Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

Questions tagged [quantum-operation]

For questions about quantum channels or more generally quantum maps and the related formalism. For questions about unitary operations, please use quantum-gate instead.

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If all quantum gates must be unitary, what about measurement?

All quantum operations must be unitary to allow reversibility, but what about measurement? Measurement can be represented as a matrix, and that matrix is applied to qubits, so that seems equivalent to the operation of a quantum gate. That's…
auden
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Counterexamples in quantum information theory

As was already asked about in this phys.SE question many years ago—which, sadly, got closed and never received an answer—is there a collection of counterexamples in quantum information theory, "in the spirit of books like [...] Counterexamples in…
Frederik vom Ende
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Significance of The Church of the Higher Hilbert space

The term "Church of the Higher Hilbert Space" is used in quantum information frequently when analysing quantum channels and quantum states. What does this term mean (or, alternately, what does the term "Going to To the Church of the Higher Hilbert…
user3483902
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Twirling Quantum Channels: Pauli and Clifford Twirling

I am currently working through some papers related with approximations of more general quantum channels such as amplitude and phase damping channels to Pauli channels. The reason to do so is so that the Gottesman-Knill theorem is fulfilled and…
Josu Etxezarreta Martinez
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How does the vectorization map relate to the Choi and Kraus representations of a channel?

I know that the Choi operator is a useful tool to construct the Kraus representation of a given map, and that the vectorization map plays an important role in such construction. How exactly does the vectorization map work in this context, and how…
Tobias Fritzn
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Does higher channel fidelity imply higher entanglement fidelity?

Consider two noisy quantum channels (CPTP maps), $\Phi_1^A$ and $\Phi_2^A$, acting on a system $A$. Suppose that for any pure state $\left|\psi\right>\in \mathcal H_A$, $$ F\big(\psi, \Phi_1^A(\psi)\big) \geq F\big(\psi,…
UncertainTea
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Is acting with a positive map on a state not part of a larger system allowed?

In the comments to a question I asked recently, there is a discussion between user1271772 and myself on positive operators. I know that for a positive trace-preserving operator $\Lambda$ (e.g. the partial transpose) if acting on a mixed state $\rho$…
Quantum spaghettification
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What is the "Stinespring Dilation"?

I've consulted Nielsen and Chuang to understand the Stinespring Dilation, but wasn't able to find anything useful. How does this operation relate to partial trace, Kraus operators, and purification?
Jimit Bavishi
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How does the number of copies affect the diamond distance?

Suppose we are given two maps $\Phi$ and $\Psi$ such that $$\|\Phi-\Psi\|_{\diamond}\leqslant\varepsilon.$$ What can we say about $\left\|\Phi^{\otimes t}-\Psi^{\otimes t}\right\|_{\diamond}$? Is it upper-bounded by $t\varepsilon$? Is the result…
Tristan Nemoz
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How does the invertibility of a quantum map reflect on its Kraus operators?

Consider a quantum map $\Phi\in\mathrm T(\mathcal X)$, that is, a linear operator $\Phi:\mathrm{Lin}(\mathcal X)\to\mathrm{Lin}(\mathcal X)$ for some finite-dimensional complex vector spaces $\mathcal X$. In the specific case in which $\Phi$ is also…
glS
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How to find the operator sum representation of the depolarizing channel?

In Nielsen and Chuang (page:379), it is shown that the operator sum representation of a depolarizing channel $\mathcal{E}(\rho) = \frac{pI}{2} + (1-p)\rho$ is easily seen by substituting the identity matrix with $$\frac{\mathbb{I}}{2} = \frac{\rho +…
user1936752
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What is the relationship between Choi and Chi matrix in Qiskit?

I'm struggling with the framework for quantum process tomography on Qiskit. The final step of such a framework is running fit method of ProcessTomographyFitter class. Documentation states that such function gives a Choi matrix as output.…
Daniele Cuomo
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What does it mean "less than identity" in the operator sum representation?

In Quantum Computation and Quantum Information by Nielsen and Chuang, Section 8.2.3, $\mathcal{E}=\sum_{k}E_k\rho E_k^{\dagger}$ gives the operator-sum representation. In general, it requires $\sum_k E_k E_k^{\dagger}\leq I$. But, what does it mean…
czwang
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Entanglement-assisted hashing bound for asymmetric depolarizing channels

I reading the paper EXIT-Chart Aided Quantum Code Design Improves the Normalised Throughput of Realistic Quantum Devices, which proposes the use of QTCs in order to do quantum error correction for realistic quantum devices whose error model can be…
Josu Etxezarreta Martinez
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What is the difference between quantum gates and quantum channels?

I'm not sure if this is a dumb question, since they seem to be very basic building blocks of quantum information theory; however, I can't seem to wrap my head around the difference between the two. As I understand it, both quantum gates and quantum…
learner1234
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