Coherent control and distinguishability of quantum channels via PBS-diagrams

  title={Coherent control and distinguishability of quantum channels via PBS-diagrams},
  author={Cyril Branciard and Alexandre Cl'ement and Mehdi Mhalla and Simon Perdrix},
Even though coherent control of quantum operations appears to be achievable in practice, it is still not yet well understood. Among theoretical challenges, standard completely positive trace preserving (CPTP) maps are known not to be appropriate to represent coherently controlled quantum channels. We introduce here a graphical language for coherent control of general quantum channels inspired by practical quantum optical setups involving polarising beam splitters (PBS). We consider different… 

Figures from this paper

Universal control of quantum processes using sector-preserving channels
The standard notion of control is extended to more general notions, including control of multiple channels with possibly different input and output systems, and a theoretical framework, called supermaps on routed channels, which provides a compact representation of coherent control as an operation performed on the extended channels.
Minimising Resources of Coherently Controlled Quantum Computations
This paper extends the PBS-calculus, a graphical language for coherent control which is inspired by quantum optics, and introduces an efficient procedure to minimise the number of oracle queries of a given diagram.
Addressable quantum gates
We extend the circuit model of quantum comuptation so that the wiring between gates is soft-coded within registers inside the gates. The addresses in these registers can be manipulated and put into
Operational models of temperature superpositions
When thermodynamical quantities are associated with quantum systems a question arises how to treat scenarios where the notion of temperature could exhibit some quantum features. It is known that the
LOv-Calculus: A Graphical Language for Linear Optical Quantum Circuits
The LO v -calculus is introduced, a graphical language for reasoning about linear optical quantum circuits with so-called vacuum state auxiliary inputs, and the axiomatics of the language are presented and its soundness and completeness are proved.


Communication through coherent control of quantum channels
This work shows that, when quantum channels are controlled coherently, information about their specific implementation is accessible in the output state of the joint control-target system and allows two different implementations of what is usually considered to be the same channel to therefore be differentiated.
PBS-Calculus: A Graphical Language for Coherent Control of Quantum Computations
The PBS-calculus is introduced, and the language with an equational theory, which is proved to be sound and complete: two diagrams are representing the same quantum evolution if and only if one can be transformed into the other using the rules of the PBS-Calculus.
Completeness of Graphical Languages for Mixed States Quantum Mechanics
A new construction, the discard construction, is introduced, which transforms any †-symmetric monoidal category into a symmetric Monoidal category equipped with a discard map, which provides an extension for several graphical languages that are proved to be complete for general quantum operations.
Error filtration and entanglement purification for quantum communication (17 pages)
The key realization that led to the emergence of the new field of quantum information processing is that quantum mechanics, the theory that describes microscopic particles, allows the processing of
Indefinite Causal Order in a Quantum Switch.
A photonic quantum switch is realized, where two operations A and B act in a quantum superposition of their two possible orders, on the transverse spatial mode of the photons; polarization coherently controls their order.
Implementing quantum control for unknown subroutines
We present setups for the practical realization of adding control to unknown subroutines, supplementing the existing quantum optical scheme for black-box control with a counterpart for the quantum
Quantum computations without definite causal structure
It is shown that quantum theory allows for transformations of black boxes that cannot be realized by inserting the input black boxes within a circuit in a pre-defined causal order, and that the quantum version of this transformation-the quantum switch- produces an output circuit where the order of the connections is controlled by a quantum bit, which becomes entangled with the circuit structure.
Functional quantum computing: An optical approach
Recent theoretical investigations treat quantum computations as functions, quantum processes which operate on other quantum processes, rather than circuits. Much attention has been given to the
Perfect discrimination of no-signalling channels via quantum superposition of causal structures
It is proved that two no-signalling channels that are not perfectly distinguishable in any ordinary quantum circuit can become perfectly distinguishability through the quantum superposition of circuits with different causal structures.
Environment and classical channels in categorical quantum mechanics
We present a both simple and comprehensive graphical calculus for quantum computing. We axiomatize the notion of an environment, which together with the axiomatic notion of classical structure