Bell inequality for quNits with binary measurements

2003 ◽  
Vol 3 (2) ◽  
pp. 157-164
Author(s):  
H. Bechmann-Pasquinucci ◽  
N. Gisin
Keyword(s):  
Quantum Cryptography ◽  
Bell Inequality ◽  
The Other ◽  
Entangled State ◽  
Maximally Entangled State ◽  
Von Neumann ◽  
Chsh Inequality ◽  
Intermediate States ◽  
Von Neumann Measurements

We present a generalized Bell inequality for two entangled quNits. On one quNit the choice is between two standard von Neumann measurements, whereas for the other quNit there are N^2 different binary measurements. These binary measurements are related to the intermediate states known from eavesdropping in quantum cryptography. The maximum violation by \sqrt{N} is reached for the maximally entangled state. Moreover, for N=2 it coincides with the familiar CHSH-inequality.

scholarly journals ON THE EQUIVALENCE OF THE CH AND CHSH INEQUALITIES FOR TWO THREE-LEVEL SYSTEMS

2003 ◽  
Vol 01 (01) ◽  
pp. 115-133 ◽  
Author(s):  
JOSÉ L. CERECEDA
Keyword(s):  
Quantum Efficiency ◽  
Quantum Systems ◽  
Optimal Choice ◽  
Entangled State ◽  
Von Neumann ◽  
Chsh Inequality ◽  
Realistic Description ◽  
Von Neumann Measurements ◽  
Chsh Inequalities

In this paper we show a Clauser-Horne (CH) inequality for two three-level quantum systems or qutrits, alternative to the CH inequality given by Kaszlikowski et al. [Phys. Rev. A65, 032118 (2002)]. In contrast to this latter CH inequality, the new one is shown to be equivalent to the Clauser-Horne-Shimony-Holt (CHSH) inequality for two qutrits given by Collins et al. [Phys. Rev. Lett. 88, 040404 (2002)]. Both the CH and CHSH inequalities exhibit the strongest resistance to noise for a nonmaximally entangled state for the case of two von Neumann measurements per site, as first shown by Acin et al. [Phys. Rev. A65, 052325 (2002)]. This equivalence, however, breaks down when one takes into account the less-than-perfect quantum efficiency of detectors. Indeed, for the noiseless case, the threshold quantum efficiency above which there is no local and realistic description of the experiment for the optimal choice of measurements is found to be [Formula: see text] for the CH inequality, whereas it is equal to [Formula: see text] for the CHSH inequality.

scholarly journals MAXIMALLY ENTANGLED STATES AND BELL'S INEQUALITY IN RELATIVISTIC REGIME

2009 ◽  
Vol 07 (01) ◽  
pp. 395-401 ◽  
Author(s):  
SHAHPOOR MORADI
Keyword(s):  
Ghz State ◽  
Entangled States ◽  
Entangled State ◽  
Maximally Entangled State ◽  
Expectation Value ◽  
Spin Observables ◽  
Chsh Inequality ◽  
Relativistic Regime ◽  
Maximal Violation ◽  
Maximally Entangled States

In this letter we show that in the relativistic regime, maximally entangled state of two spin-1/2 particles not only gives maximal violation of the Bell-CHSH inequality but also gives the largest violation attainable for any pairs of four spin observables that are noncommuting for both systems. Also, we extend our results to three spin-1/2 particles. We obtain the largest eigenvalue of Bell operator and show that this value is equal to the expectation value of Bell operator on GHZ state.

ENTANGLEMENT, PURITY AND VIOLATION OF BELL INEQUALITY

2009 ◽  
Vol 07 (07) ◽  
pp. 1313-1320 ◽  
Author(s):  
DONG-LING DENG ◽  
JING-LING CHEN
Keyword(s):  
Bell Inequality ◽  
The Other ◽  
Two Dimensional ◽  
Entanglement Of Formation ◽  
Other Hand ◽  
Chsh Inequality ◽  
The One ◽  
The Relationship ◽  
Qubit States

We use the Clauser–Horne–Shimony-Holt (CHSH) inequality to investigate the relationship among entanglement, purity and violation of the Bell inequality. On the one hand, we show numerically that all two-dimensional (qubit) states, whose entanglement of formation (EOF) is larger than [Formula: see text], violate the CHSH inequality. On the other hand, any state with purity smaller than 0.5562 may not violate it.

scholarly journals Quantum nonlocality enhanced by homogenization

2014 ◽  
Vol 12 (06) ◽  
pp. 1450040
Author(s):  
Xu Chen ◽  
Hong-Yi Su ◽  
Zhen-Peng Xu ◽  
Yu-Chun Wu ◽  
Jing-Ling Chen
Keyword(s):  
Hardy Inequality ◽  
Bell Inequality ◽  
Bell Inequalities ◽  
Quantum Nonlocality ◽  
Entangled State ◽  
Maximally Entangled State ◽  
Ghz States ◽  
Partial Correlations ◽  
Hardy’S Inequalities ◽  
The Hardy Inequality

Homogenization proposed in [Y.-C Wu and M. Żukowski, Phys. Rev. A 85 (2012) 022119] is a procedure to transform a tight Bell inequality with partial correlations into a full-correlation form that is also tight. In this paper, we check the homogenizations of two families of n-partite Bell inequalities: the Hardy inequality and the tight Bell inequality without quantum violation. For Hardy's inequalities, their homogenizations bear stronger quantum violation for the maximally entangled state; the tight Bell inequalities without quantum violation give the boundary of quantum and supra-quantum, but their homogenizations do not have the similar properties. We find their homogenization are violated by the maximally entangled state. Numerically computation shows the the domains of quantum violation of homogenized Hardy's inequalities for the generalized GHZ states are smaller than those of Hardy's inequalities.

scholarly journals BELL'S INEQUALITIES DETECT EFFICIENT ENTANGLEMENT

2004 ◽  
Vol 02 (01) ◽  
pp. 23-31 ◽  
Author(s):  
ANTONIO ACÍN ◽  
NICOLAS GISIN ◽  
LLUIS MASANES ◽  
VALERIO SCARANI
Keyword(s):  
Quantum Key Distribution ◽  
Bell Inequality ◽  
Entangled State ◽  
Secret Key ◽  
Bell’S Inequalities ◽  
Maximally Entangled State ◽  
The Status ◽  
Bell's Inequalities ◽  
Key Extraction ◽  
Secret Key Extraction

We review the status of Bell's inequalities in quantum information, stressing mainly the links with quantum key distribution and distillation of entanglement. We also prove that for all the eavesdropping attacks using one qubit, and for a family of attacks of two qubits, acting on half of a maximally entangled state of two qubits, the violation of a Bell inequality implies the possibility of an efficient secret-key extraction.

scholarly journals Self-testing quantum systems of arbitrary local dimension with minimal number of measurements

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Shubhayan Sarkar ◽  
Debashis Saha ◽  
Jędrzej Kaniewski ◽  
Remigiusz Augusiak
Keyword(s):  
Bell Inequality ◽  
Quantum Systems ◽  
Entangled State ◽  
Local Dimension ◽  
Maximally Entangled State ◽  
Testing Protocol ◽  
Self Testing ◽  
Minimum Number ◽  
Bell Nonlocality ◽  
Testing Protocols

AbstractBell nonlocality as a resource for device-independent certification schemes has been studied extensively in recent years. The strongest form of device-independent certification is referred to as self-testing, which given a device, certifies the promised quantum state as well as quantum measurements performed on it without any knowledge of the internal workings of the device. In spite of various results on self-testing protocols, it remains a highly nontrivial problem to propose a certification scheme of qudit–qudit entangled states based on violation of a single d-outcome Bell inequality. Here we address this problem and propose a self-testing protocol for the maximally entangled state of any local dimension using the minimum number of measurements possible, i.e., two per subsystem. Our self-testing result can be used to establish unbounded randomness expansion, $${{{\mathrm{log}}}\,}_{2}d$$ log 2 d perfect random bits, while it requires only one random bit to encode the measurement choice.

scholarly journals Maximal nonlocality from maximal entanglement and mutually unbiased bases, and self-testing of two-qutrit quantum systems

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 198 ◽  
Author(s):  
Jędrzej Kaniewski ◽  
Ivan Šupić ◽  
Jordi Tura ◽  
Flavio Baccari ◽  
Alexia Salavrakos ◽  
...  
Keyword(s):  
Quantum Information Processing ◽  
Bell Inequality ◽  
Bell Inequalities ◽  
Weak Form ◽  
Quantum Systems ◽  
Point Of View ◽  
Entangled State ◽  
Mutually Unbiased Bases ◽  
Maximally Entangled State ◽  
Self Testing

Bell inequalities are an important tool in device-independent quantum information processing because their violation can serve as a certificate of relevant quantum properties. Probably the best known example of a Bell inequality is due to Clauser, Horne, Shimony and Holt (CHSH), which is defined in the simplest scenario involving two dichotomic measurements and whose all key properties are well understood. There have been many attempts to generalise the CHSH Bell inequality to higher-dimensional quantum systems, however, for most of them the maximal quantum violation---the key quantity for most device-independent applications---remains unknown. On the other hand, the constructions for which the maximal quantum violation can be computed, do not preserve the natural property of the CHSH inequality, namely, that the maximal quantum violation is achieved by the maximally entangled state and measurements corresponding to mutually unbiased bases. In this work we propose a novel family of Bell inequalities which exhibit precisely these properties, and whose maximal quantum violation can be computed analytically. In the simplest scenario it recovers the CHSH Bell inequality. These inequalities involve d measurements settings, each having d outcomes for an arbitrary prime number d≥3. We then show that in the three-outcome case our Bell inequality can be used to self-test the maximally entangled state of two-qutrits and three mutually unbiased bases at each site. Yet, we demonstrate that in the case of more outcomes, their maximal violation does not allow for self-testing in the standard sense, which motivates the definition of a new weak form of self-testing. The ability to certify high-dimensional MUBs makes these inequalities attractive from the device-independent cryptography point of view.

scholarly journals NON-MARKOVIAN DYNAMICS OF SYSTEM-RESERVOIR ENTANGLEMENT

2011 ◽  
Vol 09 (07n08) ◽  
pp. 1715-1726 ◽  
Author(s):  
F. PLASTINA ◽  
S. MANISCALCO
Keyword(s):  
Direct Interaction ◽  
The Other ◽  
W State ◽  
Entangled State ◽  
Cavity Field ◽  
Bipartite Entanglement ◽  
Maximally Entangled State ◽  
Exact Approach ◽  
Markovian Dynamics

Using an exact approach, we study the dynamics of entanglement between two qubits coupled to independent reservoirs and between the two, initially disentangled, reservoirs. We also describe the transfer of bipartite entanglement from the two qubits to their respective reservoirs focussing on the case of two atoms inside two different leaky cavities with a specific attention to the role of the detuning. We present a scheme to prepare the cavity fields in a maximally entangled state, without direct interaction between the cavities, by exploiting the initial qubits entanglement. We discuss a deterministic protocol, working in the presence of cavity losses, for the generation of a W-state of one qubit and two cavity fields and we describe a probabilistic scheme to entangle one of the atoms with the reservoir (cavity field) of the other atom.

scholarly journals Robust self-testing of steerable quantum assemblages and its applications on device-independent quantum certification

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 552
Author(s):  
Shin-Liang Chen ◽  
Huan-Yu Ku ◽  
Wenbin Zhou ◽  
Jordi Tura ◽  
Yueh-Nan Chen
Keyword(s):  
Bell Inequality ◽  
Bell Inequalities ◽  
Alternative Proof ◽  
Entangled State ◽  
Maximally Entangled State ◽  
Self Testing ◽  
Measurement Devices ◽  
Shared State ◽  
Qubit States ◽  
Single Set

Given a Bell inequality, if its maximal quantum violation can be achieved only by a single set of measurements for each party or a single quantum state, up to local unitaries, one refers to such a phenomenon as self-testing. For instance, the maximal quantum violation of the Clauser-Horne-Shimony-Holt inequality certifies that the underlying state contains the two-qubit maximally entangled state and the measurements of one party contains a pair of anti-commuting qubit observables. As a consequence, the other party automatically verifies the set of states remotely steered, namely the "assemblage", is in the eigenstates of a pair of anti-commuting observables. It is natural to ask if the quantum violation of the Bell inequality is not maximally achieved, or if one does not care about self-testing the state or measurements, are we capable of estimating how close the underlying assemblage is to the reference one? In this work, we provide a systematic device-independent estimation by proposing a framework called "robust self-testing of steerable quantum assemblages". In particular, we consider assemblages violating several paradigmatic Bell inequalities and obtain the robust self-testing statement for each scenario. Our result is device-independent (DI), i.e., no assumption is made on the shared state and the measurement devices involved. Our work thus not only paves a way for exploring the connection between the boundary of quantum set of correlations and steerable assemblages, but also provides a useful tool in the areas of DI quantum certification. As two explicit applications, we show 1) that it can be used for an alternative proof of the protocol of DI certification of all entangled two-qubit states proposed by Bowles et al., and 2) that it can be used to verify all non-entanglement-breaking qubit channels with fewer assumptions compared with the work of Rosset et al.

scholarly journals Optimal teleportation via noisy quantum channels without additional qubit resources

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Dong-Gil Im ◽  
Chung-Hyun Lee ◽  
Yosep Kim ◽  
Hyunchul Nha ◽  
M. S. Kim ◽  
...  
Keyword(s):  
Quantum Computing ◽  
Quantum Teleportation ◽  
Quantum Communication ◽  
Quantum Noise ◽  
Single Copy ◽  
Entangled State ◽  
Quantum Network ◽  
Quantum Channels ◽  
Maximally Entangled State ◽  
Near Term

AbstractQuantum teleportation exemplifies how the transmission of quantum information starkly differs from that of classical information and serves as a key protocol for quantum communication and quantum computing. While an ideal teleportation protocol requires noiseless quantum channels to share a pure maximally entangled state, the reality is that shared entanglement is often severely degraded due to various decoherence mechanisms. Although the quantum noise induced by the decoherence is indeed a major obstacle to realizing a near-term quantum network or processor with a limited number of qubits, the methodologies considered thus far to address this issue are resource-intensive. Here, we demonstrate a protocol that allows optimal quantum teleportation via noisy quantum channels without additional qubit resources. By analyzing teleportation in the framework of generalized quantum measurement, we optimize the teleportation protocol for noisy quantum channels. In particular, we experimentally demonstrate that our protocol enables to teleport an unknown qubit even via a single copy of an entangled state under strong decoherence that would otherwise preclude any quantum operation. Our work provides a useful methodology for practically coping with decoherence with a limited number of qubits and paves the way for realizing noisy intermediate-scale quantum computing and quantum communication.

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