We prove that the known formulae for computing the optimal number of maximally entangled pairs required for entanglement-assisted quantum error-correcting codes (EAQECCs) over the binary field hold for codes over arbitrary finite fields as well. We also give a Gilbert-Varshamov bound for EAQECCs and constructions of EAQECCs coming from punctured self-orthogonal linear codes which are valid for any finite field.
We show how to protect a stream of quantum information from decoherence induced by a noisy quantum communication channel. We exploit preshared entanglement and a convolutional coding structure to develop a theory of entanglement-assisted quantum convolutional coding. Our construction produces a Calderbank-Shor-Steane (CSS) entanglement-assisted quantum convolutional code from two arbitrary classical binary convolutional codes. The rate and error-correcting properties of the classical convolutional codes directly determine the corresponding properties of the resulting entanglement-assisted quan…
Université de Bourgogne Franche-Comté（勃艮第-弗朗什孔泰大学）；Auburn University（奥本大学）
We review supervised learning and deep neural network design for learning membership on algebraic varieties. We demonstrate that these trained artificial neural networks can predict the entanglement type for quantum states. We give examples for detecting degenerate states, as well as border rank classification for up to 5 binary qubits and 3 qutrits (ternary qubits).
Almost a decade ago, physicists encountered a strange quantum phenomenon that predicts an unusual death of entanglement under the influence of local noisy environment,known as entanglement sudden death (ESD). This could be an immediate stumbling block in realizing all the entanglement based quantum information and computation protocols. In this work, we propose a scheme to tackle such shortcomings by exploiting the phenomenon of exceptional points (EP). Starting with a binary mechanical $\mathcal{PT}$ symmetric system, realized over an optomechanical platform, we show that a substantial delay …
University of Oxford（牛津大学）；UiT The Arctic University of Norway（挪威特罗姆瑟大学（北极大学））；Carnegie Mellon University（卡内基梅隆大学）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）
Entanglement is a physical phenomenon, which has fueled recent successes of quantum algorithms. Although quantum neural networks (QNNs) have shown promising results in solving simple machine learning tasks recently, for the time being, the effect of entanglement in QNNs and the behavior of QNNs in binary pattern classification are still underexplored. In this work, we provide some theoretical insight into the properties of QNNs by presenting and analyzing a new form of invariance embedded in QNNs for both quantum binary classification and quantum representation learning, which we term negation…
