scholarly journals Semi-device-independent certification of indefinite causal order

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 176 ◽  
Author(s):  
Jessica Bavaresco ◽  
Mateus Araújo ◽  
Časlav Brukner ◽  
Marco Túlio Quintino
Keyword(s):  
Quantum Theory ◽  
Higher Order ◽  
Causal Order ◽  
Intermediate Regime ◽  
Quantum Operations

When transforming pairs of independent quantum operations according to the fundamental rules of quantum theory, an intriguing phenomenon emerges: some such higher-order operations may act on the input operations in an indefinite causal order. Recently, the formalism of process matrices has been developed to investigate these noncausal properties of higher-order operations. This formalism predicts, in principle, statistics that ensure indefinite causal order even in a device-independent scenario, where the involved operations are not characterised. Nevertheless, all physical implementations of process matrices proposed so far require full characterisation of the involved operations in order to certify such phenomena. Here we consider a semi-device-independent scenario, which does not require all operations to be characterised. We introduce a framework for certifying noncausal properties of process matrices in this intermediate regime and use it to analyse the quantum switch, a well-known higher-order operation, to show that, although it can only lead to causal statistics in a device-independent scenario, it can exhibit noncausal properties in semi-device-independent scenarios. This proves that the quantum switch generates stronger noncausal correlations than it was previously known.

scholarly journals The Multi-round Process Matrix

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 384
Author(s):  
Timothée Hoffreumon ◽  
Ognyan Oreshkov
Keyword(s):  
Information Exchange ◽  
Higher Order ◽  
Side Channel ◽  
Order Process ◽  
Causal Order ◽  
Quantum Operations ◽  
First Case ◽  
The One

We develop an extension of the process matrix (PM) framework for correlations between quantum operations with no causal order that allows multiple rounds of information exchange for each party compatibly with the assumption of well-defined causal order of events locally. We characterise the higher-order process describing such correlations, which we name the multi-round process matrix (MPM), and formulate a notion of causal nonseparability for it that extends the one for standard PMs. We show that in the multi-round case there are novel manifestations of causal nonseparability that are not captured by a naive application of the standard PM formalism: we exhibit an instance of an operator that is both a valid PM and a valid MPM, but is causally separable in the first case and can violate causal inequalities in the second case due to the possibility of using a side channel.

scholarly journals Quantum clocks and the temporal localisability of events in the presence of gravitating quantum systems

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Esteban Castro-Ruiz ◽  
Flaminia Giacomini ◽  
Alessio Belenchia ◽  
Časlav Brukner
Keyword(s):  
Reference Frame ◽  
Reference Frames ◽  
Quantum Systems ◽  
Indefinite Metric ◽  
Causal Order ◽  
Quantum Operations ◽  
Unitary Dilation ◽  
Local Quantum ◽  
Fixed Space ◽  
Quantum Clocks

AbstractThe standard formulation of quantum theory relies on a fixed space-time metric determining the localisation and causal order of events. In general relativity, the metric is influenced by matter, and is expected to become indefinite when matter behaves quantum mechanically. Here, we develop a framework to operationally define events and their localisation with respect to a quantum clock reference frame, also in the presence of gravitating quantum systems. We find that, when clocks interact gravitationally, the time localisability of events becomes relative, depending on the reference frame. This relativity is a signature of an indefinite metric, where events can occur in an indefinite causal order. Even if the metric is indefinite, for any event we can find a reference frame where local quantum operations take their standard unitary dilation form. This form is preserved when changing clock reference frames, yielding physics covariant with respect to quantum reference frame transformations.

scholarly journals Theoretical framework for higher-order quantum theory

2019 ◽  
Vol 475 (2225) ◽  
pp. 20180706 ◽  
Author(s):  
Alessandro Bisio ◽  
Paolo Perinotti
Keyword(s):  
Quantum Theory ◽  
Convex Sets ◽  
Mathematical Structure ◽  
Higher Order ◽  
Equivalence Relations ◽  
Full Generality ◽  
Special Cases ◽  
Different Types ◽  
Causal Structures

Higher-order quantum theory is an extension of quantum theory where one introduces transformations whose input and output are transformations, thus generalizing the notion of channels and quantum operations. The generalization then goes recursively, with the construction of a full hierarchy of maps of increasingly higher order. The analysis of special cases already showed that higher-order quantum functions exhibit features that cannot be tracked down to the usual circuits, such as indefinite causal structures, providing provable advantages over circuital maps. The present treatment provides a general framework where this kind of analysis can be carried out in full generality. The hierarchy of higher-order quantum maps is introduced axiomatically with a formulation based on the language of types of transformations. Complete positivity of higher-order maps is derived from the general admissibility conditions instead of being postulated as in previous approaches. The recursive characterization of convex sets of maps of a given type is used to prove equivalence relations between different types. The axioms of the framework do not refer to the specific mathematical structure of quantum theory, and can therefore be exported in the context of any operational probabilistic theory.

scholarly journals On the Brukner–Zeilinger approach to information in quantum measurements

2015 ◽  
Vol 471 (2183) ◽  
pp. 20150435 ◽  
Author(s):  
A. E. Rastegin
Keyword(s):  
Quantum Theory ◽  
Invariant Measure ◽  
Critical Points ◽  
Natural Extension ◽  
Quantum Measurements ◽  
Quantum Operations ◽  
Total Information ◽  
Complete Set

We address the problem of properly quantifying information in quantum theory. Brukner and Zeilinger proposed the concept of an operationally invariant measure based on measurement statistics. Their measure of information is calculated with probabilities generated in a complete set of mutually complementary observations. This approach was later criticized for several reasons. We show that some critical points can be overcome by means of natural extension or reformulation of the Brukner–Zeilinger approach. In particular, this approach is connected with symmetric informationally complete measurements. The ‘total information’ of Brukner and Zeilinger can further be treated in the context of mutually unbiased measurements as well as general symmetric informationally complete measurements. The Brukner–Zeilinger measure of information is also examined in the case of detection inefficiencies. It is shown to be decreasing under the action of bistochastic maps. The Brukner–Zeilinger total information can be used for estimating the map norm of quantum operations.

scholarly journals Higher-order interference and single-system postulates characterizing quantum theory

2014 ◽  
Vol 16 (12) ◽  
pp. 123029 ◽  
Author(s):  
Howard Barnum ◽  
Markus P Müller ◽  
Cozmin Ududec
Keyword(s):  
Quantum Theory ◽  
Higher Order ◽  
Single System

scholarly journals Consequences of preserving reversibility in quantum superchannels

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 441
Author(s):  
Wataru Yokojima ◽  
Marco Túlio Quintino ◽  
Akihito Soeda ◽  
Mio Murao
Keyword(s):  
Quantum Mechanics ◽  
Physical Interpretation ◽  
Quantum Circuit ◽  
Quantum States ◽  
Quantum Circuits ◽  
Causal Order ◽  
Quantum Operations ◽  
Coherent Superposition ◽  
Physical Implementation ◽  
Quantum Objects

Similarly to quantum states, quantum operations can also be transformed by means of quantum superchannels, also known as process matrices. Quantum superchannels with multiple slots are deterministic transformations which take independent quantum operations as inputs. While they are enforced to respect the laws of quantum mechanics, the use of input operations may lack a definite causal order, and characterizations of general superchannels in terms of quantum objects with a physical implementation have been missing. In this paper, we provide a mathematical characterization for pure superchannels with two slots (also known as bipartite pure processes), which are superchannels preserving the reversibility of quantum operations. We show that the reversibility preserving condition restricts all pure superchannels with two slots to be either a quantum circuit only consisting of unitary operations or a coherent superposition of two unitary quantum circuits where the two input operations are differently ordered. The latter may be seen as a generalization of the quantum switch, allowing a physical interpretation for pure two-slot superchannels. An immediate corollary is that purifiable bipartite processes cannot violate device-independent causal inequalities.

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