projective measurements
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Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 106
Author(s):  
Abraham G. Kofman ◽  
Gershon Kurizki

The consensus regarding quantum measurements rests on two statements: (i) von Neumann’s standard quantum measurement theory leaves undetermined the basis in which observables are measured, and (ii) the environmental decoherence of the measuring device (the “meter”) unambiguously determines the measuring (“pointer”) basis. The latter statement means that the environment monitors (measures) selected observables of the meter and (indirectly) of the system. Equivalently, a measured quantum state must end up in one of the “pointer states” that persist in the presence of the environment. We find that, unless we restrict ourselves to projective measurements, decoherence does not necessarily determine the pointer basis of the meter. Namely, generalized measurements commonly allow the observer to choose from a multitude of alternative pointer bases that provide the same information on the observables, regardless of decoherence. By contrast, the measured observable does not depend on the pointer basis, whether in the presence or in the absence of decoherence. These results grant further support to our notion of Quantum Lamarckism, whereby the observer’s choices play an indispensable role in quantum mechanics.


4open ◽  
2022 ◽  
Vol 5 ◽  
pp. 1
Author(s):  
David Ellerman

We live in the information age. Claude Shannon, as the father of the information age, gave us a theory of communications that quantified an “amount of information,” but, as he pointed out, “no concept of information itself was defined.” Logical entropy provides that definition. Logical entropy is the natural measure of the notion of information based on distinctions, differences, distinguishability, and diversity. It is the (normalized) quantitative measure of the distinctions of a partition on a set-just as the Boole–Laplace logical probability is the normalized quantitative measure of the elements of a subset of a set. And partitions and subsets are mathematically dual concepts – so the logic of partitions is dual in that sense to the usual Boolean logic of subsets, and hence the name “logical entropy.” The logical entropy of a partition has a simple interpretation as the probability that a distinction or dit (elements in different blocks) is obtained in two independent draws from the underlying set. The Shannon entropy is shown to also be based on this notion of information-as-distinctions; it is the average minimum number of binary partitions (bits) that need to be joined to make all the same distinctions of the given partition. Hence all the concepts of simple, joint, conditional, and mutual logical entropy can be transformed into the corresponding concepts of Shannon entropy by a uniform non-linear dit-bit transform. And finally logical entropy linearizes naturally to the corresponding quantum concept. The quantum logical entropy of an observable applied to a state is the probability that two different eigenvalues are obtained in two independent projective measurements of that observable on that state.


Author(s):  
Michael J W Hall ◽  
Shuming Cheng

Abstract The Horodecki criterion provides a necessary and sufficient condition for a two-qubit state to be able to manifest Bell nonlocality via violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality. It requires, however, the assumption that suitable projective measurements can be made on each qubit, and is not sufficient for scenarios in which noisy or weak measurements are either desirable or unavoidable. By characterising two-valued qubit observables in terms of strength, bias, and directional parameters, we address such scenarios by providing necessary and sufficient conditions for arbitrary qubit measurements having fixed strengths and relative angles for each observer. In particular, we find the achievable maximal values of the CHSH parameter for unbiased measurements on arbitrary states, and, alternatively, for arbitrary measurements on states with maximally-mixed marginals, and determine the optimal angles in some cases. We also show that for certain ranges of measurement strengths it is only possible to violate the CHSH inequality via biased measurements. Finally, we use the CHSH inequality to obtain a simple necessary condition for the compatibility of two qubit observables.


Nanophotonics ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Keshaan Singh ◽  
Angela Dudley

Abstract Vectorial structured light fields have displayed properties advantageous in many disciplines ranging from communications, microscopy and metrology to laser cutting and characterizing quantum channels. The generation of these fields has been made convenient through the implementation of nanophotonic metasurfaces amongst other static and digital techniques. Consequently, the detection and characterisation of these fields is of equal importance. Most existing techniques involve using separate polarization optics and correlation filters to perform the projective measurements – or are only able to perform such measurements on a subset of possible vector states. We present a compact, fully automated measurement technique based on a digital micro-mirror device (DMD), which facilitates the complete, local and global, characterisation of the spatial mode and polarization degrees-of-freedom (DOFs) for arbitrary vectorial fields. We demonstrate our approach through the identification of relevant hybrid-order Poincaré spheres, the reconstruction of state vectors on these spheres, as well as the recovery of the non-separability and states-of-polarization for a variety of vector beams.


2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Yun-Guang Han ◽  
Zihao Li ◽  
Yukun Wang ◽  
Huangjun Zhu

AbstractBipartite and multipartite entangled states are basic ingredients for constructing quantum networks and their accurate verification is crucial to the functioning of the networks, especially for untrusted networks. Here we propose a simple approach for verifying the Bell state in an untrusted network in which one party is not honest. Only local projective measurements are required for the honest party. It turns out each verification protocol is tied to a probability distribution on the Bloch sphere and its performance has an intuitive geometric meaning. This geometric picture enables us to construct the optimal and simplest verification protocols, which are also very useful to detecting entanglement in the untrusted network. Moreover, we show that our verification protocols can achieve almost the same sample efficiencies as protocols tailored to standard quantum state verification. Furthermore, we establish an intimate connection between the verification of Greenberger–Horne–Zeilinger states and the verification of the Bell state. By virtue of this connection we construct the optimal protocol for verifying Greenberger–Horne–Zeilinger states and for detecting genuine multipartite entanglement.


2021 ◽  
Vol 3 (4) ◽  
Author(s):  
Niraj Kumar ◽  
Ulysse Chabaud ◽  
Elham Kashefi ◽  
Damian Markham ◽  
Eleni Diamanti

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Isaac Nape ◽  
Valeria Rodríguez-Fajardo ◽  
Feng Zhu ◽  
Hsiao-Chih Huang ◽  
Jonathan Leach ◽  
...  

AbstractHigh-dimensional entangled states are promising candidates for increasing the security and encoding capacity of quantum systems. While it is possible to witness and set bounds for the entanglement, precisely quantifying the dimensionality and purity in a fast and accurate manner remains an open challenge. Here, we report an approach that simultaneously returns the dimensionality and purity of high-dimensional entangled states by simple projective measurements. We show that the outcome of a conditional measurement returns a visibility that scales monotonically with state dimensionality and purity, allowing for quantitative measurements for general photonic quantum systems. We illustrate our method using two separate bases, the orbital angular momentum and pixels bases, and quantify the state dimensionality by a variety of definitions over a wide range of noise levels, highlighting its usefulness in practical situations. Importantly, the number of measurements needed in our approach scale linearly with dimensions, reducing data acquisition time significantly. Our technique provides a simple, fast and direct measurement approach.


Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 484
Author(s):  
Anubhav Chaturvedi ◽  
Máté Farkas ◽  
Victoria J Wright

The predictions of quantum theory resist generalised noncontextual explanations. In addition to the foundational relevance of this fact, the particular extent to which quantum theory violates noncontextuality limits available quantum advantage in communication and information processing. In the first part of this work, we formally define contextuality scenarios via prepare-and-measure experiments, along with the polytope of general contextual behaviours containing the set of quantum contextual behaviours. This framework allows us to recover several properties of set of quantum behaviours in these scenarios, including contextuality scenarios and associated noncontextuality inequalities that require for their violation the individual quantum preparation and measurement procedures to be mixed states and unsharp measurements. With the framework in place, we formulate novel semidefinite programming relaxations for bounding these sets of quantum contextual behaviours. Most significantly, to circumvent the inadequacy of pure states and projective measurements in contextuality scenarios, we present a novel unitary operator based semidefinite relaxation technique. We demonstrate the efficacy of these relaxations by obtaining tight upper bounds on the quantum violation of several noncontextuality inequalities and identifying novel maximally contextual quantum strategies. To further illustrate the versatility of these relaxations, we demonstrate monogamy of preparation contextuality in a tripartite setting, and present a secure semi-device independent quantum key distribution scheme powered by quantum advantage in parity oblivious random access codes.


Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 472
Author(s):  
Adel Sohbi ◽  
Damian Markham ◽  
Jaewan Kim ◽  
Marco Túlio Quintino

This work analyzes correlations arising from quantum systems subject to sequential projective measurements to certify that the system in question has a quantum dimension greater than some d. We refine previous known methods and show that dimension greater than two can be certified in scenarios which are considerably simpler than the ones presented before and, for the first time in this sequential projective scenario, we certify quantum systems with dimension strictly greater than three. We also perform a systematic numerical analysis in terms of robustness and conclude that performing random projective measurements on random pure qutrit states allows a robust certification of quantum dimensions with very high probability.


2021 ◽  
Vol 12 (1) ◽  
Author(s):  
M. J. Degen ◽  
S. J. H. Loenen ◽  
H. P. Bartling ◽  
C. E. Bradley ◽  
A. L. Meinsma ◽  
...  

AbstractA promising approach for multi-qubit quantum registers is to use optically addressable spins to control multiple dark electron-spin defects in the environment. While recent experiments have observed signatures of coherent interactions with such dark spins, it is an open challenge to realize the individual control required for quantum information processing. Here, we demonstrate the heralded initialisation, control and entanglement of individual dark spins associated to multiple P1 centers, which are part of a spin bath surrounding a nitrogen-vacancy center in diamond. We realize projective measurements to prepare the multiple degrees of freedom of P1 centers—their Jahn-Teller axis, nuclear spin and charge state—and exploit these to selectively access multiple P1s in the bath. We develop control and single-shot readout of the nuclear and electron spin, and use this to demonstrate an entangled state of two P1 centers. These results provide a proof-of-principle towards using dark electron-nuclear spin defects as qubits for quantum sensing, computation and networks.


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