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Questions tagged [fidelity]

For questions about the fidelity between quantum states.

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Qubit fidelity of DWAVE device

Since DWAVE quantum device is constructed using superconducting flux qubits, each qubit cannot be produced identically so that the fidelity of the qubit must be different. DWAVE only provides the ...
peachnuts's user avatar
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What are the "nice" properties of the diamond norm and why is it used?

I have heard about the diamond norm, and from what I understood it is a "nice" tool to quantify quality of quantum gates in the NISQ era. I would like to know a little more before going in detail in ...
Marco Fellous-Asiani's user avatar
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149 views

How large can we make the fidelity between mixed states by allowing unitaries?

For pure states, it is known that one can always find a unitary that relates the two i.e. for any choice of states $\vert\psi\rangle$ and $\vert\phi\rangle$, there exists a unitary $U$ such that $U\...
JRT's user avatar
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Explanation of the generalized SWAP test: the permutation test?

I am reading this paper on the state separability problem, and came across the term “Permutation Test.” This is on page 7 section 2.3. Apparently, the more famous SWAP test is a special case of ...
TwentyCents's user avatar
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Interpretation of the PVM $\mu$ whose Bhattacharyya coefficient equals the fidelity: $\|\sqrt P\sqrt Q\|_1={\rm B}(P,Q|\mu)$

(Bhattacharyya coefficient vs state fidelity) Given two vectors $u,v$ with nonnegative entries, their Bhattacharyya coefficient is $$\mathrm B(u,v)\equiv \sum_a \sqrt{u_a v_a}.$$ Given two positive ...
glS's user avatar
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What is the best quantum process tomography method?

This question is somewhat related to this question. What is currently the best method for quantum process tomography? By best I mean, the one that can achieve the best accuracy of estimation per qubit ...
Quantum Guy 123's user avatar
4 votes
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How to derive the higher terms in the Taylor expansion of the Bures fidelity?

The Wikipedia article for the quantum Fisher Information mentions that one can expand the Bures fidelity and the quantum Fisher Information will appear as the second-order correction term. However in ...
I1ussion's user avatar
4 votes
1 answer
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Infidelity as distance measure

Let $\mathcal{X} \in {\rm CP}(\mathcal{H}, \mathcal{K})$ and unital (compositive positive and unital maps). Let $\mathcal{Y} \in {\rm CPT}(\mathcal{H}, \mathcal{K})$(complete positive and trace ...
Michael.Andy's user avatar
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113 views

Are there any systematic tools for estimating expected error rate?

Like we all probably know, today’s NISQ computers are, as their name implies - very noisy. Hence, if we desire to obtain valuable results then we should come up with circuit designs that minimizes the ...
Ohad's user avatar
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Why is the fidelity, rather than the trace distance, the standard choice to compare quantum states?

I don't think it's particularly controversial to say that the "standard" way people use to compare quantum states is via the fidelity. Yes, sometimes the trace distance is used as well, but ...
glS's user avatar
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Is (square root) fidelity strictly concave?

We know that (square root) Fidelity which is defined as $\text{F}(\rho,\sigma) = \| \sqrt{\rho} \sqrt{\sigma} \|_1 = \text{Tr}(\sqrt{\sqrt{\sigma} \rho \sqrt{\sigma}})$ is satisfies the property of ...
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How can I get fidelity of a gate from randomized benchmarking?

I found (page 33) the method of finding fidelity from fit by "interleaved and reference decay" according to the sequence fidelity formula: $$F_{ref}=Ap_{ref}^{m}+B,$$ where $p_{ref}^{m}$ is ...
Curious's user avatar
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Given $\rho,\sigma$, bound $\min F(\bar\rho,\sigma)$ over $\bar\rho$ such that $F(\bar\rho,\rho)\ge1-\epsilon$

Let $\rho, \sigma$ be states such that $$F(\rho,\sigma) = \delta >0,$$ where $F(\rho,\sigma) = \|\sqrt{\rho}\sqrt{\sigma}\|_1$. Now consider all possible states $\bar{\rho}$ such that $F(\bar{\rho},...
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Bounds relating min-fidelity and induced one-norm

Consider two CPTP maps $M_{A\rightarrow B}$ and $N_{A\rightarrow B}$. Let $\Phi = M - N$. To distinguish between the two maps, there are several measures but here I want to compare two of them. The ...
user1936752's user avatar
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Fidelity and Uhlmann's theorem in the context of source coding

In quantum source coding, we have an encoder $\mathcal{E}$ and a decoder $\mathcal{D}$ which are some quantum channels. Given a state $\rho_A$ on Hilbert space $\mathcal{H}_A$, we wish to encode and ...
user1936752's user avatar
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What is the best method for estimating average channel fidelity?

This thesis shows an efficient way to estimate average channel fidelity (in chapter 4). However, it is somewhat old (from 2005). Are there any better methods out there? By better I mean: are there ...
Quantum Guy 123's user avatar
2 votes
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36 views

Non-ideal coin tossing

Can someone please check if the following makes sense? We have a non-ideal coin-tossing scheme as follows. Alice and Bob know what $|0\rangle,|1\rangle$ are. Bob wins when the coin is 1. Honest Alice ...
user777's user avatar
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The lower bound on the probability of error in quantum hypothesis testing

Prove the following lower bound on the probability of error $P_e$ in a quantum hypothesis test to distinguish $\rho$ from $\sigma$: \begin{align} P_e \geq \frac{1}{2} \left(1-\sqrt{1-F(\rho, \...
Michael.Andy's user avatar
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What are the similarity and difference between quantum fidelity estimation and parameter estimation problem?

Quantum fidelity (1) estimation is to estimate the similarity between two quantum states or process. Could quantum fidelity be viewd as a parameter? And what are the similarity and difference between ...
Michael.Andy's user avatar
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Do the eigenvalues of $|\sqrt\rho\sqrt\sigma|$ have a physical interpretation?

The (square-root) fidelity between a pair of states $\rho,\sigma$ is the quantity $$\sqrt F(\rho,\sigma) = \|\sqrt\rho\sqrt\sigma\|_1 = \operatorname{tr}|\sqrt\rho\sqrt\sigma| =\operatorname{tr}\left[\...
glS's user avatar
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Pure Product State Problem Clarification about $\alpha$-closeness and $\beta$-farness

I am reading a paper on entanglement, specifically, determining if a state is close to being entangled or not. The problem first introduces the $(\alpha, \beta, l)$-Pure product state problem. This ...
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What are the estimate-estimate and estimate-project algorithms for quantum overlap?

In this paper on improvements to the traditional SWAP test to measure quantum state overlap (or fidelity), they mention two methods called estimate-estimate and estimate-project. I googled about these ...
Loic Stoic's user avatar
1 vote
1 answer
202 views

Why can't Quantum Fisher Information be negative?

Quantum Fisher Information is proportional to Fidelity susceptibility. Mathematically the equation is: $QFI=-\frac{\partial^2 d_B(\epsilon) }{\partial \epsilon^2}$ where above equation shows QFI is ...
Chetan Waghela's user avatar
1 vote
1 answer
138 views

Calculating state fidelity and space complexity of Minimum Eigen Optimizers (VQE, QAOA and Grover Optimizer) in qiskit

I'm a beginner in using Qiskit and my Computer Science background is not extensive. But I understand the Quantum Physics aspects of it relatively well. I solved a QUBO problem in Qiskit using VQE (...
Janani Ananthanarayanan's user avatar
1 vote
0 answers
270 views

Problem with fidelity value range obtained from this python code

I'm calculating for instance the fidelity between two pure two qubit state, using the following python code: ...
Farhad's user avatar
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426 views

What is the relation between fidelity and concurrence for a two qubit maximally mixed state?

I am trying to understand the relation between Fidelity and Concurrence for a two qubit maximally mixed state. When I calculate the Fidelity and Concurrence, I observe that Concurrence is zero whereas ...
Ganesh M's user avatar
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Calculating fidelity for mixed states: are there tricks or it is "brute force" calculations?

The fidelity between two density matrix $\rho$ and $\sigma$ is the following: $$F(\rho,\sigma)=\operatorname{Tr}\left[\sqrt{\sqrt{\rho} \sigma \sqrt{\rho}} \right]^2$$ If one of the two state is a ...
Marco Fellous-Asiani's user avatar
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Commutative operators

I have got a 2-qubit circuit with the following instructions: ...
Марина Лисниченко's user avatar
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What scheme should be used in case of applying non-Cliffords to estimate probability of success?

For Clifford gates (when performing randomized benchmarking and starting from ground state) the final state is always ground. It is acquired by applying at the end recovery gate, which transfers the ...
Curious's user avatar
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