Unifying framework for spatial and temporal quantum correlations

Costa, Fabio; Ringbauer, Martin; Goggin, M. E.; White, A. G.; Fedrizzi, Alessandro

doi:10.1103/physreva.98.012328

Cited by 31 publications

(31 citation statements)

References 56 publications

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“…Examining properties of its structure, as we have in this Article, provides fundamental insight into understanding the space of quantum processes and temporal correlations. Indeed, similar objects that are not necessarily causally-ordered, such as the process matrix, are developing into a tool for studying the most general spatio-temporal correlations allowable [14,16,52], shedding light on the defining features of quantum and post-quantum theories. On the practical side, the process tensor contains all the information one could ever hope to learn about a process.…”

Section: Discussionmentioning

confidence: 99%

“…Thus equipped, we can now apply standard correlation tools to understand properties of processes. It is important to note that all processes can be represented in this way as (unnormalized) quantum states, but not all quantum states represent valid processes [52]. The set of possible temporal correlations are restricted, compared to their spatial counterparts, because the process tensor must satisfy a hierarchy of trace conditions which encode a proper causal-ordering, ensuring that the future process cannot influence the past [11-13, 19, 20, 53]:…”

Section: A Preliminariesmentioning

confidence: 99%

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Structure of quantum stochastic processes with finite Markov order

et al. 2019

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Non-Markovian quantum processes exhibit different memory effects when measured in different ways; an unambiguous characterization of memory length requires accounting for the sequence of instruments applied to probe the system dynamics. This instrument-specific notion of quantum Markov order displays stark differences to its classical counterpart. Here, we explore the structure of quantum stochastic processes with finite memory length in detail. We begin by examining a generalized collision model with memory, before framing this instance within the general theory. We detail the constraints that are placed on the underlying systemenvironment dynamics for a process to exhibit finite Markov order with respect to natural classes of probing instruments, including deterministic (unitary) operations and sequences of generalized quantum measurements with informationally-complete re-preparations. Lastly, we show how processes with vanishing quantum conditional mutual information form a special case of the theory. Throughout, we provide a number of representative, pedagogical examples to display the salient features of memory effects in quantum processes.

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Section: Discussionmentioning

confidence: 99%

Section: A Preliminariesmentioning

confidence: 99%

Structure of quantum stochastic processes with finite Markov order

et al. 2019

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“…Together with the concepts of Bell nonlocality and entanglement, EPR steering forms a hierarchy, and as such acts as an intermediate quantum correlation that lies in between the others [4-6], i.e., EPR steering is, in general, weaker than Bell nonlocality but stronger than quantum entanglement. Research on EPR steering in the past few years has seen the development of several interesting new avenues of study [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. In addition to these theoretical developments, EPR steering has also been observed experimentally [24?…”

Section: Introductionmentioning

confidence: 99%

Hierarchy in temporal quantum correlations

Chen

Lambert

et al. 2018

Phys. Rev. A

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Einstein-Podolsky-Rosen (EPR) steering is an intermediate quantum correlation that lies in between entanglement and Bell non-locality. Its temporal analog, temporal steering, has recently been shown to have applications in quantum information and open quantum systems. Here, we show that there exists a hierarchy among the three temporal quantum correlations: temporal inseparability, temporal steering, and macrorealism. Given that the temporal inseparability can be used to define a measure of quantum causality, similarly the quantification of temporal steering can be viewed as a weaker measure of direct cause and can be used to distinguish between direct cause and common cause in a quantum network.

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“…Nevertheless, this way of looking at quantum processes naturally resolves the ambiguity of what makes a quantum processes Markovian [35] and when the memory is quantum [18]. It leads to a unifying framework for spatio-temporal correlation [11,39], where a space-time version of the Born rule appears [62]. Later we also generalised Kuah's idea [37] to fit restricted control process tensor [41].…”

Section: Process Tensor and Higher Order Mapsmentioning

confidence: 96%

George Sudarshan and Quantum Dynamics

Modi

2019

Open Syst. Inf. Dyn.

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These are my recollections of working with George Sudarshan from 2002 to 2008 when I was a PhD student in his group. During these years I learnt a lot of physics and also witness to some remarkable occurrences.When I began my PhD studies at the University of Texas at Austin in late 2001, I already knew the name George Sudarshan. He was famous for his discovery (as a grad student) of one of the fundamental forces of nature, the weak force. However, before coming to Austin I had spent the summer of 2000 at Fermilab. There I learned at least one thing; I didn't want to study particle physics. Thus I didn't bother looking Sudarshan up. I was interested in complexity and computation and wasn't really interested in the condensed matter group or the nonlinear group. Of course, at the time I didn't know that Sudarshan hadn't worked on particle physics for a long time. And I certainly didn't know of the many other things that he had done, at least two which were worthy of the Nobel Prize.Ultimately, it was clear that Sudarshan was one of the few theorists interested in the structure of quantum mechanics and the physical world. Working with him was easy in many ways. During the semester we spent either two or three days hanging out in his office for several hours and discussed all sorts of things. During summers, he was usually away, this was a good time for the students to get the writing done. All is all, in the years I spent in his group I got to work on two of these topics and was exposed to, at least to the fascinating history, of a third topic.Sudarshan's major achievements include the V-A theory (weak force), inventing the theory of quantum optics, discovering quantum maps, the quantum semi-group master equation, quantum Zeno effect, and tachyons. Yet, many physicists I meet don't know the name George Sudarshan. Some know him for his work on quantum optics, some for open dynamics, but very few know his contributions to particle physics, symmetries, and tachyons. Many will know of the Zeno effect, yet not Sudarshan. In many cases, someone Exemplary OSID style

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Unifying framework for spatial and temporal quantum correlations

Cited by 31 publications

References 56 publications

Structure of quantum stochastic processes with finite Markov order

Structure of quantum stochastic processes with finite Markov order

Hierarchy in temporal quantum correlations

George Sudarshan and Quantum Dynamics

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